Texture Features, Low-Level Texture Features, Tamura Measure, Random Field Models, Transform Domain Features (21.04.2011)

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Texture Features, Low-Level Texture Features, Tamura Measure, Random Field Models, Transform Domain Features (21.04.2011)
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10.5446/339 (DOI)
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Technische Universität Braunschweig
Institut für Informationssysteme
Balke, Wolf-Tilo
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In this course, we examine the aspects regarding building multimedia database systems and give an insight into the used techniques. The course deals with content-specific retrieval of multimedia data. Basic issue is the efficient storage and subsequent retrieval of multimedia documents. The general structure of the course is: - Basic characteristics of multimedia databases - Evaluation of retrieval effectiveness, Precision-Recall Analysis - Semantic content of image-content search - Image representation, low-level and high-level features - Texture features, random-field models - Audio formats, sampling, metadata - Thematic search within music tracks - Query formulation in music databases - Media representation for video - Frame / Shot Detection, Event Detection - Video segmentation and video summarization - Video Indexing, MPEG-7 - Extraction of low-and high-level features - Integration of features and efficient similarity comparison - Indexing over inverted file index, indexing Gemini, R *- trees
Point (geometry) Software engineering Group action Texture mapping Multiplication sign Letterpress printing Database Matching (graph theory) Average Distance Graph coloring Magnetic stripe card Invertible matrix Quadratic equation Cross-correlation Different (Kate Ryan album) Cylinder (geometry) Term (mathematics) Color space Multimedia Pairwise comparison Geometric quantization Area Metropolitan area network Histogram Texture mapping Assembly language Computer-generated imagery Surface Reflection (mathematics) Database Bit Measurement Distance Category of being Type theory Uniform resource locator Computer animation Quadratic equation Royal Navy Universe (mathematics) Multimedia Video game Table (information) Identical particles Spectrum (functional analysis) Spacetime
Ocean current Point (geometry) Trail Recurrence relation Beat (acoustics) Group action Texture mapping Model theory Multiplication sign Patch (Unix) View (database) Computer-generated imagery Artificial neural network Control flow Mathematical analysis Grass (card game) Regular graph Mereology Mathematical model Fourier transform Magnetic stripe card Measurement Information retrieval Natural number Object (grammar) Energy level Wallpaper group Data structure Descriptive statistics Data type Texture mapping Cellular automaton Structural load Surface Memory management Field (computer science) Machine code Grass (card game) Flow separation Computer animation Raster graphics Information retrieval Natural number Statement (computer science) Pattern language Object (grammar) Representation (politics)
Recurrence relation Randomization Group action Texture mapping Multiplication sign Archaeological field survey Grass (card game) Mereology Disk read-and-write head Neuroinformatik Formal language Different (Kate Ryan album) Multimedia Textursynthese Descriptive statistics Area Texture mapping Repetition Parallel port Computer Hand fan Category of being Digital photography Natural number Helmholtz decomposition Freeware Ocean current Transformation (genetics) Real number Computer-generated imagery Artificial neural network Theory Element (mathematics) Causality Term (mathematics) Authorization Data type Information Surface Planning Database Line (geometry) Grass (card game) Cartesian coordinate system Computer graphics (computer science) Computational complexity theory Uniform resource locator Word Computer animation Visualization (computer graphics) Personal digital assistant Speech synthesis Video game Table (information)
Area Dialect Texture mapping Texture mapping Structural load Real number Computer-generated imagery Branch (computer science) Machine code Mereology Regular graph Demoscene Graph coloring Computer animation Different (Kate Ryan album) Green's function Helmholtz decomposition Whiteboard
Satellite Point (geometry) Texture mapping Real number Multiplication sign Computer-generated imagery Control flow Water vapor Fault-tolerant system Disk read-and-write head Semantics (computer science) Graph coloring Field (computer science) Neuroinformatik Medical imaging Mathematics Population density Different (Kate Ryan album) Term (mathematics) Object (grammar) Forest Single-precision floating-point format Query language Directed set Pairwise comparison Area Noise (electronics) Satellite Texture mapping Characteristic polynomial Closed set Reflection (mathematics) Water vapor Cartesian coordinate system Ähnlichkeitssuche Degree (graph theory) Computer animation Personal digital assistant Network topology Different (Kate Ryan album) Website Quicksort Table (information) Freezing
Satellite Classical physics Point (geometry) Group action Building Pixel Transformation (genetics) State of matter Texture mapping Direction (geometry) Computer-generated imagery Characteristic polynomial Set (mathematics) Menu (computing) Client (computing) Fourier series Mereology Graph coloring Measurement Mathematics Different (Kate Ryan album) Energy level Physical system Distribution (mathematics) Satellite Texture mapping Matching (graph theory) Block (periodic table) Building Structural load Cellular automaton Physical law Line (geometry) Transformation (genetics) Similarity (geometry) Computer animation Personal digital assistant Blog Order (biology) Interpreter (computing) Energy level Block (periodic table)
Standard deviation Dataflow Complex (psychology) Pixel Histogram Distribution (mathematics) Texture mapping Orientation (vector space) Patch (Unix) Direction (geometry) Mathematical analysis Client (computing) Mereology Causality Natural number Different (Kate Ryan album) Single-precision floating-point format Ideal (ethics) Information Pixel Pairwise comparison Social class Physical system Covering space Histogram Standard deviation Texture mapping Inheritance (object-oriented programming) Information Kolmogorov complexity Line (geometry) Flow separation Similarity (geometry) Type theory Computer animation Computer science Orientation (vector space) Pattern language Energy level
Point (geometry) Probability distribution Pixel Functional (mathematics) Distribution (mathematics) Moment (mathematics) Texture mapping Direction (geometry) Chaos (cosmogony) Shift operator Expected value Order (biology) Mathematics Different (Kate Ryan album) Queue (abstract data type) Energy level Right angle Pixel Position operator Area Covering space Shift operator Distribution (mathematics) Texture mapping Matching (graph theory) Polygon mesh Information Direction (geometry) Moment (mathematics) Gradient Cartesian coordinate system Position operator Category of being Positional notation Computer animation Function (mathematics) Order (biology) Right angle Energy level Quicksort Matrix (mathematics)
Point (geometry) Ocean current Pixel Confidence interval Texture mapping Letterpress printing Distance Computer programming Number Energy level Software testing Pixel Identical particles Rule of inference Shift operator Matching (graph theory) Point (geometry) Gradient Equivalence relation Distance Hypothesis Discounts and allowances Number Computer animation Different (Kate Ryan album) Thumbnail Energy level Figurate number Metric system Euklidischer Raum Matrix (mathematics) Local ring
Pixel Building Texture mapping Direction (geometry) Multiplication sign 1 (number) Sheaf (mathematics) Shape (magazine) Neuroinformatik Measurement Digital photography Mathematics Dedekind cut Different (Kate Ryan album) Matrix (mathematics) Area Texture mapping Smoothing Closed set Gradient Demoscene Digital photography Vector space Computer science Linearization Acoustic shadow Summierbarkeit Point (geometry) Line (geometry) Image resolution Computer-generated imagery Color management Regular graph Graph coloring Wave packet Quadratic equation Mixture model Regular graph Cross-correlation Energy level Data structure Contrast (vision) Tunis Metropolitan area network Matching (graph theory) Image resolution Direction (geometry) Dimensional analysis Volume (thermodynamics) Basis <Mathematik> Line (geometry) Rectangle Computer animation Contrast (vision) Video game
Area Neighbourhood (graph theory) Pixel Gradient Neighbourhood (graph theory) Content (media) Maxima and minima Mathematics Arithmetic mean Computer animation Average Different (Kate Ryan album) Energy level Energy level Pixel Window Physical system Window
Area Pixel Group action Distribution (mathematics) Matching (graph theory) Texture mapping Image resolution Multiplication sign Computer-generated imagery Fitness function Maxima and minima Maxima and minima Digital photography Mathematics Computer animation Personal digital assistant Different (Kate Ryan album) Energy level Pixel Window Window
Web page Pixel Histogram Confidence interval Computer-generated imagery Caustic (optics) Maxima and minima Average Mereology Number Causality Arithmetic mean Different (Kate Ryan album) Selectivity (electronic) Data structure Pixel Game theory Window Area Covering space Histogram Texture mapping Operator (mathematics) Menu (computing) Maxima and minima Number Arithmetic mean Computer animation Estimation Different (Kate Ryan album) Table (information) Window
Point (geometry) Probability distribution Standard deviation Group action Statistics Distribution (mathematics) Moment (mathematics) Modal logic Computer-generated imagery Sheaf (mathematics) Mereology Number Expected value 4 (number) Centralizer and normalizer Uniformer Raum Different (Kate Ryan album) Queue (abstract data type) Energy level Software testing Acoustic shadow Contrast (vision) Kurtosis Area Mobile Web Modal logic Histogram Focus (optics) Distribution (mathematics) Standard deviation Moment (mathematics) Model theory Measurement Hand fan Computer animation Oval Contrast (vision) Acoustic shadow Energy level Musical ensemble Bounded variation Kurtosis Row (database)
Pixel Gradient Direction (geometry) Angle Graph coloring Order of magnitude Element (mathematics) Number Mathematics Analogy Energy level Pixel Metropolitan area network Tunis Physical system Direction (geometry) Gradient Order of magnitude Line (geometry) Machine code Measurement Element (mathematics) Process (computing) Computer animation Computer science Identical particles
Pixel Divisor Gradient Texture mapping Direction (geometry) Multiplication sign Computer-generated imagery Calculation Angle Average Distance Thresholding (image processing) Rotation Number Measurement Spacetime Data structure Pixel Tunis Rotation Histogram Texture mapping Direction (geometry) Cellular automaton Closed set Gradient Physical law Thresholding (image processing) Measurement Distance Similarity (geometry) Number Digital photography Computer animation Personal digital assistant Uniform resource name
Pixel Model theory Texture mapping Real number Multiplication sign Computer-generated imagery Similarity (geometry) Distance Regular graph Graph coloring Logic synthesis Power (physics) Different (Kate Ryan album) Pattern language Boundary value problem Pixel Descriptive statistics Physical system Area Matching (graph theory) Polygon mesh Texture mapping Model theory Sampling (statistics) Zufälliges Feld Machine code Logic synthesis Type theory Sample (statistics) Stochastic Computer animation Network topology Endliche Modelltheorie Pattern language Game theory
Point (geometry) Asynchronous Transfer Mode Statistics Pixel Texture mapping Model theory Texture mapping Multiplication sign Computer-generated imagery Model theory 3 (number) Field (computer science) Parameter (computer programming) Matching (graph theory) Parameter (computer programming) Magnetic stripe card Computer animation Different (Kate Ryan album) Pattern language Right angle Pixel
State observer Pixel Group action Distribution (mathematics) Model theory Texture mapping Parameter (computer programming) Magnetic stripe card Variable (mathematics) Mathematics Hypermedia Matrix (mathematics) Pixel Category of being Rhombus Area Parameter (computer programming) Maxima and minima Bit Category of being Process (computing) Maximum likelihood Uniformer Raum Chain output Summierbarkeit Right angle Pattern language Metric system Bounded variation Random number Statistics Computer file Computer-generated imagery Characteristic polynomial Maxima and minima Distance Event horizon Latent heat Statement (computer science) Data structure Implementation Random variable Distribution (mathematics) Matching (graph theory) Model theory Physical law Neighbourhood (graph theory) Principle of locality Computer animation Estimation Social class Table (information) Matrix (mathematics) Local ring
Neighbourhood (graph theory) Distribution (mathematics) Texture mapping Model theory Direction (geometry) Computer-generated imagery Parameter (computer programming) Disk read-and-write head Different (Kate Ryan album) Endliche Modelltheorie Category of being Pixel Summierbarkeit Shift operator Distribution (mathematics) Texture mapping Moment (mathematics) Neighbourhood (graph theory) Physical law Model theory Measurement Markov chain Computer animation Video game Endliche Modelltheorie Social class Right angle
Neighbourhood (graph theory) Pixel Randomization State of matter Texture mapping Model theory Direction (geometry) Image resolution Characteristic polynomial Letterpress printing Parameter (computer programming) Mereology Variance Mathematics Roundness (object) Causality Arithmetic mean Different (Kate Ryan album) Operator (mathematics) Physical law Endliche Modelltheorie Pixel Multiplication Tunis Probability space Area Noise (electronics) Distribution (mathematics) Multiplication Texture mapping Matching (graph theory) Image resolution Neighbourhood (graph theory) Model theory Parameter (computer programming) Maxima and minima Symbol table Type theory Wave Computer animation Integrated development environment Personal digital assistant Different (Kate Ryan album) Endliche Modelltheorie Social class Pattern language Right angle Figurate number
