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Chain Codes, Area based Retrieva, Moment Invariants, Query by Visual example (05.05.2011)
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00:00
Last lecture we were trying to figure out how to work with she in what makes a shape up to 6 men shades of of images were talking about not basic interaction with images way just of defined vessels and say you know like are not of the images made be on to some kind of like a part of the images may be background or the ex object of wrestling algorithms I'm on the other hand were a kind of discussing out what makes an engine edge so was part of become too and what is not and were talking about the gradient of based reasons to to to find out where they are shift significant shift in the intensity distribution and set to shift makes for a good edged because it has shifted the intensity distribution I'm also are all vigil at perches and can can be recognised the shifting can see what happens in the image and that means what the value of Oakland to a few conceded the I'm building on segmentation in that way was kind of good segmentation and we can see some of the pictures which can meant The big images quite well you know what we see the basic traits of the of the image and the Duke will and talking about metallurgical operate as a little bit so cleaning the data removing some Moyes I'm a filling Holmstrom in income but where we did not talk about and lost pointed out at the end of the lecture is that we still have no way to represent shape shapes but with no idea how to stop them what we do with them and this is what to do today big we go into shape based features so what is the actual feature the which full representing which which are about some very simple but features like chain codes C a chapter C a and the and the want to Dubai example just to see what what happens somehow be straight features and can be used
03:00
This is C a Areas some help about figures out so if you got active Qantas Allwood lost a talking but Watership turned from Asian get this image that is kind of like shows Ali's lit bullet lines
03:38
That it would you basically have an image Which does not help you to much of the time this and all we have to now we have to see about what to do with the shape but we of extracted from the and as well as we could either represent the individual objects so we found a phase in the pictures that represent the space as this is the fate of her that we could benefit represent the entertainment and what your own images from the day with whether to faces on the winner of this does not only needs the reputation of each individual shape but also the connexion of the shape of suspected each of was something like a tree which could be kind of like something here in the UK like for like a boy he obtained so the different shapes 1 could be drawn down he said Rodrigo shape way and the other 1 but this Welch's thing appeal which is good but not good but there was together make the tree in the likes of the Hold image Some information carry some Syms's some more semantics and if we go down to describing individual objects of all the images with the of something that is at stake in the than the and we basically talk about the description of a column to those on 1 soloist as and shaped and this is closed growth usually that we could save it will be area that look like a tonight not become to may be occluded somehow but the timing and to have a big area and the and the and the and the and the something that something like like the trunk is very specific the find the area has a certain from the area and that is a big difference brought over the and there the of a simplistic and the but you could also take a basically the shape announced that there must be something like this trying to steal area here to make the elephant and as a pin sozzled the description of the shape off the area factories carry some some information And some of us would you might after not end up with is you use a lot the state of intellect but that takes some information from the area for example but the area is full lodges can immediately distinguish hummingbird from from an elephant but the respective size of the area coming but will take a little area where the elephant with the help of the space And to get a was that you could also take something of a curse some characteristics of this kind of hybrid representation taking area based and come to a based features into account of what I do with the Intel image tonight would you do if you don't want the individual Object only the elephant but you just say you might from the image has a certain pattern of edges and this is why want described the this for a long to retrieve The body basically do there is that you figure out what the dominant and 1 of the early recognising part of the of the picture the out all the noise and then work on the edges such and we can do the same thing basically wooded with the colours and some of cost comparing the image pixel by pixels in terms of colour was very tedious talks with in want to do that sort but we do we use his to grab a we use of OK so much yellow and so much to them Madrid the 1 of the in the White and we do the same with with the edges basically so much edges of certain Langford somewhat edges of certain direct in the image with don't care where they actually are But it won't read faces you not like that would have 3 ovalshaped somewhere in the image and the skies we all images of 3 faces and also in the tune of 3 eggs so and so We are losing information in leg by the by going to the aggressively definitely information that it gives us a on and more efficient ways of Comparing images on far better than pointbypoint pixel which doesn't help you the images shift just won't accept left of something I Molecular takes about pixel of compilers of the same name will result in basically Australia said that can do this kind of Her book So this kind of how we represent shapes all plentiful today when we want to talk about but firstly says the document which is very good for the recording By the way idea K was a recording said that helpful
09:31
UK Good so end If we have the shapes In some images with Sigmund the match correctly and weekend interpret the shake was Different to the notions of all familiarity images we could help ways look for images was simply shape up the basically the images that contained and somewhere the date the Gray and went in the middle the picture and all the photo off some hit with an elephant toy like a touch and go as a No something that as long as elephant shape It's OK and in the pictures that does not mean however that the 2 images of the same perception loathsome levity The image of a man and In certain It is totally different from perception a point of view And the image of kids following a blue clash at a pig and you get you get on with the difference between the 2 of them are similar in terms of an elephant of some kind of being in the pink The could save known all value on images was simply dominant shape enough at don't care about If there somewhere is an elephant in the case told the and a 3rd of their value as and on some advertising campaign posters in the background of the movie was a Web but rather on images that are similar in a perceptual said that it was a big and in the middle of the picture it out and get it out again again with books 1 hour but were enough that it looks very similar to me up in the Derby and shapes Are the same And this is actually a totally In put which What we do in representation and will be doing simulator 2 matches and it is just different notions of American and but fact the value you can ideas about this now no right all right The best possible and depends on your reputation for you want to have what you want to see And that was a reasonable ideas and king and a meaningful definition of Logic you want SAS or which depends on the particular application found a way if we go to country based comparisons from than we find all the images was similar shaped objects and the outline refugee just seen as close computer and you grow like that would be good for you need to take them
12:54
Fadse a not not to get and elephant shaped close come to of just take and whom away drawing the wrong thing about so that you know on the might of the funds would be made nice so with the money they were but the And you can get those close to of basically of for segmentation out what we've seen in segmentations that for example you remove the from last time that the the contains very many different Pattinson because of the shady of of the skin and then and part like legs so it was all so different colours on the back of streets of sometime Street and and and I thought this is most took the lead segmenta to death United was not live shaped it was this which talks but and pieces of that even on the and and ideas and and and and some straight from the back the and this has of this was a more left it to the very often aloft not by determining the actual shape that he won the FA difficult thing from 6 am But the semantics at all success with the bat described such a common to than just by looking at the the edges and the image and where walked so that kind of like chokecherry semantics of the same and if we look at it and matching of shapes celebrity measures that we have just had a new comedian distance or something pixel wise comparison is not work any more because when comparing shapes would you agree that the state of the same all the difference
14:58
But seem to be saying the and the pixel was comparison does not period because this 1 is bigger And they'll want this 1 is kind of Shifted removed just about 0 rotated by some degree but still sustained shade sustained calm and what we need is a simpler to measures that is in the air he was respected should of metal where the Apple or Corus on non on the picture which was paid to scaling the mesh big the Apple actually with a small at political with what you can do upload movement And it should be very and was the 3rd rotation And that's not easy to build a huge something that we after best summed some kind of intelligence into to make your measure his American measure invariance to those 3 Linear from the book a this
16:16
But we want on the questions it and what as with some of the public part of that But it's it and if you ask me I'm if you can You don't something like he occluded and then you say or what is the apple shape the Bush it obviously like that and then it goes in the UK They have to possibilities you can say well and this is not ambush a with this kind of like a take a bite out of the Apple something like this different and of course it is the semantic to decide whether an Apple is just cluded that whether there really is a piece missing and whether it's supposed to be that way again if it but it's not a decision that computer can make And you can you can all was Colin member experience and say no apples around and the something that Apple shaped but by missing a all with completed but then you're making rules of to interpret the image The images show A print But is there something missing in their something uprooted them well at this point we have to live with it A print Yes Part of the microphone ferry But each year the teaching that If you like for Apple like exactly That's not the way without having a read I model of the elephant that I can build a I'm and a measure of the to measure that really matches the site few of knowledge and the head of the will of and the review of its just possible without having to complete model of the of the and So purely from images you come to that because and as you say the perception that it looks totally different From and seeing a cat from the back of the book from the bad May leave you and out what it actually is Seeing them from the front Will probably not be fell a means something that looks at City left from from from certain a deal on This definitely not looks to move from and that shows that the building a similar to measure that can reduce the which between these things that is not an easy time without having domain knowledge
19:19