Neighbourhood (graph theory) Texture mapping Multiplication sign Direction (geometry) Computer-generated imagery Parameter (computer programming) Heat transfer 2 (number) Neuroinformatik Time domain Frequency Mathematics Bit rate Insertion loss Different (Kate Ryan album) Natural number Personal digital assistant Vector space Energy level Spacetime Information Pixel Data compression Prolog Condition number Physical system Domain name Texture mapping Polygon mesh Information Model theory State of matter Zufälliges Feld Line (geometry) Markov chain Computer animation Maximum likelihood Contrast (vision) Different (Kate Ryan album) Condition number Endliche Modelltheorie Right angle Energy level Local ring Singuläres Integral
Point (geometry) Beat (acoustics) Transformation (genetics) Gradient Line (geometry) Computer-generated imagery Heat transfer Frequency Goodness of fit Knowledge representation and reasoning Representation (politics) Information Data conversion Domain name Information Point (geometry) Gradient Moment (mathematics) Line (geometry) Measurement Computer animation Different (Kate Ryan album) Video game Representation (politics) Spacetime Singuläres Integral
Mountain pass Texture mapping Multiplication sign Single-precision floating-point format Personal digital assistant Set (mathematics) Row (database) Series (mathematics) Pixel Algebra Presentation of a group Polynomial Texture mapping Real number Point (geometry) Moment (mathematics) Sound effect Sequence Degree (graph theory) Type theory Frequency Cycle (graph theory) Freeware Spacetime Row (database) Point (geometry) Web page Polynomial Statistics Functional (mathematics) Real number Computer-generated imagery Coordinate system Graph coloring Product (business) Sequence Degree (graph theory) Coefficient Well-formed formula Representation (politics) Data structure Metropolitan area network Matching (graph theory) Information Discrete group Line (geometry) System call Polynomial interpolation Number Uniform resource locator Computer animation Function (mathematics) Form (programming)
Context awareness Functional (mathematics) Presentation of a group Texture mapping Real number Multiplication sign Fourier series Number Time domain Web 2.0 Frequency Sign (mathematics) Different (Kate Ryan album) Summierbarkeit Area Scripting language Beta function Sine Real number Discrete group Moment (mathematics) Special unitary group Symbol table Number Frequency Computer animation Function (mathematics) Series (mathematics) Right angle Quicksort
Functional (mathematics) Histogram Presentation of a group Multiplication sign Fourier series Disk read-and-write head Computer icon Time domain Revision control Frequency Sign (mathematics) Knowledge representation and reasoning Different (Kate Ryan album) Information Summierbarkeit Domain name Simulation Matching (graph theory) Information Density functional theory Structural load Computer simulation Independence (probability theory) Bit Frequency Computer animation Function (mathematics) Series (mathematics) Musical ensemble Figurate number Spectrum (functional analysis)
Point (geometry) Functional (mathematics) Pixel Variety (linguistics) Real number Correspondence (mathematics) Computer-generated imagery Fourier series Number Sequence Wave Frequency Sign (mathematics) Coefficient Motion blur Spacetime Nichtlineares Gleichungssystem Pixel Sine Density functional theory Real number Discrete group Physical law Core dump Volume (thermodynamics) Transformation (genetics) Trigonometric functions Sequence Demoscene Number Word Frequency Computer animation Personal digital assistant Order (biology) Video game Quicksort Representation (politics)
View (database) Multiplication sign Caustic (optics) 8 (number) Mereology Storage area network Sign (mathematics) Matrix (mathematics) Information Pixel Formal grammar Area Simulation Clique-width Real number Computer simulation Parameter (computer programming) Bit Trigonometric functions Frequency Series (mathematics) Dew point Right angle Figurate number Representation (politics) Point (geometry) Functional (mathematics) Computer-generated imagery MIDI Fourier series Oscillation Sequence Time domain Wave Coefficient Spacetime Summierbarkeit Sine Density functional theory Discrete group Projective plane Matter wave Transformation (genetics) Number Computer animation Function (mathematics) Video game Family Form (programming)
Complex (psychology) Functional (mathematics) Presentation of a group Transformation (genetics) Correspondence (mathematics) Connectivity (graph theory) Computer-generated imagery Fourier series Discrete element method Perspective (visual) Emulation Sequence Oscillation Time domain Wave Frequency Coefficient Population density Vector space Matrix (mathematics) Motion blur Harmonic analysis Spacetime Pixel Formal grammar Information Sine Density functional theory Clique-width Real number Discrete group Length Parameter (computer programming) Transformation (genetics) Matter wave Trigonometric functions Position operator Number Frequency Computer animation Object (grammar) Representation (politics) Form (programming) Spectrum (functional analysis)
Presentation of a group Group action Variety (linguistics) Multiplication sign Numbering scheme Distance Mereology Magnetic stripe card Oscillation Frequency Population density Spacetime Multiplication Information Real number Quadrilateral Category of being Frequency Computer animation Commitment scheme Order (biology) Right angle Quicksort Family Thomas Bayes
Complex (psychology) Presentation of a group Implementation Algorithm Multiplication sign Computer-generated imagery Control flow Set (mathematics) Discrete element method Computer programming Machine vision Neuroinformatik Power (physics) Sign (mathematics) Goodness of fit Knowledge representation and reasoning Different (Kate Ryan album) Hypermedia Tower Queue (abstract data type) Spacetime Divisor Nichtlineares Gleichungssystem Density functional theory Sine Kolmogorov complexity Database Machine code Fast Fourier transform Subject indexing Type theory Wave Prime ideal Frequency Computer animation Order (biology) Social class
Programming paradigm Commutative property Complex (psychology) Functional (mathematics) Presentation of a group Group action Mass flow rate Algorithm State of matter Ferry Corsten Transformation (genetics) Division (mathematics) Maxima and minima Infinity Arm Emulation Neuroinformatik Supersonic speed Causality Hypermedia Reduction of order Moving average Energy level Nichtlineares Gleichungssystem Drum memory Rule of inference Metropolitan area network Key (cryptography) Density functional theory File format Kolmogorov complexity Fast Fourier transform Number Word Moore's law Computer animation Uniform resource name Normed vector space Order (biology) Figurate number Cuboid Wide area network
Point (geometry) Spectrum (functional analysis) Functional (mathematics) Pixel Transformation (genetics) Texture mapping Multiplication sign Computer-generated imagery Analogy Mathematical analysis Heat transfer Fourier series Time domain Frequency Sign (mathematics) Coefficient Different (Kate Ryan album) Term (mathematics) Personal digital assistant Representation (politics) Codierung <Programmierung> Pairwise comparison Data compression Area Domain name Pairwise comparison Distribution (mathematics) Information Density functional theory Uniqueness quantification Discrete group Cartesian coordinate system Trigonometric functions System call Measurement Power (physics) Computer animation Function (mathematics) Calculation Pattern language Wavelet transform Coefficient Simulation Curve fitting Resultant Spectrum (functional analysis) Singuläres Integral Data compression
Point (geometry) Spectrum (functional analysis) Wavelet Functional (mathematics) Transformation (genetics) Multiplication sign Computer-generated imagery Shape (magazine) Menu (computing) Mass Mereology Approximation Ideal (ethics) Local ring Physical system Social class Area Covering space Image resolution Basis <Mathematik> Frequency Computer animation Function (mathematics) Different (Kate Ryan album) Social class
Gateway (telecommunications) Wavelet Functional (mathematics) Group action Divisor Multiplication sign Orthogonality Shape (magazine) Mass Mereology Power (physics) Moving average Divisor Area Distribution (mathematics) Scaling (geometry) Sound effect Basis <Mathematik> Wave Computer animation Basis <Mathematik> Personal digital assistant Sampling (music) Function (mathematics) Website Right angle Wavelet transform Discrepancy theory Integer Local ring Spacetime
Scale (map) Shift operator Functional (mathematics) Scaling (geometry) Divisor Online help Model theory Plastikkarte Set (mathematics) Exponential function Computer icon Wave Uniform resource locator Multiresolution analysis Computer animation Function (mathematics) Set (mathematics) Video game Divisor Row (database) Spacetime
Point (geometry) Wavelet Functional (mathematics) Scaling (geometry) Divisor Image resolution Uniqueness quantification Image resolution Moment (mathematics) Mereology Limit (category theory) Computer icon Number Database normalization Computer animation Root Different (Kate Ryan album) Function (mathematics) Representation (politics) Website Damping Divisor
Covering space Point (geometry) Wavelet Information management Functional (mathematics) Divisor Multiplication sign Model theory Electronic mailing list Wave Coefficient Multiresolution analysis Computer animation Function (mathematics) Divisor Wavelet transform Family Physical system
Point (geometry) Wavelet Information management Building Functional (mathematics) View (database) Model theory Combinational logic Basis <Mathematik> Arithmetic mean Coefficient Population density Multiresolution analysis Computer animation Function (mathematics) Telecommunication Linearization Wavelet transform Coefficient Family Physical system
Area Wavelet Information management Functional (mathematics) Model theory Letterpress printing Volume (thermodynamics) Database normalization Wave Coefficient Computer animation Function (mathematics) Dew point Divisor Wavelet transform Family Physical system
Random number Model theory Texture mapping Computer-generated imagery Mathematical analysis Parameter (computer programming) Shape (magazine) Mereology Emulation Measurement Information retrieval Frequency Causality Energy level Endliche Modelltheorie Multiplication Descriptive statistics Texture mapping Information Image resolution Structural load Shape (magazine) Computer animation Function (mathematics) Energy level
had everyone of and a welcome to the wonderful world of multimedia databases and that last time we were beginning to talk a little bit about how less about it just go and we had about
0 0 on a flight out we would we saw colour as of the 1st and the primary impression to what the steps of Saudi immediately notice of public is kind of the contest and the and the colours that are in the image and the make an immediate impression on new and of course could before a Lisle were talking about couples of policy faces the are to be space for example seemed like a like you use for printing but also spaces some of for full of building the actual if the grand for building the eye of features a we we from reflected on each this week I'm that anybody still know what we were for them as we exactly a kind of like bit of a psychological colours space but usually the distances all the measurement of distances and it has to be a have have a pretty good notional told you move kind of like distinguish between colours and the basic for what they just 3 was cylindrica firm so you call who which is kind of like the rock and pop of cylinder and then you have the situation from the inside to the outside of the of the colour of the cylinder and you have the brightness are beginning very bright on top and going down all way to to dock area and sell were talking about a couple of full from Mahal colours can be mixed and how can be subjected all added or something but in the end we were kind of interested in what we could achieve do with high all could be computer images based on colour and the and the idea that really make the greatest colleges to grab with a well highly much more percentage of each colour is in the picture and then you can do with all kinds of tricks of with the layout ways saying all you have to of you also have to consider the way up to collect she is so from the location of the colour and the you you can do a lot to expect and get more complicated but in the end what you get is a feature of victory and the different ways to come for a few temerity between the 2 it is beginning from simple out his the distances still just I'm subtracting different columns from each other up to quadratic measures although with distance which kind of like takes the cold I'm correlation between different colours and assembler which between different colours and the spectrum into him into into consideration and today will be moving on from the simple colours for something that is also a very interesting in recognising the images for describing the images and the US text was the texture anybody went to Wenger for a definition at wise the surface of the stable but not like the surface of the gulf but West the difference and the material a few step but coming you cannot see materials and obstruct from the colourful this from this greatest and that but this still also in terms of the 2 impression yes need the it paid off so different each year out life reflection somewhat of that could be described the good of the table before you and what he described it in a way the of the group and of group at huge Greece moved to to look at and it is up to all names its move for this kind of stripy in the way of life with wooden stripes and you know this is kind of point the don't know but it's a very hot to describe what it actually is and what makes it so different but weekend immediately recognised the before the universe would do the same in it in the same kind of pruned the same kind of colours all in the same type stripped off your legs movement of of those of us of the vital take exactly the same on reflection properties your early immediately see that this surface looks some old different from the surface over here and the idea of this lecture is to describe the Highways different and this is what we call the texture right so