So all we can do is kind of like we can we can talk about Linear transformations very simple Linear information making things bigger shifting things space rotating things and where we can say 1 working with kind of based images is that the wisdom that the image gives his W different we can see that he's damning with the circus shape and this question and we have the squad shape here and the way in the shape yet again with the same shapes the visual impression of the images of a different kind
20:07
It says 1st talk about some of the features that we could use to focus on all that we could use to represent some of the kind to feature and 1 of the things that we could talk about the number of overseas so it is it They shape that goes in 1 smooth lines policy points I'm Another possibility is what area actually closed By the shape of the shaped like that it is close law of area if became shaped like that Enclosed very little area of the length of the to of what is probably the same or even longer than the case of So basically high all over what would amount of areas in close and you can almost argue about the holes and some shapely say OK this distinctly was this year and closed a lot of area what if something like the same size like this with this being the shape of the world Distinguish under different Gallen all those round of 3 of the 4 Grand has along Area included the other 1 has not so you can or you want the also talk about eccentricity and stuff like that of how stop like the shape 0 elongated is the shape of the typical indicators of for so a week and say this is more squalor this Thesis more rounded in this is eccentric this century And of course indicators of could be used for a 1st indications depending Mauriac if I'm really my application is to distinguish not from by as the last of its easy to use some of these represent the shapes because and offers roundish and the ball would is long dated so measures simple measure very simple measures like the eccentricity of the shape But why would I be sufficient distinguish between the 2 Of over can not distinguish elephant from the night of from the board and of the Met competition 8 gets and the more different shapes in semantic me to her The more complex the measure Sometimes load of the features to could bombs
23:08
But if you have such numbers in like you just have the absolute centre of the she the area that has some of the time by the by the by the kind to of enclosed by the kind to basic has something to do with the length of the country If the country was very small can not out of the area it can only those love out so you don't have scale invariants if he of the same Come to adjust blownup it contains more area but it's not the different kind and you can unreconstructed shaped from what you know about the eccentricity or the area and And you are likely the Exel simulator he of shapes justified by eccentricity is is very doubtful you know that if you something that you would would like that to a be different shapes eccentricity is the same so that might be very much misleading Boston Inchape description below the foetus can either be used if you very specific application in mind not really distinguishing up from both methods and then it can be done that you need other features need to stay up a I've semantic finish for example a one you all know that in the subprime are like these these waiting machines the scales and you take a vegetables and put them on the scales and some supermarkets sexy I'm very modern scales that that tried to recognise what you put on top of it was little camera and that they can like figure out what it is and that it doesn't work particular well tried out denied a bunch of of apples and said all these seem to be on Repsol Apple oranges and the way it's all not of pineapples would have you now like and seemed seemed follow random scene from colour driven to me but I know where my eye In a sense in this scenario it works in all but because there will you have a new way of vegetables that arrival languished like like the lead all be are must on the end of walled boiled longish which occurred in like things like that you will through that are all round his like the apples on the pan and strawberries and 1 of enough so basic distinctions with simple features with simplistic feed may be working together with out because it can help you because they are such a shape in our the shade what is that What kind of food Now it's a cucumber because screen you just don't see that who could not get it could be that yes it could be that you can that yes Edwards orange cucumbers dream of unknown with a screen Ike and immediately enough limited the possibilities of what it actually can be It could be that the ban would be yellow of and so if you if you computer huge during the combined in certain features was restricted each other you can do but not can also and not the media But the simplest M Africa and taste of shapes of so called chain codes Freeman
27:03
And this is actually a very old The world reputation in the Sixties beginning of the Sixties model thinking know what I'm I have this close come to somehow fell by fund Getting the right but not 1st time that could well have some hope of Prime but the Omega Some said some kind to could be Edie represented if you just take a certain point like Don't you And then you just follow come to the end kind of the way you do so I'm going straight ahead now I'd turn right now and going straight ahead and I'd left and and going down and blowing up the something like that you travel around the country from some point And you do what you do and of course this is not like any Meyer Lecea live round it because the full of the kind that if you have a higher resolution and basically bring to pixels for close come to what choices to you have made your with peaks of the dispute current picks and then you have the pixels that are But decided now And you can either go there all their goal with the amount of I'd and just need to do not just have a very limited number of ways to help from pixel to picks up and David close Kontilai will not have holes in them quite easy but by simple said they would do is exactly what I'm just saying you like that you want pixel not direct Shinko where the next big than the country and I'd have to decide what you conduct all plot walked out of the way and a can do attitude and the same way for although images of my collection for the shape of my next and every for every time that goodnessdirect idea No 1 room for every time I've gone this direct 19 0 0 and the White called chain code because it basically the gives me a chain of numbers just without being what steps to take in what directions to take the step of the easiest ways so do is basically OK I'm starting with some big soap opera and this is the 1 year and the 1st ago up here which is why ideal 1 then I'd go following which
30:01
Is the noted by 0 0 up and 1 step here again this not want and this kind of like is the chain code of the image of The easy to do the simple to By L The Blue on the black or you like into the red on the black Her and that's kind of like He notes the change up so this kind of simple but with its gains in the yen not because it Viagra along the way these ideas are now of the numbers
30:44
With virtually certain and that and are all because of the relative something I'd go in different directions with its translation in value Yes it here because it doesn't know but it does matter whether shape a person the pictures from really just the noting from some point Not related to any pick the picture public onto a space never do the same thing only in the same kind of money problems and comparing the codes Is basically the rotation and the scale and the to a case that figure out what can we do with skin and so long squid here we want to win those squid with the difference Eigo 5 and that the new make 5 0 by goal Who 1 7 Picasso's in this direction he makes 7 0 up and if you're going on but if you scale it's kind of the same direct she of So we could do is could just the No 1 0 year and 1 0 here it doesn't really matter What I'm doing a penny And then out of the same year appeal Sixes up here even more Essex's again Iwas do not 1 The following year Fares Following the murder of fans Again would be just the same sort of Kent And then down here and I don't need to Same coach OK Different scale Rectangle saying code British Workshop
32:59
From back doesn't work happily who noted the difference It Now that kind of like yes you in the workings of the rectangles really have the same codes quest it doesn't matter whether whether something looks like that all something like that on because you just don't Oosterhuis as the surge in the same if you can of skin in down
33:35
Has not raced Kate and to all basically by making it scale in very at losing summoned from killing some of the difference But is it really so bad amid if you complex shapes But it's also bad because they will change very often so you don't have many big part that are put together and and basic change of such a for giving you impression so you don't lose much and the squares direct and that is on Some degree of bombed
34:17
Less to do with it is to say but it doesn't really matter if the go out of a go down Because whether the rectangle is like that of the writing is like that The three man again so we do it is kind of reduced the chain code more 1 said that the basic the the opposite direct and I'd just the same way it doesn't matter if I'd go there and then got out of there and then go down from this is basically a rotation of all think of care so it by consider this point it's just A rotation of the image up and that can use the PM reduced thinkers and the and the opposite Various just get the same code time
35:14
The next where can do use like him Either take all just look what happened that can say what they they I'm not not to interested in in what happens from a perspective of how many different possibilities I'd have going somewhere that just want to see what happens with respect to the last pixel So if Island in some direct The question is not really Today goal into some of the direct sum But that change slightly The deaths follow the direct she further So how long the German during the same directional what what makes she tried into some some of some area Well basically do it because you Take hitting coach and just the nerves what happened between 2 parts of the And checking that happens here so for example if a year and just have come enough To opinion go here just as the other 2 So I had just taken difference between the points and The row minus to make money is to and to minus 0 Take the 2 of them and if to my to pick 0 up Kent Just take the difference between each to each each neighbors each adjacent numbers and then Nike and began to take the difference tank at the reduced tinkles and say that it doesn't really matter whether going up of going down to No pick the same thing for it and then icons and reduced the tanker wouldn't say Well doesn't really matter how many zeros I'd have a joke the just folded into 1 and that its main oppression of what actually be was the advantage of this For the advantages as we have with the UK and the multi multi resolution announced We get very small numbers and a lot of serious he in the code because every time I walk into the same directly to get 0 but don't have to be note that 3 of the 6 0 1 of the Many 0 4 shapes that the went to some sort direction and there you change for breaking point only would review Edgeworth where lips to some 6 or something from and that some of which are at the very pretty good idea for compression clutching a lot of all along of shapes that computer and this compression mesh may be worth of this is just what you just did for each of Other my this because take the difference between 2 and Jason peppers This year old minus to his minus to appeal get to minus to is 0 To minus 0 8 is to UK a you your with the difference between adjacent you remember what we did in in a month the resolution and the with the difference and and every which is kind of the same tricky like it takes the average and and I just take the difference was that 1 of a pop up a menu no difference to the other public and to to use this Everett up at same thing here Take two adjacent has been the difference and to minus to of must
39:17