we will be out on to a text of a statement retrieval today are would go into the basics of pictures and then find out what makes the texture of a structure and a surface at 1 or the you may call it I'm 8 texture and we wouldn't talk about some some features that could be used to measure all to describe such texture and as 0 in this time we will also introduced to the idea of a low level features and high level features of the new features are various very basic descriptions of something high level features are I'm well basically intrinsic descriptions of that are built by mathematical model so can be pretty complicated but usually give you that impression that load of Austria features that on track as much but both of them use cell hope into
the cell Texas described the nature of the typical current patterns in pictures and they look at the surface of the table that of the strides and that is not just a single stride but that is this kind of layoffs stripes on of each other and then of regular so owned goals that talk that say this is shaded somehow but the stripes off different crying now like some off some are perpendicular on perpendicular from not but some of vertical some are little bit angled although but skewed you like so it's there is a regularity though it's not as regular as either would go out of consumer the blackballed and the and the and the real world that she became that the idea why now that this is a patch of is that it is really poker if repeat several times was wouldn't recognise that of some of the of pattern and and and that is the view of the basic ideas for that it is to recover and shading is only a fading fast their several like it just a single 9 nobody would cause to shady of the same goes for the full of spent on offer Cobbittee that's rather pointy or not to call it actually that this part of the problem because the if I'd don't know how to call it he would not understand what I'm 1 I know what I'm talking about the of a key but try to describe the pattern of the paper of the of the Cup with all the phone to somebody approve a difficult time for like a great pointy Kopecky the and the impression of not but 1 really need is a good description of those and it was packed and iPad could use and 1 hand the object of this is the structured and everybody knows what I'm talking about the way up but it it had unlike for because the different kinds off well different in the way of that kind of stimulus which it via the stripes is all these the groups that they have not goals boldly from and everybody knows what a talking point that playing but everybody has an idea what can only do that with the things that are in the on that trillion-dollar the grass everybody has an idea what what the pat on off of Amanda just the of grass side each other the gravel on a heap of rubble code of the look like old will be both different sizes of will be the cost of thought official things like a brick will a brick wall look like what usually of 1 of breaks next week to the next but the given idea though a don't really say what it is what makes a break for beat the break up but the basic idea that that with looking at
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is to that and some described random Texas real current images masseuse kind of their regular those the Metro Plymouth bamboo so OMX how do we described the kind of parallel to lines my debut as easy it turned off not and perpendicular users of something grass rebel and he is part of you that you want to do will try to its kind this it is clear what I'm getting at but it's totally I'm clear how a true presented in a computer pop because evening talking to you and and talking a self that for language speech of 1 of the most effective and efficient way of transporting information I'd let in and and that kind of a computer of no kind of computer most 1 mins 0 0 and this is something that we have to consider and action is not only useful
for bomb for for multi media databases but the description of the pictures is a billion Poland and many area of Computer Science so all will also revisit a couple of techniques are that you may well know from from for my lectures like for example before you transformation I'm to Beguiler feature because pictures are used in many of applications so wrong problem is all with the head of the segmentation of text the by talk about certain texture at about a certain location in the image of the talk about a wooden texture Mobylette as has a wooden texture but only this stable give us that the step aside wooden taxes a pink so it has something to do with segmentations and talking about the texture of and and time image would need to be answered in which to be kind of bomb well Terekhov in the text which does not make too much fans because most pictures and take take any photo that he did recently it doesn't so single text will show may be happy people and maybe it's we that has the that and and maybe the seas and the author of It up my best elements in the paper and in the picture trying to Fiat which Elementis which is very for cause extra segmentation then we took classified the text which only talking about case the area a over the is of the wooden texture the area but I over use of the image is of the property texture the area seed is at texture the mood with described but it it up with text is because the regular enough because of some words and this is why it was a reunion of the smoke free text such so some parts of the images may be very hot described in terms of texture also that is something we have to think about but this is basically the classification for the head of the texture and these 2 pops up after the death of the need for multimedia if we have to investigate incoming pictures so picture of put in to bat with the pictures of The put up with a theory picture of what it was all contained which need segment and we need to classify those taxes to compel them between different images of Kent so we need the classification of the text of the populace billion plans but that will be that we will not go into a so called texture and and this is 1 of the major features of for example computer graphics think about being Sri the engines was trick that the trick is to protect textures on surfaces and that makes it futile realistic from texture mapping and for those kinds of techniques to sustain problem over and over again you need to classify the pictures to me to see how the pictures in the 2 2 retracing on whatever you know the complexity of algorithms to get a group of visual impression of the texture and impression that could for the of survey believing the real this is going well in the computer game of all this is 1 table will immediately recognise that if you see just because the texture seems would be up and so on creating texture and that is something that it with a big of politics to research but we will not go
into that he has developed extra segmentation will want to find to regions of the United which have a certain texture and a new 1 1 incredible seeing the competition for example he is the GRAPE you texture and board of the movie and the texture over here and the rest of the picture is leafy very October to describe intellect load of colours nothing really regular of and but finding out the difference between the 2 weeks to understanding what the Mitchell's does the image shows it shows a bunch of grapes and someone leaves with Leeds UK every collections of highly I look like what textured left maybe this classical here with the them and little bronchus Olaechea obtained this is kind of like a leaf look like and the branches even branch of the ball but and this is what you would expect of the with the grapes it's Kia kind of like a where we you you you you know like old this 1 trophy grapes so very regular texture this little circles that if he can do what you would
expect and the colour and texture IIU he related to the sale of what you are doing them in and texture segmentation is is look at the colour of the image so for example if you find the brand colour here in the 2nd the part of the message out that gives you a certain texture all well there is basically no real regularity there but that as soon as we look at the Green pop over here we find the best the certain that and which is kind of like the change between light green and thought green part that has something to do with the colour but if not it not true that I'm Texas all ways to come in the same colour of the can be very colourful or a mixture of different coloured still out the about area the cavity of the path of the real codes of colour that might be very detained at what I'd texture really is what you want area of a picture it is really texture and if
we do not want the segmented reason with the predominant text that might also have the benefit of the site just being able to focus on the single texture because they left the images areas with a certain texture the land to the same entity in the real think about Osama sonographic all well x-rays to some degree the idea basically is to make things visible that I'd inside the body and very often that kind of colour coded and seat of this is live Olivia its this area but has the same stood before me usually but also a certain texture that reflects the sound waves and and in February of its Osama gram of if you have are tomography I'm it will be on a kind of grace that penetrate the body of the all too layers of the body and are affected in the way and his way of reflection will be a picture for where current that was imposed on the area for a specific point in your body and doctors are key can't see things before Complin ONg quality you looking at cancer the of possible to seek you most just because this some change in texture of some changes in the way that the race reflected singles for satellite images if you look at satellite images began immediately see you was water and was flat because the Water has decided car has has a different texture kind of like long accused drive which are and the way eastern in the area close to close and a very for that no texture area in the middle of the ocean burst on landmasses usually have some mountains some cities have some now like forest of something that will change the texture very quickly and if you look at the images of density populated every as way agriculture for example the way this Scot that after in all like with different kind fields and what sort of to so what we have to do not what classification is with the described the cost on the text of the some features stalwarts all what of al that can be used by computer to compel the pictures of different for the same for 2 different pictures and how close matching pictures of yacht
because case on Monday and can can be semantics fate well with something as picked up like that the medical image it is live up her for the 1st something looks rather bubbly and X rays it might be like to so as semantic need to the fact that this is very strongly dependent on the application of and and and medical imaging 1 can do that in many other kinds of remote sensing also but that's just not not possible to say what it actually is and that's like lexemes something on the radar economic there is something that you have no idea what she will be that you can you can see out that it's not the background if not the background noise saying happens if you look at felt that as a friend he would immediately recognised where the person is in the image and whether background as you get idea of that just by looking at the use because that's something that I had textured around later the head of a person of the Tree of more often than not it at the end that best something that kind of like Texas he has to the break example of text today I'm away I would expect that the show would be exactly the refined regular Texas new would need to be focus on on these area that out more interesting to and the good thing is above the text of that you can actually see get those pops that offer Texas because you recognise it and then you go all this is the church no interest in this is the face after look at it to see who it is and so also found by segmenting the images this classification is also very helpful and if we consider the classification not to be you know like in real terms this is the shirt of this is that air a personal something like that but it would rather say this is a striped area of this as they want textured area now whether at the table and care of bullpen 0 1 about this is just look at an area and that allows us to compute back between images from because they are this is an image that has a Woodcote of what happened area and this is not the image that has away from the care of 1 shows a table the other shows to now but not semantic in move that it's just the vigilant fashion that put on and that the time allows us to compel between in compel described the visual impressed is kind of the same take that we did with the colours last time we didn't care about what the colours actually depicted for that a and and that was shown they all that a car but that will shown that all the Sylvia that will show that works of with the of but I'm with it but at it that left just focus on the colour weekend as saying he and we can also do something spoke to by example we just so OK if I'm look for looking for a for wooden tables and were just give you a piece of land patterned where it may be now and their pictures and this would be at in freeze me from having to do something like some and a tasting every image what a table computer before they
were publicly sification off of images of 1 of the classic examples of satellite images where do semantically so you look at the thing find out on this year is the river with the race moves fixture from this year it sand was light texture and cost so that you can use it for late segmentations of what you looking
out of the question is really hot to describe text for the measurement and that on 1 hand load of which shows that the state law was 1 of the building block of the text of what makes the picture of the text Soweto shading stops with a single line the menu at the Parallel line from the near the 3rd lined and Group shaving at some point of the crew order of high levels he just the kind of like by a mathematical into interpretations of part of things different pectins different different of all the different statistical characteristics of at reflect on the use of soul typically example here are gobble filled of the you transformation will go into that during the because of the fact