Just If it were for a against what you their Yes Habit of the But I'm you different Archaic the which coming to let than you would notice and it is the sort it out the rigour point so stopping the tinkled from here Give you a totally different image of Tinker and stopping the chain code from here A Something different will result in different chink of Wigan into that an amount and So if you take the reduced difference chain coats you have been another ExoMars the and other advantage because you get some conditions potatoes and very and getting taste and very interesting codes obviously is this not an easy thing because they like if you should something also you you change and And what happens with the reduced difference change is that if you take the reduced chain code him out of some image and the and slipping it to a different image
40:55
You will find The difference between things a Kent Of the shipping my 2 of us to And the different Basically you between things angle of It just the same See So basically without taking the or minus tool that 1 minus 3 It doesn't matter up can also hatred of coffee mind to But 2 months to go up Wrong the slight The chamber tell the reduced difference chink other same because it just described the right not but it was the verdict of life in the horizontal but and the while something in between Oka
42:05
The slow pace it happened and the problem really is that it works only with for patients by multiples of of 45 degree because than the writing of state is a riot and of what happens if you take shapes of smaller shape hugely in a pixels Peta in out in a grid and them not by 45 degrees he will not get proper battles that you will get some up affects what basically happens is if you have a squad shape the and this is shifted some the good some some some some may be a 70 degrees of something like that again What happens if is that this Canopy expressed by the pixels and more way it has to be some But step But And this of cost difficult because not yet differences of 0 The difference Here again the differences of the road here different you don't have a right Anglo any more because we ought to take the stand and and broke not and will be end up his this chain code him so why this is the 1st I'm now not is to get this kind of the 1st To follow go 1 in the direction and the vertical direction 1 in the eye her the original the Bagenal before starting again 1 in the world to go direct The bond of will pay in the region you talk and bomb and this is constant breaks is constant differences and this you might want to see you want this month 1 can produce it because the changing all the time boys 1 step the vertical 1 step ahead of wants to put her 1 step that it's supposed as being Esquerra it's supposed to be a line that you follow straight becalmed because of the grid a This is 1 of the problems that you that you have with the taking of the 2nd problem is what NASA The 2nd of numbers is not unique Because you stop at different point You get a different set of numbers From this approach opprobrium but
45:01
A point in and and surrounding the public is that you could have bought a nett couldn't the suffered some sort of shape numbers wages Satan and not so much interested in the idea from pixel to Pixel I'm interested in what happens to the kind to of bread right angles just go straight ahead and do the end of that are concave for the climax enough they describe different Destructive and shapes and it had actually dalmatica so much whether this is the right thing or all this is kind of like a man like that It's still a similar kind of shape simmer kind of come to die would just the note these to by coach Street because these are concave point and don't care whether it's really you now like the concave quality as a 19 Greek or not or whether it's do not like it Gives you again loses some information but also deals was out facts and a good way
46:31
I'm So that you want to do it is to to to deal with the problem of in the future and like start at every point and get different that sell and Yes represented in a way that was a prop 40 could do it is to shake numbers I'd take the psychic from which stations of the chain but So basically a stop from every Pixo on the country to and build the shake up to the same this the squad that we had there was 1 0 minus 1 basically a came up as a bid by London 0 minus 1 in the world the 0 minus 1 of the 0 0 1 and finally of the mind of 1 0 1 0 0 is the 3rd permutations which basically 8 Kameni tournament from starting on the different edges this is the 1 that stops the and the goes back to the wall stuff he that it could happen this is the 1 that starts here And goes there because it is the 1 the stuff here Those the and this is the 1 starting here during the UK and different just psychic from a taste of the same things and I want and not can is icons So list lexicographically by take I'd take this most 1 1 starting was 0pc and no 1 starting with the minus whom is the smell and the list for a new lexicographical starting with their most negative point is that you tinkered having the same beginning and look at the 2nd Place a pan if that was the same in the 2nd place look at the place and took on the pitch to take it to permutation side executive the same band And in the shade symmetric can sell if 5 some other something that he had going round what after the wings and going round the other way although we could also stopped on their way to the still of all the other wings and different direct it doesn't matter just that kind of thing that would have threatened the said that exactly the same at the matter because and those the shape after be stomachic but you might have not want will be the smallest and a used exactly that smallest representations full and building The shape of not solve the problem of where to start complex with sold in the problem of the view that in the including building or the permutational during the month in taking over from the book so good
49:47
But Now we still have to figure out how do we see you will see How do we compared to end the and when we do that But at the same thing as as as comparing to strain what we do if we competitor work And was also the use of so called distant from all changes to add to or a make in 1 string To transcended into the other 1 from so out for example the words caps And have In terms of strings After similar because after changes the to an age To kind of transferring them into each of the singles while the follow word checked Because they have to do is kind of like after being Intramuros 1 led India The age of 20 and and that the basic notion and its distant wanted transfer 1 straying into the of was the chain curbside just of strings containing numbers of want to get them into each other and then has a lot of different distances living standards advantage and the and and the and the slightly different in in and what they do but the basic principles the state They defined basically the
51:37
That number has from transformation hot to deal was drinks and what you could do it you could have a substitution you could like added with the cat and the and exchange letter What I could and should do is insertions again just been stood a July get chapter of the N word to use which of could just be viewed the age from the Gentlemanlike kept book these different But transformations all different different things like an applied OMX OMX OMX string and a 2nd of the different transformations If found Any seconds Will incur a some kind of costs stop at just say are basically substitutions cost so so much that the insertion processor and so much and that is basically the idea that a have some highly changes strange inserting 1 thing I'm I never tanker of 1 0 0 1 9 0 0 and the London 0 1 0 1 0 0 is a very similar way or just inserted something new It's not too difficult operation in the UK if it doesn't change much led by the fire in the exchange something like this 1 0 2 0 1 0 something and and a really make this changed that might be more difficult than it semantical terms saw what now basically do if it is that just say substitution will cost me sound so much and the insertion will cost me some so much and the smoke of the sounds of much and this is what I have to minimize along the minimum wage of transforming string ale chain code a into tinkled beat Based on the street operation and found The basic idea is that when the minimal costs because they can be found by for about number of of different seconds but the minimum is kind of a unique and this is what a defined as the distance between a and B The less costs is incurred to go from strength to stringbean the better DeNiro they are and even
54:34
But the advance the standard and kind of generalisation off of the living sound as if some additional operations where it's which between letters and that are basically part of club part of a chain called so I'm if you have to a is and beat way go to 1 a and B so the and comes earlier and then you go the more into It was a shift that could be made also duplicating some things longer in 1 direct before the possibilities for short make something and edges some hope for all of operations Lawton generalised the advance the clinched understand and calls the also have cost that are anchored and now we you 3 of the minimum total value of all the information that it is again the advance to the UK
55:40
The advantage of chain code is that they are literally easy to calculate that also we had some problems with the scaling invitation and similar Amin discuss them away and we say it's not really rotations by 45 to Greece we get problems with the big 4 all of that in our American happened a lot of things now In any case much of the information that he actually have it is it is basically Molecular you can't really distinguish where from rectangles and more than the stuff like the lure of and and compelling to chain code but it gets kind of difficult because of the need to find a minimum of and other tree number of of transformations to cancel 1 string into each other basic do that Efficient ways of doing that Basically Alinea Programming of open for you Jews you use Linear Program Fault which tries to figure out what the what the optimal strategies or use greedy strategies trying to make a little of the cooking Corus little costs of possible analytical with the size of of of those caught that stuff like that but it's its work no gives the not something with the help of 2 of this kind of what you read Get question floating codes
57:24
Some of the things The to area based retrieve and on the day idea of area a based retriever is that you don't really follow the and shade of this cost shaped in a way that you could see the interior of the stable of what happened and this sort of based very good if you have very complex shaped like faces and I'm and what what he's seen faces usually that you have different designed the going for the face which may mean something all might mean anything but the basically all round shape alike and if you again like now fruity sample take the colour into account you can distinguish them more often than not from from the background says something left at no flesh colour and and and slightly will in shape is very off some of the image of pace and the spacing do what you do all of when describing the interior of shape and from again you can Preserve the information that even though all the image transformation of for a features and Suffolk to describe how to shape the you could again go to the future and says to typical things like about the size of the area enclosed or something like that these are numbers that means something
58:59
So I'm over for the transformation of a lot different transformation that I could do with the transformation we of the or the but only you transformation Walter information different transformations just transforming the shape and calm to it said it had reviewed the into a different phase and and that different space you can see some things you can describe basically the The area by some of the and the the number of Coefficients is unique for the area and you can actually reconstructed using the Scottish structure representation you could or always go was primitive shapes and say this like shape rectangle shaped like where shape of trying the shape not like and and you just work with the primitive and try to figure out how the the I'm image looks like well you could have geometric representations sold area of the shape of mumble Fault compactness the symmetry the moments of some of the expected value something I'm that that you could use actually will reveal that in a moment 1 of the possibilities of the moment and very invariants
1:00:21
Some As the feature this allways of calls goals in the area and the number of pixels of that belonged to the shape of the of the shape the higher the number of pixels the wrong as you take the pentameters Was suspects to the surface For circles this is minimal because circle and clothes but the largest number of space the highest well as soon as yet something elongated unique Come to around of up little space and if you to kind of breaking down to something like that you know you can't However of the area in side is long upon by the are the number is kind of like the number of connected component of the shape and the number of the hotels in the world you just try to out the difference between between them so a few simple Discriminations of that type in out here as a whole and on the other side is not so the or number of shows you that the same number of connected component of the order number for the ring is smaller because the holes take care
1:01:53
If you go for structure sentation than the questions or Hawk in the shape because it was a minimum number of primitive and was primitive shape circle singing rectangles means you may be the thing and going from the tennis record to the structure reputational tennis May help you very much because the I'm in a different types of of records and that they are all different and and small things but If show you something like that Many people would have said about looks like like a tennis racket so like fryingpan low that maybe you know that you get a feeling what actually is and Mapping at on telly images finding the shapes he though it's kind of like not exactly a shade It is very helpful to say OK what do we have something like this large area here And do something like this area and this kind of cover the basic shapes
1:03:04
I'm not as good as your of soft for example of the production of a were introduced by bomb been 81 and when he where the basic I did he said want to correct rise everything's by circles Every shape is basically a circle sometimes the Serbia is elongated and stretched led like circle can be distorted into a lips is that it can be distracted if you go further into a but Wilson rectangle because you don't want them here these round Kaunas and because it stems from a told of the circle so you would have some some some on part the spots on not really perpendicular also the kind of like various slightly from case of him And if you do that you can't basically build the huge number of films that usually is sufficient to describe an image and just playing
1:04:17
On top of the image these 2 occurred that takes where I want to do it is you want to cover as much of the area By combination of suburban verdict as you can The palm the of minimisation problem that you want To have a simple firms as possible so the distracted circles as much longer all much complex a more complex representation Then A simple circle of the symbols of the representation this ellipsoid all 1 of the Civic erratic wrecked in the kind of shapes things as a very complex because you need to look know that you need to record the disclosure that he did to the circle of and what I want to do is you wanted and the shape and the length depending on the complexity and the and the Met primitive you The highlight will be to cover the shape to cover the area where I'm it from where shape side he was it more complete shaped the you The complexity of the representation grip The fate of the men they should problems that similar auto to what we didn't active come on to the to energy of something was the Exeter and some so he the Internet and the G of keeping the shape as simple as possible was the extra energy off really covering the shapes that I'd in the image recovered in the area that should be become Talking and that the trade is now shape the used detailed lengths of the pool in the height of the IRA's smart there is more complex data used at length of the building site of the air Rose Bowl and so on so you minimize awaited some consisting of the length of the encoding and the going So covered Part of the area that should become so the 5 some area like that The iPad of offers just say OK I would take it in the Solent Covering and the and the representation of the life has a certain things so simple And what do I get as Rose was rose again this part of the shape because of not out And this part of the shape because it should not be covered and also this part of the shape Because it again should not become minimising the black area Why Minimising the reputation of this is the trade off the with a bucket every other such works Catch
1:07:44
Upload to describe shapes and there was basically by skeleton So other some goes back to the Seventies by Bloom and what I wanted to do it is you want to say what I'm basically the and area It should have some tax and if I'd like a Squid than the excesses something like that if a circle that it does not have access but it just a point because of stretches even the and in all directions and is only did he had the notion of a central access and what it takes The symmetric points between different parts of the country And stops to blow up circles from until they touch But as part of the country Then all of these new points or care And it and move the circles that have the biggest of possible this from the image and still stay in the state the smooth point of the circles what kind of draws line A Case And this is where like old Centro exit the soul I'd take this wonderful image of the whole osea The of or missing I'd take a point at the top the circuit OK wanted touches on the site A record this point Because of the Middle point Start moving the circle But like a lot more to circle because it's limited overs erections the blown up to the biggest size a camp And the UK in mood and so this not access But the front of Rectangular for 4 And start blowing up the circle around this point Olivia It was touch and that can would around and move it into this direct obtained a sinking leaving interested Except a middle points In this career also committed points this work beat exit So rectangle does have amex's The squalor does not have the next because of justice and prefer Every emanated shape the excesses of sometime crew from the real impact shape of much of this basic to the idea of 4 4 4 4 x more get off but if I'd do It was shown in the picture basically point line he line here line here and for the lack of also and the more complex the state's get means the more you have to work with the circles that the the I'm beat the ideas all ways that you blow up circles on to the maximum area that can be inscribed in the in the in the shape and if you then start moving them around with
1:11:36
I'm only could do is kind of like the because of cost so this is not a skeleton justice gives you the mid access and some some disconnected points so we did and it was the kind of Ireland to to do to focus on domestic 500 point I'd take the circles that are next to each other or with the highest interest and I'm I'd look at those circles that touch to line any to line of the image and blow them what happened then is basically somebody have this life and this is the central line as we had before Given by the circles And to stop the move basically also the rectangle that makes the whole cisplatin music and I'm and not take The point here And blow up circuit here and it touches 2 different parts of the boundaries A Kent In the move that he here A candidate up even more Growth bigger and to find the here it stops to touch the the point A and by recording also these exes eye get something that is a little bit better than the central excess baggage actually connected skeleton Of all shades of all at the UC his Yes we are at But the storey of how to the fight for those who like that sort Yes that was actually if you stop with a with any 2 points on the on the on the rectangle you can do that but this is a different techniques that was invented the some mutilated it's called the Schalk's that we would get to that in a minute But this is 1 possibility of acute doing and
1:14:05
And then comes the chalk said what exactly the stop with the point of the A stop with the points on the board and Shake the shape from the area and like like if you throw a stone into some some ponder something it will be if the concentric rings at a kind of like growing in in size you know this is what coach talks that actually because you put the shape at some point now and it concentric circle the waste will go through the problem for the US the area and suit The state touch Some other than a point You kind of like a stop And I would go away So this is the maximum supply can do year a because it touches of I'm good with a from start from the edge of the same speed and the skeleton is them provided by touching After the speech from different and if I've point here and point you for example of this with a small circle until it touches this UK and so he has a point in the show So when our eyes got away from them some some some point and immediately from some of the point Where the circles meat and the Green Bay will come of struggling with the same speed is the then is kind of like a little bit more help before for example here And here they will meet on the same axes puppet The same goes for him and he also meet on the same axes just because the opposite to each other even if the slightly different in all like after and with the different points below the shoppe solve what happens is this kind of these are the facts that the If 1 of these areas the 6 because if you start the and here but at the top of the me But Jacobo before that and
1:16:31
So I'm What then do it is kind of Hugh you you use display a graph of the scale and the and use this for compilers This is not a 2nd of numbers as you have been in the tank But this is now a graph it shows you how to head of looks like And what of that it's a skeleton all the holes and the interesting thing is that you the kind of like the Kent in the early distinguish for example between reduced shapes moving circled the direct and getting the scope of the ring and That was good because I was the skills of the circle It's just the 1 point because you go up the Pope and although action but to the boundaries and the city has now candle don't have any any any lines like you don't have here in the Cabinet the circle around in the inside the circle of the appeal So easy to distinguish between things that are follows in it and the more complex and and the PM easy ash This kind of the idea and abroad example year this is images of dogs or to of blogs and and what we can see it is that these very similar looking back
1:18:04
The also have very similar looking skeletons and the and matter would do even now look at the shops that are look at this and access to a of fine and from which he a move for their their with this line is basically line earlier of care and the same happened here she This is kind of like over here but where we can see is that it slightly different because if we look at the circles of talks will find that the dog is called the slightly more rectangular the and the stock was like large part you a pig and a very large part in front of you but not as rectangular is a reason why this is a very long and this is a shot that because this is slightly different here Basically Bacall's something missing to year but there you can make for the better part of the wreckage of the basic you have the less like variations and we can see from the skeletons drawn to similar time but sometimes annoyed where of life
1:19:29