I'm being facing questions that that they waste remains saw that is their once he wanted to 0 2 0 2 2 2 to build a system that of the 3 useful to use this kind of how the people of English text how do you find out that this is a regular at some which what would you say and part of that yes have up to a 3rd that the lot from the little black Landsea as you can see from by cell the line of Kent so if we kind of walks with image picks by and at some point we will hit the black lined and 1 go but we have kind of the same distribution of pixels of colours of intensities than before the what happens if we walk in this direction we will not be let clients but the for the change of light intensity or colour when walking in different direct public image it seems to be something that could be used to guests other things the Britain well would you say that text is different in different parts of the image various I'd just go to the Blog party of the much harder to see the texture there and looking at this part of the match case by set of looking at this part of 1 can see it looking at this part by what they want to see it that way by said yes the of the the are so if we do what you exactly set we walk that way the and we do the same over here in the UK but they are not we find that we had very fine lines of black but as you say in the law top are in the right part of the picture we find that there is a lot of thought so we have a lot of stretches of black that might be long to a shading all might be not and it's also this is kind of what care to rise of the text and this is
kind of whom would be of what the hell are among in the 1st ideal from sale that basically 3 main criteria want is the repetitive us something not the texture if it does not repeat the and some of it in 1 black line is not enough that it necklines at regular intervals upon that are to something to do with it that with the way miserably through the match because and 1 way you might make bid the client periodically in the UK you may nothing of or which makes it shady basically for this orientation and the other thing is the complexity of part the very simple pedants and recording like for like prop beating the amount the very simple published just tried to review the way you want was elaborated flow patterns and everything about this is also a patch of the Brighthaupt described because it's more complex for all low that she had find the criteria the 0 repetition the orientation and the complexity of some of some patron of that actually make for the on the possibility to on this cover its nature to describe nature and the question of classes can mesolect do we have any chance things were to with and
the and the chance to I'm to find out and in the Sixties and Seventies actually about the idea of describing such happens 11 computer science fiction is a psychologist book or any interest in the long before Computer Science Adaptive the problem because they wanted 1 2 4 3 D ego should I'm the Sixties and Seventies basically focus on parade of another as it has something to do with going all the pictures in different directions and finding wanted the Blacklight or so that we do it is we we kind of like take the great value of the big so far and we have the intensity of the 2 big soap Robillard histogram on that and just don't have any money in like pixels all their home in dock pixels while and so we get the system of the system and could be kind of like from compatriot other like we did with the to brands up and weekend use some statistical information about the system that left just a single peak other several peaks something very are the baby was suspended deviation review of peaks was expected value or the meat of median old of and the idea of cause was that similar path and or produced a similar kind of his to grab the type of his and Cynthia spected from the colour by just taking the great value of but just taking the intensity of the to look at the end of looked like in the ocean lookalike him in the Super there are
in and if you then take moment of the 1st order which is basically the spectacle you are you throw away all the information or where each fixes located on so they're the best 50 per cent Black pixels and 25 per cent great pixels and 25 per cent White it could be that his chaos the bad that pixels about great pixels about a bigger for 4 4 that takes those but it could also be that kind of shade and that they owe well mixed which makes it very hot to see the property to see the from the if of look at his picture year as basic know period of sticky and we get the colonies of looks like that can't would the tell us well that's kind of like a very little black and those of the but something like that was expected value of here in the middle grey area this is where you would expect but it from the way all the information where each pieces looking by using this his to grab the and them the
solution to that is kind of the level Colker's I want to find out where different bomb but different intensities of pixels called Walker with other pixels if you have a fixed at some sort of this and it has an eye turned intensity take you can and the more of the 1st approaches all 1 of the 1st investigations all that out of all the Bombay psychology at cost of such a mesh found in 61 and he said Well basically we have to do is to look at each pixel income image here for it from the picture and then I'll have to see taking its great value which was here the brewer for what happens if I'm move in some direct once the expectation that this Grabau who changes locate and if I'd for example like this and take a pixel a White on the list but and that changed the direct into the start of the expectations of the intensity changes 0 but changes in this direction the expectations that changes very high a and that is the same for all the pixels here that is something that is interesting not for because now had not really looking at the exact point where pixels located against describe some correct eristics offered from for each picks up anywhere in the picture of the the regular texture shifting at indifferent direct you should result in the same probability distribution of changing it colour value or changing the intensity of update this is a clever idea psychologists say so 1 day and it was kind of like a calculated the empirical probability distribution for intensity changes from of the value at takes so shifts and he just used to shift to the right so with the lot basically my peak so as the intensity of queue and the I'd shifted the positions the right than intensity and and want to know the potency ability and with that idea the probability Distributed although picture echoes is the probability distributing for do pictures is identical textures identical well well I of Qwest this is also why the true if you have money to changes car it's a takes a like that was happy with because and a flight will change so out the and cover of his later Mueller said world yomp ICI that lets generalise it shifts different direct stop at the end of applications that will also pictures we need the probability distribution and then hand as 2 lemon NEMO distribution function for every single pictures we get the ball off but ability of dementia and this gives those actually the grade level called match 4 4 in the direction by just say it was the expected pixel change yes from the great over
Kolkotans metrics basically confidence that although picks up at was in the Ukrainian distance of the and for speaks the entry in the match is the probability of a shift up and so it was up a point ex-wife 1 why want has equivalent of why and appoint X 2 white to has agreed a new of date and that means rebellious usually the wrote to 200 55 it's easy to you will be fined in the match fixing the great level Calker metrics further fuelled by the entry of the lot the number of pixels Pao's that have exactly that shift if the distance in a direct book and a discount of harmony in the pictures are the pixels out in the pictures that if I'm not the pixels in any direct I'd get a shift from intensity I'd print and to judge Foca bake Metrix what can you do was asthmatics while what I can
just happen to the wettest to was metrics you from can compelling to other kinds of matches Bertie fishing to actually if you have 1 of these Maddox by every pictures the and the Texas should be the shy think I'm actually it's the faces of 2 lurch that was found I'm in 97 to sweet stating that if 2 pictures show the same the same credit local current tactics and it's not possible for unions to distinguish between the Almighty the of low interest in the new a perceptive psychology shows that but it's not like that and actually 1 of the psychologists doing it was commissioned self of his later and see what the figure is not but the test work out so well humans don't be like that toast you usually I'm especially not that 0 to see something by grade level Colca Maddox said the WRU of some summer programs Madrick's indeed to point to the same Texas but it's not really true that it has to be the thing you can't trick versus UK and some of some of interesting
enough sums was the 1st idea that was actually along the lines of yet if I'd had a bad loans from the picture and hit the black allowing you like said the big 4 a intensity changed yet this is what I'm doing is that it is a good place the idea that the people at the Sixties they seem to be kind of a Sixties man and that and the has a good idea and it was the basis of colour management and that when it became clear that this is not the whole truth and up on the 1 hand the CBI's grade level Caulkins mattresses of very hot to compute on it and it's very I'm not efficient because you have to shift every picks up and they have to look at different coloured well used that you get from the ship and you have to count many after kind of like but into the match with knee of to that for all the pixels and the up this is rather tedious work and will even in the age of computer science of and very quick computers and need a lot of computation time to prepare images and also prophetic really image and this is the time that really if this needed so I'm some real and and some of the photos in mountains 78 well basically may we take into match all we don't go from every pixel and every direct and look of maybe there are some basic direct eristics that more or less describes the image and we can have a summer of future vector than this huge quadratic grave volume Metrix which in the East resolution is to 56 cross to 56 Matrics you consider mangrove grey values that will grow and they said Sidwell basically when we can see is that the granularity the close of the which has something to do with the perception of because the gravel was sand Santa's was a very very fine grain you looking at it it's a smooth kind of texture the gravel and a few see the individual pebble of and a different coloured so but it has cost impression than the contrast time that area of light that area of shape the Murschetg there is the more kind of like the area has disclosed into each other the less contrast you have the man different will be the perception of the of the texture of direct melody if I'd in some direct tunes the intensity of the peaks of change very quickly ago go in August think of the bamboo going along the pain not the bamboo little changeable was saying colour picture of the UK life and lightness doesn't look rather point she and elongated there is rather bubbly the pebbles a can immediately with the regularity of the pepper as after half time but that doesn't really repeat is that the earlier this city and finely the roughness that is the impression that red this this would structures seemed very smooth to us the top of Structured does not seem smooth the following a scene from here to where the car of that it seems rather smooth but if either directly ICI I some regularities which to not make it also this could be and and that they were actually it measuring or trying to Fiat how to measure the things and found out that well basically these seemed to be correlated with the other 3 but you got this read the are the ones are now or less Linear are combinations of long before they seem to be dependent on the of what if you have a strong direct melody your also will have a strong record of or if you have a strong directionality line like going to increase the Solar that they looked at the different correlation between them and cross all the last 3 so that is what we want to do for
granularity it has something to do with the image resolution of accomplished look at area photographs from different takes you will find that he and you can see the buildings on the left hand side of the road as a picture just 2 different resolution is both Manhattan and that seems to be Manhattan and so this is the point of Manhattan statue of which he time and this is the house broke in Manhattan and you can actually see the different houses to different skyscrapers upon this year the tone different impression but how do you measure it and ideas scaling remember if you if he stay in each image not to end up with the individual picture of the health during day after yet take the peak said that is yes yes that we go for the Eighties meant so why don't we look at different sides pictures of trains in the image and look whole regular the colour of car so basically the ideas by taking a rectangles size and and but over the pitch and if they do that was the same size rectangle here and there and humane this is the same size rectangle eye were found out that this rectangle here real it houses of the same colour Hugh it will not it is also all with a mixture of different colours this is 1 way of describing the
granularity that this is actually wanted to be examined the neighbourhood of each Pixo Fault brightness changes not actually colour but the brightness is now so you work but you you 42 peaks of have a window of size one to one stop with 1 to 1 and go to 33 a 32 to 30 to pixel so different sizes a Kent and you just recall for every pixel in the image was the brightness change was in this area publicist for example via the typical values of idea to here of image content that lost 1 of the 1st running systems for my immediate and and then for each side of the windows He recalled the average grade level and the across from England or you get wonderfully because of as well as a base for the size of the distribution of grave 0 useful different sizes but then
compute the difference of means of grey level between this windows and the window next to it through the window on the other side of Kent went to the top you well if you have we windows directly at taste and of the same size roughly and there was a change integrate level this 2 Putian but it means that is not a regular area if there is no change Over little change the 3 values of the 3 Windows ME belonged to the same area so going back to opt for example year if I'd