And I'm not would question again a installed graphs yet to above that image of the competitors And the question of so we do with different skirts and is we again he used the and distance with different editing cost but now it's not transforming the string all and and a letter industry into some other but transforming allowing in the skeleton into something And for that and the basic edging operation began supply life which basically means a completely remove skeleton brought the like that and I like that Removing the ScotAm branch will transfer them into each other again Coach contract Which basically Takes to schism branches and a note with the Sri brunch a so a something like that can just moved into something like that But at just contract the to branches and this is the point was 3 branches and she A distraught to act and merged which basically remove the note between 2 ScotAm branches what happened here is a 5 1 of these skeleton Brown just get life like this was going round which has a turning point those basic to BrontÃs like just remove this point and take them to be a single from and the fans basically branchlike that have brought like that and at just before into look up at a stretch
1:21:33
Said these of different branches and their coated in different colours to make sure they are different line annoyed that are a result of different trucks and this was kind of like a bid from moving the circle around it up but this year was not built by moving the same around because the shock of stopped here this way The blueprint for this was basically built by another circles that kind of acidity not the same circled the circles and a move away The same size and and and basic the this resulted in this blind and this is a total of different circles that results in a supply of the public of Growth So what I'm doing now is under 20 Fleming The skeleton of a blog into liskula some of the cash for a book he had here An old make it easy so for example if Look at the sceptical to do it but I still see them Resulting in a different but and skill eye don't have any yes the at the the ball Identity and thinking I can't so to due to Forget is out held 1st take The contract operations on these 2 you Entrants them into 1 A pink Because this nothing here and a comparison OK but the dock has no usable so for my next operation Will be removing This book Nothing it up and the same goes for the large affect over here in the books Paul being 2 and a fetched thing because the again in this way because the this little In session and and she was different Sukkoth's again Different circles different groups and seats to the out here again contracting remove the offer For a man to be done now is that the formation of an because this is kind of like the typical of waiting Taylor shape and this is the real ex at tape shape but needed before mation of fees to find the match which And why can't do is and see what I'm basically discos there is a similar this discalced their similar this there was a seminal thought a compel the skeletons piece by pieces And by just doing a couple of operations on the skeleton 5 basically from into and the UK It disturbs the same thing as we have industry Ngema tangled good the mob difficulty of Everywhere and still held works Yes But I have no the for the But The transformation Hoping to prove that she could The The 4 of the Look Basically no we don't This is basically would Linear Programming that it tried all the different possibilities Innovative ways becomes computationally feasible you know if I Fuifui kind like start cutting off but if you start cutting off legs you incurred by a law of costs And you would immediately see that needs to nothing so you cut off the ground so that are promising to a 2 2 new and any good idea of what the result will be out but basically a you end up with a solution that is the minimal solution Basically you try or the different possibilities you have no notion of this is the the hand and the IoS must go up yet but you do have the notion of what we can do that to part of skeleton I'd just contract in calls cost act of an hour there was a some part of the skill in all they are reduced to remove it from an eyelid and growth cost wife saw already have expressed why on this way And it was at some point I'd basically Arrived at the skillet of the dog close enough to the scope of the dock and the UK in this way is a one way after following them and it has some cost signed with the celebrities that already have no cost and what has been now can not be correct Some and pruning all the different branches that cannot be correct the county to to Optimo Ariza and I'm trying or the other Real tried and error With all but they Exactly There might be similarly expensive but then it doesn't matter because we arrive at the same either man but the exit what the exact segment of the information it just members will be incurred cost and the minimum costs is unique A press So might be different ways of of arriving the and you can find out by the new programme so that they could be you guys have been a programming and Previous lectures And while 1 1 load of 8 of the scope But bomb over revisited and a way to defy the will of the said that when we do that the audio between the cell We would
1:28:52
But I'm sure bred for break is very good and that we go down to some probabilistic approach self of the time and the 1st of 5 minutes
1:29:15
Who knows how to do it to describe the new entrepre transformation Scaling grow taking Translation But Yes But the case No Like include the transformation reflects the trades blogs and jet The other control Inflammation translation And there of the ball and making it stand up like the moment the and making it very and was suspect a rotation now and was suspected of translation and and all that kind of stuff problems and we still have a bomb saying it is not if we have an image of a certain size and that has a different shape in it it's observation of and intensity function is to be usual And a certain distribution creates shape of a similar was the mistake was limos because of the public distribution OK but that But if there really understood that Then are aimed to use the statistical properties of the intensity function as shape That's your to latest of plastic before you revisit the moment and if we have a discrete probability distribution on some set of real numbers and we know how things 1st a probability distributions allways of down no a negative from the end
1:31:29
The mass of a probe into 2 beautiful with what some of the band's given by the distribution have to put it I'm and 6 possible all come But every single 1 of the out from could be the result of 1 of them has to be the result The dice cannot be balanced on some and all whatever be if just work And this is the probability distribution for rolling and ice franchise is 1 takes of the masses for every sign of the Some whom and quality for different that if you take a random variable was suspect with some certain distribution them The distribution function give you the probability that the random variable takes a certain that you are so for example if a take the probability function for growing die And random The probability that the result whom Is given by 1 fixed a pin Easy to see
1:32:57
The ISA The random variable is basically that all the different out comes up and you take The outcome times the probability of this all come And Moments means that you factory or you you have an expat and also of the view that all come for each more And what we know from the some of probability of a ball from so the hostages 1st moment everybody knows that is the expected value of the probability function Like much The 1st moment is the expected the At But said a moment Over and a good way Sept moment The skewness right basically by The gradient of the slopes Search for a moment Very good the Kurtosis exactly what Catullus's led to distinguish But The modalities if you have to we of all a single nodal that to basic to distinguish between Such distribution of APEC fell this can be but I'm These are the big moments and their calculated like that Paul onedimensional function of The function reusing is the intensity from Paul ability distribution over the intensity and each distribution
1:35:16
Can be Describes What occurred and the but you need to Described by its moments 40 basic the doomed Is You take and and like in the case of the likened the case of the For a provision if you know where the features that few distribution Then You can reconstruct the actual published from under the expected value and no where the mass of things of under about very and and Ohio broadened the skewness and no it leads to some direct it under the purchases and or whether it's actually want people to peak of 3 what it is in a and them now and then Last the greens of freedom This probability distribution does doesn't OK so that the non in from from statistics the immediacy during began reconstruct 8 density function of all the different uniquely from the 2nd of moment is All other mistakes so if you are never find it through a fine of probably so beat the number of adult comes of A
1:37:02
But before I can do it this weekend The fine only moments but central moments but as central moment from the central moment By will always be different for each outcome With the C spected value The and US smuggler 1st moment already in the thick What is the the 1st Moment Obviously 0 because take the expected value minus the expected value which use nothing a pink but was the trick of the whole thing Doing with the central a moment What if I'd do that it doesn't really matter whether such a distribution for whether such a distribution because and normalised them by their expected value shift the expected values to 0 exit OK so what happened is a by take this to these 2 distributions what I'd get is basically 1 distribution that it to be the same as a by the UK and the 2nd distribution Coca So this is kind of like making them central and not complain compared with 2 of them without looking at whether peak actually is where the mass tree because the demand and the centre of the mass is Owais shifted to 0 point of is what makes a sentiment and the 2nd central moment and as we all worry that is a very and idle cat where It actually exist upon by just look at left off 0 0 right of 0 7 and the of cost them distribution following a higher very and and distribution showing a pretty small of the UK and this is basically The 2nd central moment for the But as other said 1st and moment of old 0 because subtracting the expected value of the spectacle you use nothing at all but for a game but that is the the central moments I'm very and shifts Doesn't matter whether my shape as he think about the state do want to create Like round shapes and cause do that was Intensity function yes after of this fund despite the on the spot this funk And the same Here The cover of this woman is 1 of this on the pitch from the spot What the probability distribution of probably distribution is Basically that It's light here and black year up and the provinces bution here is is that he and light here She did by the expected value It's just the same because the shift the coordinate system to here A Case And now the 1st Moment as 0 the 2nd moment is the very and exactly the same Sir moment skewness executives and the download not OPEC It's translation Invariant just centralising self centralising and is a good idea
1:41:38
Not that's moves to true that mentionable book All picture is to them for a job and so rebuilt the doing is based to be take tools With possible space of adventures the and that could happen Which basically is where the pixels life and space into a major space and then the probability function just the intensity function for all the people and based are Again has to be positive again mass has to be 1 of following the same as before just to dementia now take a random Becta to win the variable together But the distribution
1:42:31
But I find the idea and days moment Exactly like before Just With to them in a pan nothing happened and the central moment of that kind is just by shifting Those with good expected value in X and and why the exit of So again Revives space here for the distribution I'd just shifted to the origins of this is the the mass of the 2 dementia distribution and just shifted to the origin by taking the expected valued at the expected here and there Today the differences in excellent direct up nothing This is the 1st Moment in X direct you expected value with respect to the excesses of the First moment in wide direct you and 0 1 The expected value disrespect to the wife up pet We actually know some of these moments Wieck you was to put some of these moments before example of 1st 1st central moment is the cold area of to random variables But Onedimensional The 1st central moment is the very of someone Nemanja distribution single random the and the 1st 1st central moment spent 2 when the very well and is called the parent all the different of comes with a peach of a pet As well as we could see a slew more difficult but also in high demand and the unique see and you can show that this is the 2nd of moments is actually some of the and unique description of the of the with the example of the state and a Muchea across the who almost
1:45:14
Such So these are pixel of the The The of this is a great loss not was the intensity of distribution although it will be pixels tend to be wide of the stone to the stand to be black and distribution probability of some pick being that saying she the same area of so what we have basically as we have 10 possible takes a from the direct sum and we have 6 possible Pixels and that the erection of a and the intensity function that extra produced saying the intensity function yet for this Pixo for example is 0 0 and 4 0 this Pixo here it is 1 installed a and and just work my way through the bomb By analysing the of functioned we've obtained a true dementia discrete probability distribution for you take the intensity function and you normalizer by well possible outcome with of victory over basically just make sure that the mass of the distribution of what but and this is The distribution of This basically gives you the probability if you have enough Shapes and intensity function probability of some people being wiped off the if the Pixar in the upper left hand corner of the grid but with a white ball but distribution will With have 0 skin obtained and there for the 0 in the whole of the NHS is to be a kind of all with that The same goes the If the pixel changes sometimes black sometimes White will be some fall ability of animal 50 50 0 1 of a pet Still this is the a public distribution to damage
1:47:31
But it will not take the the unique Naseri from this probability distribution of called match moment Then we get a complete descriptions of the shape of during in the image and because it was constructed by the public to function and of crosses the same with 48 transformation you now of 48 transformation views Review on Sept of coefficients And the basic masses in the 1st few Coefficients singles followed although description of public to distribution the 1st Moment off significant so if it if you change the expected value of the fund the raw hot if you change the very and less difficult but still do not like the changes different in the very and it is not too impressed if you change the photos as it gets and flight negligible at some point so we take the 1st paid moments Of the 1st Kate moments of of the distribution to describe the probability distribute cutting off the 1st 2 the 1st player in the world not allow us to complete the read the public distribution approximately a The bomb using central moments of we already have discussed the translations of metal where it occurs in the image of the shape is all which moved to 0 the origin of all 4 code but not promos again scaling and rotation policy your problem What do we do now we can have the central moments and from having sentiment became caught the computer not licence Centrum again not as Andrew most just means that we take this Andrew moments and not analyze them about all the different
1:49:48
As abilities and the space such that the spaces become the same side Which break Saddam the to scaling invariants because if the eve and spaces have the same time at the same size for the and event contributors walkers models and in a smell of space There And less often full or an area to a bigger space normalising compressing will contract The slow or current in the biggest based into high Kearns's small of a pet You just contract space and this basic to what this factory and then you can show that the men will rise central moment I'm very and what 35 of the largest colour that and then not have some of the biggest base The normalisation just yields folding Into that small space L So you computer The moment the amount of the moment with respect to hide followed it actually is and you can and then you come along
1:51:30
But what happened here is that we take the basic Mohmet tests on different sized you may just We can see that the moments of different 1 and 64 100 92 1 Because the masses had met different point in time for this is 1 of 64 And this is 400 9 to what Kent Floating them in the queue to each other so if we centralised the moment It still gives different numbers of Kent She stood for the origin of basic origin of the origins of St PM Invariant was restricted translation Not remove to the Central mentalizes moment we find those you compressed for the size of this 1 A Case we find the both have the same value of sentiment APEC But TransAsia very Ms cheques Scaling embryo cheque 1 Linear transformations missing rotation What do we do with the rotation prop rotation skating of well can be described Selenia transformation is what you were saying it was a transformation matches and it looks like that into the image of space as certain was signed resigned as the variables I'm a certain kind of 1 of them
1:53:30
End of the world No from mini algebra basically Linear transformation works like that you have the basic function and You multiplied with some Metrix the transformation metrics And then it's just the function used on the origin of called based up and and if the A lot If the metric study multiply was looks like that This is a rotation Was angled And this is scaling factor where scaling in Britain we don't need a Kent Good
1:54:19
So why are we doing this would basically have the shapes as given by the intensity of Kent We moved the shape into some distribution But give as a prototype over probability distribution creating the shake up And now I describe this distribution function by the moment Uk and this is the central my life moments What happens now referred to as Lynch and summation to some different and density function just by rotating for example Then do the same kind of built my probability function and then arrived at different of moments again What do you want to have his own to have been very and function Such that taking the old moments and the linearly transfer moments the value of this function is the same Oka This run going to do this or looking for a question is are such function But she can do that and if out question like that of cars that some functions that can do that are set out what we are looking for is a function which transferred to the central moments to correct eristic values so that rotations your associate not change the moment match and them
1:56:14
It had something like that i could described the firm estate regardless of the should be shape Regardless of location and by And actually it will sorry 19 62 functions were developed and their called moment invariants moment because they are not like work on the statistical moments and and very and because they make of the moment invariants to Linear turned out of work into interesting the so to find Mohammed invariants we will have to look at algebra and add Roberta knows what had a break and so that the bride invariants are basically the same thing is a function that when the layout transformation is applied to some better
1:57:19
This exactly the same as it would have the origin of function of the victory Multiplied by the determinant of the match a again And there some factory and that is characteristic of the type of the various options From this it is very Transformations Linear transformation metric with no sign of signed a and basically The idea here is that if This correct erected values 0 0 The and we have the so socalled absolute in very and G Of The X is exactly the same G Which means it does not matter whether by some minute information from addicted to my intensity from and the values stay the same and the tree And looking for a set up that invariants so what what we can do is that if we have to independent
1:58:37
Invariants Then we could do is we could do to function When we take the 1st invariants Times the number of the 2nd invariants and the 2nd anniversary and times the number of the 1st things and why do we do that by up to get an absolute invariants because what happens is that if we now uses Linear transformation of games The 1st Invariant goes to this later transformation obtained by can get these out with the determining the times W whom Since I've multiplied of exponentially the them with a big to the power of W to This is added This is just multiply of and And Here is the excrement something goes here for all the South again with W to open To the power of W and And now it seems that this is exactly the same Adam the this So I'm staying with its this year and this is exactly the same as a pet So Absolutely brilliant oak and overseas
2:00:25
Easy to see of This we know some Methods from from the early other but that actually use to find resited algebra in the for of special case that we have and adult to go into that you want to show you if it is quite a complicated thing to to build the very I'm and there is a set of 7 absolute moment very for moments of degree 2 and 3 of the world's press and also by who was basically off the problem and the how look like So don't ask me where where they come from Uniloc means you can find them if you do it up and on we have the origin PayPal fluid mum on the web page whoever is interested in go into its dive into the mini algebra but it said its not really UMP filling you even though the and it is rather a tedious work Linear algebra finding the relative in very and pudding them together as a just showed to build an absolute very and and then you end up with a set of actually 7 invariants that get more complicated but basically consist of centralised moments of Kent and the and what I would do the 7 moment in various describe my shape
2:01:58
In very entity With respect to rotation Invariants the with suspected scaling since for the use of mobilised moments And invariants the suspect to their translation since use centralised OK The a restaurant duty Garde
2:02:28
What happens here is that if you take all these Invariants that are the same for all of these different for 3 different picture Different schemes to from temptation different angles executives Cook as the You seem to be to convince them that had execrate so if you find this suitable moment invariants began characterise shaped by the victory of the related characteristic of the of 7 not mention evicted to distinguish between different shapes and the comparison I'm off shapes can actually before for American met by just measuring the distance of the matches of the assemble classes of calls hominy moment invest a we need to ask 70 not fall could you use more and the answer is well of cost the more you have the bed a description because they take different moments and high 11 months into
2:03:50
The less you have to the easier calculation computation of what you do so 1 need to decide how much you need is the so called separability characters separability means that you can distinguish different shapes in your collection
2:04:14
Buy at least 1 element of the future If 4 different shapes you get the same thing to a unique model moments if you can distinguish to to be shaped by the future of every shaped of by at least 1 1 of entry of directors and the pace enough moments and this is actually do so if you and not your a collection you might need to switch to bigger the Because you get more symbolise shapes that will be strong taking just the 1st few moments on to lose in the UK and this is basically a the highly German home different moment of a very few redeeming depending on the size of a prop up the bottom
2:05:12
You can enter this get the quality of the representation of by using other types of moments of for example of this was just algebra moment showed and that just the basic statistic Mahmoud you get need Sirnak moment to each to the charity moments for a moment in the summer and the moment that you that you could consider and all of these the different slightly different view prop up the bottom the calculation of the directors can be simplified if some special come to sell them so for example if your blinds all polygons I'm all of them perimetric representations side you get you could see from the exact type of moments that you can be sure