taken this week a chastened things up Kent by will find it in this case that the grave value has not changed very much so this seems to be 1 area making this area of the image 30 costs a Case but do the same over here changes for the match showing that this area it is very fine to allowed so it's not the Sri different windows and not belong to the same area of the same of the time of this seems to be rather fine grain you can do the same based on image
was different sides windows and so each pixel by determined the maximum window size but reuters the maximum different different from its neighbors and the basic the what I'm trying to do is a 5 image a work with these little of windows of different sizes and that they should be tried to blow them up I'm to lay fit because most of the power and if of their fine Granier amid this will not be possible because already at small windows the Distribution between a chastened and windows will change if I'd stretches of the same text of the same colour this would be possible to blow them up because the adjacent windows still have the same texture the same group of used the that basically the idea what he would do where
and the granularity of being tied to hedge is the means of the maximum window size of all pixels 30 of 1 area of this recalls in 1 area where I find granular but it is basically just take take the of the percentage between them and you can also use the histogram bomb mapping the number of pixels corresponding to each window size and you would have enough like hominy caustic stallholder took caustic so is there in the image or you could just use the single cause was valued for the and entire image just as the expected failure of that has to come from the sale of
this 1 problem was that and and that is that the most selections was granularity you need to determine might itself be very small if you stick minted you sofas image in different texture area before you may be left with small places where you have to find that texture are so confident image I'm just sitting here on the table and the most of part is used he me and I see someone texture yet by many in the news that will be just a very small part most of the table structure would be cover by me and this is 1 of the problems that we have to deal with the I'm well but you can bet that the Samways than the 2 0 2 estimated the maximum of their the maximum different from smaller well you sell if you count the what the pictures of The the OMX pixel windows that you move of all the people to a certain size and still ways to do that in a probabilistic fashion papers on the web page might look
at the same spot as but easy it's a contrast so we have focus on the quality of the picture now want to folk on the contest of the picture and the contrast is is kind of like the celebrity all the stop of the colour transition to also the shadows that other for example again looking at Manhattan here we find that this is very much a grey area you know like and you Hopley can see the difference skyscrapers in some area of the pitch began distinguish some year yes but it getting getting different because the contest assesses very very low risk you you can see the cups between part of the very high complicit in this is something
that you can't use the measures are so for example a contrast values is just the expectations of the great level his to distribution to just be a great leveller Instagram for each week so you'll record of the intensity and add to the column of his of M for the intensity and then you look at the expected value of the of the sublime and the contrast of some pictures actually describes the his to grab and its of the standard deviation you by the by the Kurtosis witches the 4th central moment Evan knows about statistical moments the 1st test ago moment of some distribution is the publisher of statistics of from for the expected value basically moment off statistical values that you get from distribution to describe the kind of distribution so popular that describes such a distribution was such a distribution what to distinguish between between them by could use just the spected value this doesn't Samuel storey but this is the 1st Moment where but at this point Hawk and distinguished between such the distribution and such a distribution while I have the same expected about the value so the First moment it is exactly the same year so we can be right for the 2nd moment which is the very and a PC pop queue distinguished band mgm well this P at that point something like that the moment the skewness upon and so on so these different the statistical measures taken on the probability distribution and if you look at those distributions you could also imagine them as his digram the great 11 is to grow and this is what we you see of for describing the point the contrast book we could use the expected valued at his with variation of the PM and his about we could use the and the sky was the history of but what we use is that could tell us this which is basically the 1st central moment that divided by the standard deviation piece look at Upton you statistics books if you don't know what to interesting and the Catullus's is not to discover the demands of the distribution of the billions of the distribution of the use of the distribution but actually be number of modalities of the distribution so that means 1 we have to distinguish with the fans statistic of moment is kind of such a distribution from such a distribution can be mobile distribution union model Bhutto's this can distinguish between the up this for we
do still direct now how do we deal with that well it's kind of the predominant direct of elements and exceeding the walks with the image a woman who had met lines he of very quickly in the direct in not as quickly a misdirection but with a quickly for this is the way of doing wishing between the images and but we look at is the gradient of the colour change if absolute this image in this direct in which is highly direct you will would find that the great level values would go like this the because he was black white go to light are go back to that a go to buy a go back to the book and it was exactly what happens to let go optimized Kubicka black himself the Cook in what happens if I'd go into that direct you of it looks like that from have some Khaled and it never changes As Igelstrom the gradient here 0 agretti and until quite high book and for the Brady and is a good measure when walking out of the picture for the for the change of of of colours say because he found so here in both directions the college trained as where quickly a high gradient and all directions this is a wake code distinguish between the 2 images yes or exactly it's a problem of sought to we do and the and the of the day the the bigger computer science the solution pragmatic and works guests that
of a man who the island's where many direct what we would do well to stick to a them like in the good old nautical jobs that East West Nile solves and with the between the methods and and that is why we do so for direct analogy we just determined the strains of the magnitude of the direct of the gradient in each of the Wigan for example useful at she Tickle would every and so we fixed they closed has been well the different direct you look at the gradient the size of the gradient determines whether that is a big change for this not to be changed UK at the same year that what we do with a system remains with the direct tunes the number of pixels the of the gradient in the direction
of the cell created the his around for each Anglo P the number of pixels the gradient of all of the above the the threshold of the and is that the dominant direct and the image there will be a peak in the 1st told because many pixels will have a high gradient Oka you what could happen now is that I'm not interested in the direct and so out your like if something as she did was something stated this is the same text all not but nt dependence is a on for all and all old fault the law exactly where you are so it is kind of the same texture and 1 could log you live in certain Samantha a cookbook so City over all using for example that it might not be the same texture so what you can decide is you could say Well and my measure for direct nobody to be very with respect to the rotation alongside well basically its it sits the way the photo has been taken off this wooden structure without a photograph of this way the without photographed in this way it's the same texture and is wrong and random what kind of Photo I'd got unfit to kind of punished the of the photographer or the patent for the foot over of time that should vote for something that is in the rotation and very and that it really has a sense that something is horizontally stripe over to construct than a should but not for this is designed to sit in that we can make it would think are directionality to measure of his 2 grammes can be made both ways refine note of the different direct tunes 8 or 16 or for everyone to be happy and leave it like that but it's not potentially independent if you have a strong direct another Chenault follows direct in this is a different texture from if you have a strong direct of the East West to look at on the other hand I'm by can also say well do not look at the different columns just kind hominy columns are there was different direct maladies is there a single predominant direct noted other 2 but do that it becomes rotation and the and because don't look at the exact His 2 gram of all the exact places of his to from columns but just look at the structure of the NHS to crimes such case but tomorrow the and
went on to show that the 1st 3 measures the closeness of contest and the direct melody are not correlated so they are in need and the and with respect each other and the I'm distance measure between 2 images was suspected texture could just be the cosmos value across the country as well you last the direct another to value are beauty in distance just simple think how you guided by scaling factors which is basically the standard aviation to kind of number last between the 3 that it are first texture measure for my we can't take image as a party we can measure 3 aspects of the image and comparative was suspected of individual computer and that 1 before you don't seem so happy put and and edge to
works sell if you do it of this is the idea incubi system and took a couple of code of bombs loses some a mind up at end tried to find it in and and different pictures and you see here that with rising distance things get more and more difficult for so called back but had the 1st 1 of the next match but also the inverse coloured of slightly different happened images are immediately recognise and the more you go to walk of something from the US rival striped here he will have 5 different mesh Foca but
the 2nd possibility of computing the of the celebrity a so called random few model the you could also say that they seek the you image is a random variable I random being for each pixel the intensity and if you said the intensity of some picks that it would improve and by the pattern the seminar T of other pixels so for example if I'd do would have 1 of my by strike at on so boundary this Pixo he is red the influences the probability of a car of this Pixo OK because it would be a pet and this Pixo should be wide for Kent the same goes for this picks up it would not be regulated this pixel will not red to Sunday kind of this big if had Leason oppression it is a patent humour it is a regular at of the so wrong area 4th which preclude bucket this is basically the Vieyra deal for whom the basic idea is textures repeat area of if something is of regular of not sensible hand so that I have to do when you do the sentences of that and is basically you have a small sample of the Patent and then you just repeat political and what you do to make a realistic pet and is what of the game in the street people do to make it look realistic it off it looked like the PP they introduced some arose because it should have been a perfect that it would look off official in real Texas that on the perfect as or with those not and this is the you know what you have you have the tree was left the of their not side by side 1 may be slightly behind the of it some may be missing for some reason or the other and the same with a brick wall a brick wall as the regular but there is a chip taken off some of the brakes the some Smeagol from somewhere that makes it look realistic so introducing a certain the regularity is basically a good way of making a texture look realistic why don't we do just the opposite for from looking at a time halt through airport at we could find out what was the model of that generated the spent the statistical model with with this peplum Boston 2 sides and if we decide for a certain type of model and the power matches of this model that were used to introduce the texture with type of these Parramatta's a perfect description of all part of but the really understood the idea so and texture sentences use statistical more books to change the texture the but just slightly in to introduce a Moyes into some of get rid of the take the edge off some of the other Fischetti if you want like that knowing this model will result in simulating ecstasy just Niall Esuli opposite is true Simba Texas whose of the same model knowing what model very probably all with the height of slightly is behind the synthesis of some texture and helped us to describe the text but achievers simple idea settle issue but Mahmood you create different over similar text shows and we
do the other it the other way around so which model which parameters for some small across generates the Texas during in image and the best way of the where hot to