2:06:08
Good example for From from U by looked up the the origin of the decade and and what he did what he wanted to distinguish why he did that was I wanted to do objectivity out if you have a grids And you have a certain lecherous annoyed figuring out what the probability distribution for example for the balletic L It is what happens if there is pyxis said it just another application of the intensity function for health care and its of slightly lower probability and this is kind of like how redefined find public funds and when I found out that using Some of the moment invariants for the characters in the alphabet I'm where you represented with 2 dimensional erected he found that he could very well distinguishes some of that for example the iPad but the distinguished of from from the L of tea and some of the letters like the W and the M during hot distinguish because I'm in the W is slightly but more and 1st the M has straight edges that if you turn around the W you get and and like shape if take the W And just turn it around It looks like I am in a way because it not too far from would you would expect of a just their some accurate see the with the moment of the poll but distribution of the extra intensity functions you can operate a distinguished very well between but for most of the other that sticking to hurt this book moment for the game The well of the summit specimens some of the world conducted in and in the wake of building information systems building a multimedia databases and 1 of the earlier retrieval Systems so called stop retrieval system that by Ahmed further so that will start at the University of something for actually National University of Singapore and they were considering company Logan locals so of different company levels and they used moment in the hands of as a baseline had been got average retriever Efficiency with just 7 moment very and bomb as a teacher of 85 80 pretty good already and then the kind of like combined with all of the tools Sirnak moments of the walls and and they could even raised the retrieval Efficiency up to 94
2:09:23
Preprint neat so that kind of like very good idea
2:09:28
And this is where we go into the Dieter at popular the but are Bob was 2nd kind of of up epic ability but the beige will all but perceptual but the bird your and to book a solo with the fact that not all of the media's by the identifying shake the fuel costs either identifying shapes the and when you compare images you should be made Jim things like to have 1 in which is a paid off the and the other 1 has another back and say you're looking for a new which with a cat and the 3 men who have was back looking through the air book at its rotated but he is frustrated that you can put gather backed by a book thoughtful and on but maybe in the database and have been the media's with had the some bought some flowers and for way up the in each description what it says is that the overall impressed by the media's what for or the and their so action the only man she is what may be the fault if I'm going to want there used to be which than what they have to begin but once simulation is that these figures here is made by hand and the tree and what I'm going to say to find this simulating the database of these such because they also have a similar correlational but that and the 3 thousand rather than that of somewhat more than that the loss more power over the base of the skull Wollemi description but overall impression is what time and now the idea of recording the gritty is just taking the picture of the way before the game that made by the scandal in which it table for many ways and those of the other possibilities joined the just imagine how were people who would before the deadliest political denied the just based on what to the city history and for my drawing icon brought by the that because they use my immediately that they should go to book a access to would be that it just to see what kind of system thought what they need to what the people and that some of the wonderful by which world of 14 put their world side description is able to perform shaped simulate but I've started with the game in which during the cash and lonely based on by the full they provide more auctions ball culpable for for the 1st time that just over the next 2 or more information about the house and then the she and what they would have expected sold negative the bosses of the most with the Sun and go Web and the and other draw brought their meeting room for Parallel thousand doesn't for that but then nice will has written but she made their white not right she wanted to be based company and these were the words sold by really don't want a bold has been in full of the kind used by right though this kind of convinced me that it's not that easy tool for for for such a shame that it is not though you want find the end over the way in the US which under the return of job and couple for the provided for 9 people such a procedure that is able to their between the beaches and the White flexible who allow also bought sketch what they are basically booing use their segment of the beaches and the UK but in the end of the day remember you from the remember with both 1 last last week of some more we were discussed above some example somehow for it to get to the ball over the bulk of the gradient the book about the for both to those with your down so over this is lower the basic the also want to go they want based on the edge from the media and the public transport this year just as the speed of the deal which is in the shape or before called the body of the and the and the user will from and draw is pretty which for providing as a picture it could also be because the by the land white and extracted begins and then these for says he greatly which will be called the with the peak of the boom and entries in the victory of a and the and the result will be a world rankings based on the simulated between the mobilised pretty and the entries in the storey of the the procedure is actually not that bad difficult but there would see also quite the Greek sold escaped which followed inside the Bonomo at the edges due to the expected this same will be performed in the database sold need is for example a few days from the public and then though it expected would be for 42 images of the city that it and that by the board and the next and then made for the evening to the abstraction of or so it would be a great idea to use the site as we want for for this operation was so we some the but we use the size exist and across the globe were paid for by them but the need used for a wide world of what we have to put the Tories crippled between Computing followed the to and the the site but that was the company that gradient the gradient though of the need still just old fool bowled identify the edges and what they've basically that is a bit of weight but and a breach gradient over the whole of the land and the and their the gradient public BigSim in each of the 4 Behrajan for that every gradient of the over and they said they were for this great but then head of BigSim there is over the 1 1 0 4 painshill in order to pull on the jersey the main with the only non shape and boom and and they did what they say is OK may be these every about the for 4 in basic your would before the which is not far away with what will revoking for use with the 4th with the a pulling step but the what we actually mean is that they do which is be would enable both of them in order that he is also available on woman and her point employment and and the company that bought the is the local significance of wealth of each of the Excel 1 0 neighbour who disillusioned all the 1 by the sister of the full back in the addition of the the word of 1 of the worst of the worst of the team has also been appointed of something from the wreck of the appointment of political after this systems that they were called back to the UK for a mighty and what in for the mould here is the over the event from the United Kingdom is that when you lost it would not 100 per cent precise found sold you may he told the newspaper into the about what you leave out some of it should not interested about like were on the other side where the fund is not for playing well for the things have to be the land where and when make and that for this reason and they they've well on began from local corrugations went performing the made through the idea is users that while the divide again this for says the and the author but victory where in in the century in the by the brought them up for you will be put before the BigSim by but just because of exact the procedure for the Tory young Sylvania divided the GRAPE brought and 1 for city would be right now book on their books you would be made is that we need to and the victory of 1 and 4 the other and 1 that is paid by the ropes 1 by 1 in order to cope with this imprecisions they've said why not chief these broke but on the other 1 would enable pulled off the feat my must be and minus foreign for and add the stop is that all close to the light of these 2 will just for this year and for for made them these use was where and the some of the peaks of the same I'd been busy with the news that that she is built of stimulating the and go committee will be where we should go with the to is that they have won and brought so how we should be made and it is that you have for example 1 of the city by pre paid by the by where from the victory of the and with the might be off my most beautiful few months for the 4 weeks to just move but on though the where rejected with 42 of just before with the look on the basis with the same I'd been density for each of the various on them up some of them up and that the local simulating but the and want of their between the EU and that will be sold to some of the law of the land and the people global correlation and that was before you get this year that he could be the origin the and the and the and the and the peaks between the board and the and the job this procedure is that though the Tree beauty though would be was Bill will be joining pressure and though it's too old for that on the whole were some more restrict struggling when brought them a deserved and the easy quite expensive expensive went before being this your home their these kind of making is something we need to lower the risk that the current bull more than the 4 6 in all black but this is what you need to go for each of the evening in the UK this is like the to look of local for over had been out for 1 of the same loan procedure the world they described in this paper in in my life and I've taken as pretty check in each year and it is my duty of the police in this year of waiting for example just how we fought and world actually for good it expected ideas to move away to the the easy to use and a word for word the results of these of the votes of the fought for what did on the subgrid and on the the and the for the use it by a reduction in the need to and the correlation you can already see his with my original and this is the for 4th baby to the highest all these is the number of these is the number of pixels with the might of the in density of the book by the physical both British and is the basis for example of this is the 2nd blow to the development long and the and the more not noted the 1 that had the result of the book is so worried at the end of the lecture with discussed with the about both the world of tool for of she based features of the presented the and go on the possibilities of change for the area based the world and the world will also discussed the bald moment invariants told of the billions of for a consolation the implications of the ball to help discussed about because we went there to be I longer than the way some of the life the next leg to next lecture will start with a with during the loan move into abuse the the basics of will fall below and though the old information in in
00:00
Shift operator
Algorithm
Building
Distribution (mathematics)
Gradient
Interactive television
Operator (mathematics)
Bit
Mathematical analysis
Shape (magazine)
Thresholding (image processing)
Mereology