model generated text that's just the human we have some model quality X because of the name and using this model that are the suspected intensity values of the pixels around it 6 for some point of the and look at the around based on the intensity value of pixels and based on your statistical model Icom predict was ability the intensity of all the other places foca for example if my model created this texture is obviously Mollo that creates stripes but them noting that these pictures black should increase the probability using the model but also this pictures black and the picture is that and at the same time should increase the probability that this picture is wide and this pictures white locally but and of course in the creative texture this could also be black Schuele yes because this would be an error but in the long run you with the high ability White now we do the the other way around we take the big soap look at it the wrong and see this Sarandon as an at the evasion of up statistical more of in a tried to all what the permitted for this model this is all future back before the image of the texture of but so it would losing you it's a more complex that of so also the mobile has different parameters it would be the same the Upper and below should be wiped off because of this the black and the right and left of the back of a pick through it would then sold the some kind of stripy at her but it has to be different he for the regular patterns at the very complex model and the permit of her death the of look different left
we ascribed the image by some Matrics basically this is the image the for different picks also look in fight which take the intensity value of each week soap and put it into a metrics the you need the duo Cauca the same entries as pixels from the paper and the and the picture book at this is all Matrics at nothing happened Niall with human that opened with this match is a random variables calls the metric to diamond know this is why they call it a random few apparent that the 2 dimensional Randburg within if under the law the distribution you off across as by the Justice you some kind of a model a still have to look for the parameters that resulted in the observation so we have and they meant we assuming that it is an act of a sum of this model creating those mattress seats whenever parameters for the corresponding distribution and the streets of basically to a maximum likely destination so what are the most likely values creating this specific Metrix and there for the specific picture book the felt a picture you is seen as a Matrics was intensity values as the entries we assuming that is a common model of Elway's producing the mattress see we take for the Texas that we have As input values as at the variations of all model and then do a like a maximum likelihood estimation what other Parramatta's of model that created these observations was the highest of the but and this is what is
called so the problem is I'm dependency advise look at peak soap we looked who were pause that will it kind of influence the colour of its neighbours but it is a pattern guests otherwise it will not result in a patent if a used to probe early to distribution how about the neighbours that are a little bit more files 40 also yes for world things away the while transitivity yes but on the other hand if look at some Peta locally akinfeev very strong comic but on long distances things might have changed it might not be as regular look at this 1 structure the yes it is striped but by can see the very good and a very regular striding in smell area of the wood pulp just saying this goes on the hunt for the edge of the table but it is not true because there some a given that regularities in and in between the 4 changes so that when the of what we can do it is we can have some idea of locality and just say Well basically is the neighbours to rent left and right are high and the up and down neighbours are Blake and we have some striped think but pick so concerned that he has a very high probability of of being right and this is not influenced by some pixel over it UK and just look at the media around the of any picks up to determine if the for most of they were the 1st to use well hominy of the particular statistics who so many I'm in the thick of the no that obviously sees this Seth characteristic is this is the mock off sold probably many of you will have heard the terms mock of chains while hidden mock of model of S so just as the name and this is a 2 1 of the properties of of mock of chains salt mock stuff estic processes I'm that your with the law or with restricted to locality so the I'm the of the of probability of some event operating only depends on the probability of events occurred in the neighbourhood so immediately before to time-steps 1 of before but not 50 year before a makes it
easier to calculate so I'm we just assuming that the value of some big soap does not depend on the value of their early pictures and image but just on the values of the peaks of the neighbourhood of this picks up and will this called the mock of of public the again like in the direct nobody idea we say neighbourhood of basic to shifts from 5 takes left 5 because of look right 5 picked up 5 but the bond and the bad of so this is it enabled of some Pixo as is start from the excessive and go to eat has been summer much of the end of world we basically do it is we were just go into every direct seemed possible 1 pigs not for us at the moment but the 4 0 0 1 0 when minors 0 1 of 1 mind 1 old and this is 1 1 1 minus 1 minus 1 minus 1 of see these other through the enabled the of for excessive I'm not
only have to define a moped that reputable OREP you do since the observed distribution of what emerges in the collections of text just with the best well you with the best parameters and actually of for everybody was heard of lectures 0 worked and computer gaming found that a lot of different from the 1 they all of the drawbacks of the of the of the frontages but basically at the law firm and of course it will want to come head images from different collections because they were so let's just assumed different models and different parameters and different everything but we have to restrict also 1 club of model of and and just look at the parameters and different than the parameters would be kind of like the measurement for the difference in the in the texture quality of the so why do a popular
class of of a modified texted graffiti and also cause symbol Tania's all too progressive models facing the what they do is they take the different intensity value from the pixels enabled was parameters that changes to UK and this kind of parameters is what we later need for of each other of because this is the right to respect for each different texture enabled is the same for every textured just moving from but wave enabled is the prints by the colour of something that is different in the strike think the neighbourhood in the direct tunes is influenced the White enabled them this direct to influence the black if you have some idea gnomelike like pebbled tight patterns and enabled as influence hitting and the same characteristic of the same intensity as all picked for UK and this is basically an coated in the sector 2nd goes for victory this areas noise you just have a random area book where's a means the role and very and want to its spread and the Distribution spread over the whole probability space and every it where the of that is kind of of the same of figure respect for basic leaves just adding white not totally and and it just took 2 0 2 to account for small Ellis in the text of that a given by the operation of the S this parameters home much noise is in the image for much noise belongs to a text is characteristic and these are there for the 2 parameters that we want to expect 0 but we want to estimate with the maximum like this is what we want look at this is what describes or text of the other party are the same for every match but we look at the same size of enabled we look at the same Welsh noise Distributed from all just the intensity of the noises difference between 2 from pictures and just the way I do the colour is change in different directions is different between different fixtures from the but
that now the problem is really that some restricting also of 2 0 2 some they bowled of the picture also means that a different pro the city of Texas could be detected all not for example have a takes a like that and I've texture of like that the those are shaded fixtures if I'm looking at at the same size of Environment round certain pixels but we find that in 1 case likely to take some part in the other case I'd take nothing of the because it seems the same to me this kind of difficult and unfortunately this non-trivial problem found of the done to to solve the so called multi resolution cemetery of all the rest of what so idon't use a single model but a used different Milos of the same type also overaggressive stimulus La models with different size of the and and then I'd say where the feature victory not only the state images that and that Al for a certain they will find but the feature that is set to that the Foreign enabled size 1 Pixo tent and that from a buy to pick so that and that of enabled fastest pixels and so and this is the different resolution of the images basically the different sizes of and so this is what can do but
the and where so and well and that was really future but I don't interesting just off to use parameters but this high compression Prolog the images texture of the month 1 before we had a complete image before now with 2 well use or to use different size of labels maybe 8 fell of 16 but something like that we compressed the texture inflammation of an image to 16 that's great I'm the only assumptions that we did it is mock of conditions it colours are of Texas off of of local nature and they are repetitive and so we chose the size of enabled well for the future of the collection the them manually over by using several of them looking which were of was what used to but Dr ago for ShopRite breaktime are of the time half Boston of the time the thrill of so where
should you right now was in 2 basic ways of describing pictures with very little effort 1 was basically causes directionality calm trawl St from Metarey to determine the value of 42 picture that you're texture mesh and you can computer 2nd 1 was random few more well through the maximum likelihood estimation of the model parameters that 52 before picture of also other ways of describing textures and they always say that the right from signalled full system which because of the high the interesting to move because what is the texture of what the texture of the periodic patterned end the Compton year's intensity inflammation of the image so is the vice seeds the line of each image as a seconds of intensity inform nations to detect a Pareora Copec that 2nd use the Toulouse of the no not really of the tools of the signal processes right of looking for so and so and now he's in the as well as often as called transfer main features sold by goal from the stigma that such the intensity information such into some other domain talk about frequencies hold and no something or crowed talk about the and Pichugin all right higher the high high is the change all the rate of change in of an eye contact about these things right off in a different though may not in the image of me and I'm this something totally different than the and the low level of features of that we have before which can extract from the feature from the at took pictures of the tell you that there is a certain granularity also shading in the picture UConn freely reconstruct the picture from the granularity it will give you an idea how it looks like the kind painted on the other hand is a tell you where that there is a signal of intent cities and going along the said that measuring the amplitudes and measuring the I'm every periods and the frequencies and while not enough change right icons reconstruct the signals a Kent so icons reconstruct the actual in which the idea we don't for comfort method talking on the handle image and weekend reconstruct complete picture from its and this is what it called high left future so takes the helping to into account and the whole picture computer
reconstruct transformational transfer was basically the conversion of something of a signal in a different representation lycanthropes Womad into the domain lycanthropes called back from the Dome and the preserve of all the information so for example if I'd have the picture of a straight lined again described by 2 points a beat just starring these 2 points with a always of low tree-code struck the life this lot not some of life exactly this life and their full swoopy picture of the life of a Gretal's it will actually be 1 or 2 of the gunmen opened be just new point at the end the gradient he Ethel these 2 pieces of information it will allow me to draw exactly that line and there full reconstructed picture of it's totally different the gradient and point information is that the different to the 2 point inflammation update and cold the same thing uniquely and this is the same for the transformation of the
for example of for it is we of new Phoria transformation so this is image and this is a repetition of the for a transformation we don't see anything any more it's a different way of looking at the image and if reversible we can get it back from 40 a space and will see a moment how actually work from the house that us so the idea is that we gave information but for me to some of representations to see out of things to feed frequencies to Sri seat totally Kelechi in that we that we know about are probably contradict often of all now we can quantified we can't say how much of each is in the picture for example the and and it has is also a good measures but that's
stop with some out at a profit and before with statistics now we go for algebra I'm we take points and space and so he will across here at the end of the year and song all for and and if I've ever and points in phase of the series and the new algebra actually that can come structure appalling O'Neill L at degree and minus 1 0 touching all these points and that the only man to have a life of quiet with find a polynomials going for so for example if I'd have just a single point UK and that ways quants dropped at at this point the 5 2 points icann or the ways construct the light going through the 2 points it does not depend where they are from the creation for the line look different yes but it's the old ways the line effects free points icann Owais have parables going through the 3 points but it does not matter where they like herbs and where is the line as Pollino Mills degree 1 and the Pebble as Bonomy of degree to it was more points the Pollino get no interesting to say that these the but the degree of the product for the moment is only is and minus 1 but Cilento described the point cycle just say the given the point that look at the quality of the points and plants that will give you the early in the new that the formula for the Pollino me and and will give you suspect where you have to look at the polynomial to get the points and so for example if prolonged and as a bucket this is 0 0 1 2 3 4 5 and just knowing the blue lined by can detect the point and the representation if you dirty different from the representation of the actual page but it is the same information for good but
let's not saying that and image is just a discrete function that science each soap 1 to order a book playing and I'd 10 city value so far look at in a major Oh just take the location of each week soap and save for every Pixo in the search by 10 city time Welsh the degree of items before for example this year is light from and the people next to it the talk of the light and a strike at a kind of flying Coppet they is each image is to them and you function the somehow on told and space and and you can also use colleges and not talk about that and intensities but about the colours of calls but make things more complicated anyway I'm each row of an image can be interpreted as the 2nd of real numbers are Kent and each roles in the 1st the 2nd of real numbers and then be described by some we know meal function to do that but textures this kind of strange was because we know something about textures and that it to exactly held regular and at repeating for ever and ever and and so it's not just some some polynomial that kind of like does something and moved off into any direct you but it's actually a certain type of Pollino new that does the same the over and over again for about anybody who knows can the function that led the singer from the coastline exactly and this information is kind of like match for not
bring you but has been discovered in the 17 under but for you he was set of basically and patriotic symbol of a new area of 0 signal can be covered by signed and goals and function OK Cerezyme was a fringe might imitations and this was his great idea has said that it had failed to make signalled can be because it was in some way cities or such or seeking functions the signs on the quayside and why Web well mentioning for here in this context we just said that he had used in Blue presented expressing most based on that will be paid to its stance from buy them back the right is singer right now real numbers or this is prevention of but does he got the idea that this has been a number of them were opposed the presentation of themselves but sounds and signs on for a year says that exceed can be decomposed in some of the cities where they it presented what so in a disappointing part that in to clear cities such as some of all seeking functions this is what 48 said he said that it is that function can be because was young and I think it will be imprinted some of such such functions and I had said
to the with the basics led start with the one-dimensional signalled Buchanan imagine for example a sort of Buddhist for example now so signed is the and the to and the frequency in time for future have well this is not quite with example for some with its to it something like a step on June but in a way it's perfectly exactly the compensating for should so that they would be denied intensity and then you have the time excess and the script eyes based on look at the end some real numbers of different moments and by by for example of this 1 based 1 based on the of the sun and sand P well 1 off this would be the ludicrous a way and then other senile can be described the city's or feel numbers and only of the year the city now the cities of the numbers can then be Baekeland osteoporosis he's off sign work sign functions so
band let's start with the simple sign function and a repeat of that it was signals with the well of time spectrum causing the whole time spectrum Songo'o not located like for example the 1st signalled or so but the whole time spectrum industrial something like this would be a sign that the worst of as they can see and then we go for the win increase the frequency and I'd be sure no sign work will sign functions the bed the approximate on the original sitting out will be a judge it is actually a bit about found and so on account this thing 1 of the frequency and a different on which I would have my and high frequency and the blueprint different and to give new on either side representations which added so eye out the Serbian revision during this 1 and get such a good like this 1 just basically adding signs together would some frequency and some amputated to get there but the together but the local simulation of my seat and Blues for the with higher frequencies you see for example Shia the politicians remember 1st instead and some and in time the quality will be higher and higher and high with the height of the frequency and that not the club this year is that I'm here to win the quality in way of my is that world regional signalled like just opened up and say OK I'm going up with the secrecy and them over the head with their presentation although as they can go up and but the perfect match so this will be the idea icon and then they Klemperer's during signalled some or all simulations is seen here going up the by increasing the frequency the Independent and some of the 2 there OK
so that as said some most yen and on what it is that by some of the to Acquisti sent off efficient some frequency in the Senate signed last another signalled with some of the accused and the frequency of and so on and on visit is this some here what this helps before it was built translate my original signalled from this time between now the intensity would find until the frequency domain with or came late Monday presented the frequencies I've just below those figures seeking this frequency she this 3 grammes each year by get them out of in might frequency domain As for example in his histogram when the and the team's described by these efficiency now this histogram this is a presentation in the frequency of the main or will oversee will be the time for me and as I've said before that with high frequency is that the private dedicated if you want some young people who were up by a company has to think of some the high frequency you get the load information the high frequency on so we if you that some of the 22 thousand headed the most much because the human doesn't here the high frequencies and I also don't want that much information
OK know volume was the says is a sequence of numbers in is being billed cities in the trust point into a sequence of poor efficient but which were officials with just seem the look was signed in sign functions now and then the 1st costs where have override the frequency of these Simon Cawsand functions so that and we need that practically in order to transfer this during of the sequence of your life numbers wanted to establish was close efficiency and
complicating disquisitions were to be seeking to do is to protect the scene of the region of the world we have to each coastline or sign a when saw signal we now so we have to take this for example for the efficient of the coastline function for most of the real number we just multiplied being seeking the city now has been the corresponding point with a corresponding cost in bed to and the same point was signed question this is how we copulate a week of the way equations and and this is how we then represent
the same thought this was a planned the will not a mention of the pursued user of an inch of salt then things become law but no complicated of cost there is a generalisation for the full year and the players we have the possibility of global abuse also pulled a mention of the word for example of the way he described the pay cities in EMI Jews as some sort Simon sign consumer also dictionary so we have also dictionary people causing lipo examples she this big had the same idea high intensity the idea here is that the intensity off pixels variety finally based direct should should choose not to go down so these have the same idea and city hey I'm going for example of the White the back and if you need to be there are something like this would be a popular and which could be superbly should be made in there are something like this Clive dreadful white the well not quite but back and 1 on the back of big on with White Stripes India's Derakhshan way doesn't really distinct the doesn't want to be the case of this would be the idea a day of such a sent about the OK so they and their
families becomes a bit more complicated because they need to begin to or simulation the Palamon should stop the laminations out actually but only needs of the pizza was based on the weekend and hypothe into and then I'd have been in the same caustic sign and sign well simulations which described my function so each other and still in cities together again would be amplitudes of this Australasians now we still in can be represented a as his base a and B qualifications which now are Matrixes yes yet the people of this area for a start over the start of the World lap you mean the end but it the figures to because of physical Zola was picked of well don't actually on but you with a new project from Projections the signal over the signed these sold to say and this is how you local created and for best signed based if that is not fit to appease and that the 2 men the called which would be 0 so Ben aides are both the picture sought to say F but there set off by this Pepillo's step signori on O yet
it yet Chapin's tea on the 1st night of year days of the the the the fall of the wall of silence on the part of the world view of life but both sides were them for each of them is independent of the point is that the way do that for you at but you all I red faced by the 1st of all time by the end for the world widened this in the last year I'd call a lot more if you to for of and all of that and the you have the right to of all time by the end the year but it got off to a long all the bad 2 more are with a then more array for wall at the with a but it
so the the amplitudes again become created based on the same for 6 and 4 objection principle only this time I've local by mention a function and they may be but it could be a corresponding Simon and functions OK
now that the UK was the the of the of the transformation was built and the different images so ironic actually to be able to spend their own each with another 1 in the Big received only 1 possibility would be to compute the a and B quotations Matrixes was Simon Cawsand 1 in which with a and B Matrixes told the sentence and for the 2nd in each of us this is not of some of the best of the best solution and 1 reason would be that actually 48 where patients a complex they have a real component and an imaginary component and the 2nd would be the from actually we need and no in which they chose us the date die in a different perspective and this is the real reason they should this is where the real a presentation about how the clear presentation shows of the biggest spectrum of the idea that here His a 2nd the idea here is that the so we should the frequencies as the a well balanced with different is likely densities where ahead of for example the fundamental frequency of where a then and we have some of low and high the harmonics this frequency should invest by reaction 18 together with highlight information about this but I can see actually quite they let
me sure you a better example of a hole by brought him so the properties of the song of the same age as he found that they have some December on the fundamental frequency because people still of my son and also This is this on she and and then to mitigate the the origins so what happens a puts at once and left and right Sematech of them at the height antiques as for example in order to seek out the and the because it is which are multiples of the fundamental frequency by the example of what you see here they for example become weaker and weaker idea the strength of the frequency while the lighting density the industry presentation so the right the Ethiopians the by it is the most things like in the in which but then with the frequency now also for example for be seen each year ever again this signals here and there should be imagined that the company to be called also so it lights such about the information that they get from the spot and he added it is in this mood frequency so they might have such a signed for example salute so that you can get the same age and the time behind which to beat itself over this that action and I think that actually the which is given also and the 48 the name with the strength how much of this but that is the time each year of the 2nd half many more but that was then despite fight will be made of every MP for example also the strides humour Quad Bay presumed something like this yell of the sea which is world some of the direct shouldn't when the but the but also the size of the period so how big is the distance between these it up these PPL stripes for example in the sudden about well
if was the family had used them in end we made in something like this a popular like this then we can read the seat in the frequency of the commitment that there is something happening 1 of the globe so I'm variety that the fee for the bride go back to bribe Bobek and surround don't the frequency actually the it is not that big the in the city is quite high and I feel competitive with a clear presentation within a scheme which you can see that the direct of the part that is on the same sort of the same but the go of body should them by PM the Bank but the frequency of it is high again and that of the early days you can see that it's not a nice thing almost nothing happens on is on and in the end if you have any
which saw if I will pay the in which we previously seen them also can have though world some signs that world presentation you can or a greasy this also in the 40 accounts for mission so the americanize a both originating you can see the and the to the difference in the queue and this is how differentiate between his pop and here this by the end here and his by the you just by looking good day of William representations but
now I've said that world in order to get this week must 1st Calculate the to quit visions of those Simon all signed from the waves in order to prevent this type will show on your fellow which actually has a worldwide the complexity and so have something like for first year refuelled for avoidable program and this means that complexity of order of the power to this is not that great either would be a big blow to database with indeed using you want actually breaks 40 chimneys before you remain and then computer now he will be made in that you have 100 thousand or medium sought Hamilton a off the media's they have to extract disquisitions for each in each and index of efficiency of the equations of the GRAPE time between the 2 men met on the set of this whose own days of an unknown Efficient Implementation best the code of the heat out World which actually about in the demands
of the Bryant of the dispute was a discrete 48 race the 1st of the so called last year confirmation and the idea is to use the problem so we actually functions as the divide-and-conquer by the introduces the complexity of the horror problem was Plassmeyer public only is divides of the demand and the exit with this reduction in the world that he be the key on would result in a complete state your and real end of some of the words of the late Earl of exercises on quiet you will implement the siege of or something like this because it struggled laborious it's not that tribute to implement the and this is where the vintage the joy of my club it has liabilities
which efficiently have implemented 48 hours formation about it and just below the 4 them into a lead the summit so what you need for a media of the cause of the function what you need to produce the book is just will be Belgrade levels of when you have mean each week Collins who had been busy these so far stronger in each Belgrade levels and then just by pulling a 15 tool for their mentions the presentation the for year presentation of that of that year so it is that simple she will turn example ruled probably need these for them out of the next 0 0 more cruel group and what you just did pulled to is that the initial figures below the level of for 48 transformation and the 1st in order to be able to see something and computer something you need to send the the 40 equations has said is in should be sent on the fundamental frequency it could up that would be for
everything for both the free at times when he should 7 thinking about the future information basically like we did with the polynomial given some point the intensity domain we can't calculated unique representation in terms of finding the cold and curbs and taking the coefficient each week the and the future of the became distinguish between different at this not only to for 48 transformation of them many transformation of these kind so there is a price both the discrete because I'm transformation that restrict itself to those lined up for only and there is another 1 that won't go very briefly into which is called the leaflet and from each and the basic ideas as they all do the same all the results are but slightly different domain and other domains are sensible for different prefers sell the frequency domain might be very interesting for of things I'm in in signal-processing on West away flips can be of very interesting and and flight the of application areas like image and and this is where she found the idea
behind it is kind of the same in Poland information I'd do just the same as for a transfer made restrict myself to because lined to co the and functions and 1 application area where this is very practical is the encoding of japex images for example so into a pack your also go through the pictures for compression and you want to compressed hominy pixels following each other the same colour is the basic compression of caused this gives you a function again and you can compressus function using calls on measures this is what I basic to found that can from basic the of both all based on sign of Kulvinder of a waste of the Apollo spectrum of these coefficient mattresses is what you call the images that reveal showed use just to show how different of different how different patterns of work on that spectrum of the frequency expect from a connexion visualize it but for the comparison you will take the mattress east of the Coefficients usually you restrict yourself to only the 1st few coefficient not read the tale of the distribution because that's to coca
I'm with the wasteland transformation to approximate the eye Tendai tended to function again but with a different class of based fund each you don't he was signed to learn from James and more but you you find she polynomials that only exist in very localised and the idea is that if you functions for me different shapes will see a couple from that exist for some into a bowl and them out of the euro on the rest of the so they can be used as a new basis system for all building up your intensity function because for every point in the intensity function I have to say where it is grant in the 2nd of the time and yet to say what that value as take as the basis of their the functions that would it exist in the interval of time and put them to be a uniquely to get to dispel book this the base ideal because I'm of for for way for them to fend for me and the idea of how to reach the value is exactly the same as in the for a part to stop is the biggest with is existing to take as much as you can take of that the menu at dawn the smell of the kind of the way flits that exists in the US and a will to kind of shape the occurs for that could whom I'm the
functions that we may use of considerable that kind of like pulling down the both and also things he was spikes for example are still not really polynomials and but they are local locally integrable and each of the integral all the function 0 4 the don't have any mass from the speaking the covers out the area as down he would have exactly the same and it is true for all different way for that such and will only come to the easiest kind of function that might look like what 1 basically a step function the this area here covers this area he can't just steps function and this
the called the hallway but the soup with a as we have any such way whatever may be just quote thought we can generate a base by shifting the for the around N to buy scaling the way for in size local but the functions exist only locally for the rest of their 0 shifting that around we get us the mass of the distribution where we need it to get the via intensity for but then the each way float it has a certain shape or intensity could also subject which is used in the shape of the way so we have to even ought the problems the discrepancies in the shape what we do easily scaled down to the way and added and this subtracted where we need talk and this will then give us a reputation for so basically the as the scaling the fact that we just the by about you buy something and as a shifting effect of the just shifted left all right up there and for the way she faces usually used are part of 2 has have 1 way for that it is something that consider to which lets covering the high by consider way flits covering the Cueto's Gateway flits covering a spot of the of the whole space a came so icon of like making small up by pectorals to and these values the you that you use it doesn't have to be to bond usually used to describe a critic of what he would
do so the my simple example is the hallway for its long the half of the interval and minus 1 for the other half of the case the sea this would cover this bumpily integrale is hero of the for using this way for what do we do to scale it but easy we just gave it by half and we have a way fled that leaves only half into a but again though the area as you do not but presses use on the only half interval because of how the sites so we don't want to read too we just take a set from a 2nd instantiation offer shifted from the off Foca next step we can do we take request speed boca we have to shift at 1 time the 3 times a week at full of these classicized reflects and now we are going to want to move on them to be fined this we don't take the full amount of just be scale them also published earlier in a minute and it will be kind of like now we have also cover no basis but what we need is also a member of the saloon all night smaller wave led by by factors to make them smaller so we can't even or the fight area so I'm and effect of 2 to the power of gravitating from group and kind of like it gets the places to be all for Momo so that
happens is that if we have stop at with the model which led the biggest which we can get we get to of the smell away but also have smaller AMPI to buy these often all mummification factor a pan over a shift at end of the scale but the next generation of with led full shift for taunts for different publicly into growth and again scale to affected of 2 my other ways that has I am amplitude of 1 1st some way fled as the and accused of but 1 b fight it by squirrel to you 2nd wave that so grant child way flipped has the empty accused of 1 divided by to APEC but then
I'm wrong we can do it is we can also represented the space as a scaling back end for a highway fled scaling function that we used to 2 to to built this is just the correct eristic function on the in 2 0 0 1 and 0 0 where rather this function as 1 on the entire and it's 0 0 everywhere and if I'd have a that set of card in the sea to the polls and a few Rahim stating that icon represented and this is not a new life into a bowl of 0 and want buy a piece ice continue to find using Qt the specific scaling factors that we need end the location of where the way fled are in this into a bowl this is the correct eristic function saying I'm 1 was in the into a bowl and the row of such as of book and this basic to of scaling
function does happen the step functions we have 4 off intensity value so obviously Feeney for the image and that some point from end they have a limited number of of points then icon represented by the scaling function and the hallway for I'd take it the different highway fled was different scaling kph and different ships at the scaling function for you each part of the Gulf of of the into a bowl and function the of this the intensity and this is the role of the rich and Pixelon people to pick of free kick for and so on but of Kent then eye use the scaling function saying of kayak consider that obese little into individually and for each value in the interval by icons built the unique representation with respect my way oka the
show you an example that we can see as a step function given by the sweat for these site intensity value from 1 wrote off my 1st takes has intensity 1 2nd pick has and take it to the real because intensity minus 3 0 1 of the and on the resolution of the bases of the Sri Cytyc among the way float Tideway that and the franchise if that's the only thing that went out with the then 9 each to calculate the also moment isation factors which would be 1 to the root of the 0 0 and to to kind of scaling down to what happens not
this that I'd do it myself a characteristic function for the into well that is just 1 of the interval then add the myself the mother away flat which is basically what you for half of the interval minus 1 for the other half of the then my eye Bill myself to baby with the 1st try list and the 1st half of the interval 1 in the 1st half of the England minus 1 0 in the 2nd half of the 1st half of the interval scaling down by the also nominalisation factors to the where would of 2 and minus ascribed to of care this for the other half of the of the so that the 1st wave that covers the entire it into a book the 2 2nd cover up but the 5 the 2 2nd cover the 1st time in the 2nd half the 1st half and the 2nd half a and as I wrote in the other half of players just shift otherwise that identical the we have the grandchildren covering in the 1st quota the 2nd quota 3rd caught and last caught after we have won and model with the with to they a that we have for franchise Why do it we have 8 until also was basically a skating function behind that because
we have 8 that a point 1 2 3 4 5 6 7 8 Kent Police party that these I'd points he finds of basically hominy into both we have to and we have to be separated off all into into a but so
if we want to build anything with respect to some basis than we just make it Linear combination of the value of making something Linear communication this by just have Defaqto's basic scaling function for the correct eristic function coefficient of among the way that to Coefficients of the baby they fled L Coefficients of the grandchild placed upon and want to have wanted to represent by this is the intensity function intensity of a colonic density of fixed to intensity of pick for 3 and 4 F this basically would follow up a solo if
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occasion of the of the can do that on the night get as
Coefficients peace the and what do they mean by the means have to take half of the characteristic function 40 point as take minus 1 half of the model way at each point after taking it such and such for the 1st baby with that each of and if we now get the function from each year with away way for book and and the fact that those has the right from beyond the the McCanns reconstruct each point of Booker Crostyx function for example that reconstruct the 1st point this is the intimate OAP 0 0 2 1 8 of the intellect and where determined or into 8 they pockets of the
I want to 3 4 6 7 8 of Kent was the value UK a less tried
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one-eighth which wavelet to leave that the yes so we take 1 half the 1st day we waiting relates to the way 1st yes so we calculated and take mindful of the the 1st grandchild wave that yes and finely lost for UK and so what we do is we just to enter the values here into the function exists UK and so the 1st 1 does exist this is 1 the 2nd 1 does exist model a flat in this area this is 1 of the throat want does exist in this bond goes for print 2nd 1 does not exist On into a bowl don't take it this 1 does exist take it APEC and these don't exist on in total but and if we at this oil up we get 1 0 looking back on all
functioned the 1st volume in the 4th 1 foca we can go from the function to the way float the function again this is how it works but it is very
easy to look at it and as a summary for today a showed his some load of the text of features that will be just consider in all like the cause of the granularity or a statistical models and the parameters and showed some high-level features which cut off like and bad the image information into a different league to the frequency the description in a way for faces but evidence of Kent and want allows us to describe the taxes but not to reconstruct the image the high level features the allows us to reconstruct image and to some interesting stuffed with the feet of his compelled to it and if they
are no more questions today from Monday move from the Red Effie the and eye which they happy Easter and see again next week and will continue with texture and this the but of my to a loose and other this and and stop on the interesting part the shape features