Mathematical morphology
Shape (magazine)
Goodness of fit
Computer animation
Chain code
Representation (politics)
Object (grammar)
02:03
Query language
Pixel
State of matter
Multiplication sign
Curve
Shape (magazine)
Mereology
Area
Subset
Information retrieval
Invariant (mathematics)
Object (grammar)
Oval
Active contour model
Descriptive statistics
Area
Personal identification number
Spacetime
Maxima and minima
Graph coloring
Network topology
Phase transition
Pattern language
Code
Figurate number
Quicksort
Representation (politics)
Simulation
Row (database)
Surface
Moment (mathematics)
Computergenerated imagery
Characteristic polynomial
Online help
Chain
Term (mathematics)
Hybrid computer
Representation (politics)
Subtraction
Tunis
Histogram
Information
Characteristic polynomial
Line (geometry)
Shape (magazine)
Compiler
Computer animation
Hybrid computer
Factory (trading post)
Noise
Object (grammar)
09:27
Point (geometry)
Surface
View (database)
Computergenerated imagery
Curve
Online help
Shape (magazine)
Computer font
Computer
Area
Web 2.0
Term (mathematics)
Object (grammar)
Hybrid computer
Representation (politics)
Subtraction
Histogram
Characteristic polynomial
3 (number)
Cartesian coordinate system
Shape (magazine)
Similarity (geometry)
Digital photography
Computer simulation
Computer animation
Logic
Personal digital assistant
Right angle
Object (grammar)
Representation (politics)
Matching (graph theory)
12:25
Pixel
Rotation
State of matter
Scaling (geometry)
Multiplication sign
Computergenerated imagery
Matching (graph theory)
Shape (magazine)
Distance
Mereology
Semantics (computer science)
Rotation
Measurement
Frequency
Object (grammar)
Active contour model
Pairwise comparison
Subtraction
Invariant (mathematics)
Pairwise comparison
Computer font
Polygon mesh
Semantics (computer science)
Translation (relic)
Measurement
Shape (magazine)
Similarity (geometry)
Degree (graph theory)
Computer animation
Graph coloring
Linearization
Invariant (mathematics)
16:09
Point (geometry)
Domain name
Ferry Corsten
Scaling (geometry)
Decision theory
Scientific modelling
Multiplication sign
Letterpress printing
Matching (graph theory)
Shape (magazine)
Mereology
Disk readandwrite head
Computer
Rule of inference
Rotation
Measurement
Active contour model
Computerassisted translation
Invariant (mathematics)
Translation (relic)
Measurement
Shape (magazine)
Similarity (geometry)
Arithmetic mean
Computer animation
Website
Form (programming)
Reading (process)
19:18
Point (geometry)
Complex (psychology)
Length
Shape (magazine)
Area
Hypothesis
Roundness (object)
Pressure volume diagram
Active contour model
Vertex (graph theory)
Subtraction
Eccentricity (mathematics)
Area
Spacetime
Information
Smoothing
Closed set
Structural load
Price index
Line (geometry)
Cartesian coordinate system
Measurement
Number
Computer animation
Personal digital assistant
Linearization
Energy level
Linear map
Eccentricity (mathematics)
Identical particles
Form (programming)
23:04
Axiom of choice
Randomization
Pixel
Length
Euler angles
Multiplication sign
Direction (geometry)
Scientific modelling
Shape (magazine)
Semantics (computer science)
Area
Chaining
Image resolution
Roundness (object)
Hypermedia
Active contour model
Pixel
Descriptive statistics
Eccentricity (mathematics)
Invariant (mathematics)
Area
Touchscreen
Inverse element
Demoscene
Computer simulation
Right angle
Energy level
Code
Figurate number
Point (geometry)
Ocean current
Virtual machine
Number
Prime ideal
Chain
Latent heat
Chain code
Subtraction
Scale (map)
Scaling (geometry)
Direction (geometry)
Code
Cartesian coordinate system
Limit (category theory)
Shape (magazine)
Plot (narrative)
Similarity (geometry)
Number
Computer animation
Invariant (mathematics)
28:59
Point (geometry)
Rectangle
Rotation
Direction (geometry)
Computergenerated imagery
Translation (relic)
Shape (magazine)
Code
Number
Chain
Mathematics
Chain code
Subtraction
Invariant (mathematics)
Scale (map)
Scaling (geometry)
Spacetime
Theory of relativity
Direction (geometry)
Code
Translation (relic)
Rectangle
Hand fan
Number
Computer animation
Personal digital assistant
Code
Quicksort
Square number
32:58
Point (geometry)
Complex (psychology)
Rectangle
Rotation
Code
Direction (geometry)
Multiplication sign
Shape (magazine)
Mereology
Code
Chain
Mathematics
Chain code
Subtraction
Metropolitan area network
Invariant (mathematics)
Scale (map)
Scaling (geometry)
Direction (geometry)
Code
Rectangle
Degree (graph theory)
Number
Computer animation
Code
Writing
35:11
Point (geometry)
Pixel
Code
Direction (geometry)
Multiplication sign
Shape (magazine)
Mereology
Perspective (visual)
Computer
Code
Computer icon
Number
Image resolution
Chaining
Chain
Goodness of fit
Mathematics
Data compression
Chain code
Subtraction
Invariant (mathematics)
Condition number
Area
Multiplication
Polygon mesh
Point (geometry)
Code
Summation
Computer animation
Data compression
Lipschitz continuity
Code
Quicksort
Row (database)
40:52
Point (geometry)
Pixel
State of matter
Direction (geometry)
Multiplication sign
Control flow
Shape (magazine)
Rotation
Number
Sequence
Chain
Video game
Chain code
Vertical direction
Subtraction
Invariant (mathematics)
Multiplication
Code
Set (mathematics)
Line (geometry)
Degree (graph theory)
Number
Computer animation
Angle
Right angle
Code
Writing
44:57
Point (geometry)
Pixel
Building
Tournament (medieval)
Similarity (geometry)
Electronic mailing list
Shape (magazine)
Computer icon
Number
Workstation
Permutation
Chaining
Chain
Roundness (object)
Convex set
Inverter (logic gate)
Representation (politics)
Subtraction
Symmetric matrix
Quicksort
Metropolitan area network
Information
Electronic mailing list
Code
Shape (magazine)
Permutation
Number
Computer animation
Right angle
Code
Quicksort
49:46
Beat (acoustics)
State of matter
Transformation (genetics)
Similarity (geometry)
Insertion loss
Heat transfer
Distance
Coprocessor
Number
2 (number)
Sequence
Substitute good
Chaining
Maxima and minima
Chain
Mathematics
Spherical cap
Insertion loss
Term (mathematics)
Chain code
Singleprecision floatingpoint format
String (computer science)
Operator (mathematics)
Computerassisted translation
Pairwise comparison
Subtraction
Weight function
Operations research
Standard deviation
Substitute good
Distance
Singleprecision floatingpoint format
Number
Word
Computer animation
String (computer science)
Code
54:32
Computer programming
Rotation
Transformation (genetics)
Similarity (geometry)
Online help
Mereology
Code
Open set
Rotation
Number
Chaining
Maxima and minima
Chain
Strategy game
Chain code
Operator (mathematics)
String (computer science)
Linear programming
Information
Invariant (mathematics)
Operations research
Greedy algorithm
Standard deviation
Shift operator
Information
Analytic set
Total S.A.
Rectangle
Distance
Computer animation
Network topology
Personal digital assistant
Code
Mathematical optimization
57:20
Wavelet
Rectangle
Transformation (genetics)
Interior (topology)
Moment (mathematics)
Walsh function
Computergenerated imagery
Shape (magazine)
Area
Number
Information retrieval
Symmetry (physics)
Hough transform
Active contour model
Representation (politics)
Information
Data structure
Subtraction
Invariant (mathematics)
Stability theory
Compact space
Area
Compact space
Spacetime
Information
Moment (mathematics)
Sampling (statistics)
Transformation (genetics)
Rectangle
Shape (magazine)
Number
Computer animation
Symmetry (physics)
Circle
Information retrieval
Phase transition
Energy level
Quicksort
Representation (politics)
Invariant (mathematics)
Coefficient
1:00:20
Rounding
Pixel
Primitive (album)
Shape (magazine)
Area
Number
Circle
Data structure
Pixel
Subtraction
Area
Covering space
Spacetime
Surface
Primitive (album)
Ring (mathematics)
Rectangle
System call
Shape (magazine)
Connected space
Maxima and minima
Componentbased software engineering
Number
Computer animation
Circle
Information retrieval
Order (biology)
Energy level
Representation (politics)
Data type
Row (database)
1:03:02
Ellipsoid
Complex (psychology)
Building
Inheritance (objectoriented programming)
Length
Combinational logic
Shape (magazine)
Mereology
Food energy
Number
Summation
Roundness (object)
Video game
Internetworking
Code
Representation (politics)
Circle
Distortion (mathematics)
Area
Covering space
Product (category theory)
Length
Rectangle
Shape (magazine)
Symbol table
Coding theory
Error message
Computer animation
Circle
Personal digital assistant
Website
Lipschitz continuity
Kolmogorov complexity
Representation (politics)
Ellipsoid
Design of experiments
1:07:41
Point (geometry)
Musical ensemble
Digital electronics
Ferry Corsten
State of matter
Set (mathematics)
Direction (geometry)
Real number
Shape (magazine)
Mereology
Tangent
Area
Cartesian coordinate system
Skeleton (computer programming)
Video game
Touch typing
Boundary value problem
Circle
Subtraction
Symmetric matrix
Area
Point (geometry)
Bit
Line (geometry)
Rectangle
Shape (magazine)
Maxima and minima
Skeleton (computer programming)
Number
Computer animation
Circle
Personal digital assistant
Website
Quicksort
Boundary value problem
Row (database)
1:14:02
Point (geometry)
Cue sports
Suite (music)
Group action
State of matter
Graph (mathematics)
Online help
Shape (magazine)
Number
Wave
Maxima and minima
Goodness of fit
Skeleton (computer programming)
Touch typing
Electronic visual display
Boundary value problem
Circle
Subtraction
Area
Hidden surface determination
Scaling (geometry)
Graph (mathematics)
Concentric
Point (geometry)
Bit
Ring (mathematics)
Line (geometry)
Compiler
Skeleton (computer programming)
Computer animation
Speech synthesis
Whiteboard
Boundary value problem
Identical particles
1:17:50
Point (geometry)
Hidden surface determination
Multiplication sign
Branch (computer science)
Design by contract
Branch (computer science)
Line (geometry)
Mereology
Graph (mathematics)
Distance
Distance
Hand fan
Skeleton (computer programming)
Skeleton (computer programming)
Video game
Roundness (object)
Computer animation
String (computer science)
Operator (mathematics)
Design by contract
Circle
Bounded variation
Subtraction
1:21:32
Point (geometry)
Addition
Transformation (genetics)
Ferry Corsten
Moment (mathematics)
Multiplication sign
Computergenerated imagery
Tape drive
ACID
Design by contract
Control flow
Branch (computer science)
Shape (magazine)
Mereology
Database normalization
Maxima and minima
Skeleton (computer programming)
Operator (mathematics)
Circle
Pixel
Error message
Subtraction
Metropolitan area network
Data type
Operations research
Hidden surface determination
Information
File format
Distribution (mathematics)
Cellular automaton
Structural load
Physical law
Total S.A.
Line (geometry)
System call
Shape (magazine)
Local Group
Skeleton (computer programming)
Computer animation
Graph coloring
Function (mathematics)
Blog
output
Identical particles
Resultant
Matching (graph theory)
1:29:12
State observer
Game controller
Rotation
Addition
Transformation (genetics)
Moment (mathematics)
Real number
Computergenerated imagery
Distribution (mathematics)
Translation (relic)
Shape (magazine)
Database normalization
Pixel
Data type
Distribution (mathematics)
Moment (mathematics)
Set (mathematics)
Functional (mathematics)
Shape (magazine)
Category of being
Probability distribution
Computer animation
Personal digital assistant
Function (mathematics)
Blog
1:31:05
Musical ensemble
Set (mathematics)
Moment (mathematics)
Multiplication sign
View (database)
Modal logic
Distribution (mathematics)
Mass
Infinity
Sign (mathematics)
Goodness of fit
Random variable
Personal identification number
Real number
Distribution (mathematics)
Discrete group
Moment (mathematics)
Gradient
Skewness
Functional (mathematics)
Number
Probability distribution
Stochastic
Computer animation
Factory (trading post)
Vertex (graph theory)
Right angle
Kurtosis
Resultant
1:35:11
Purchasing
Point (geometry)
Density functional theory
Statistics
Ferry Corsten
State of matter
Moment (mathematics)
Distribution (mathematics)
Translation (relic)
Mass
Shape (magazine)
Infinity
Variance
Number
Sequence
Centralizer and normalizer
Roundness (object)
Causality
Green's function
Uniqueness quantification
Maize
Computerassisted translation
Category of being
Zentrales Moment
Covering space
Shift operator
Moment (mathematics)
Coordinate system
Skewness
Functional (mathematics)
Element (mathematics)
Probability distribution
Stochastic
Computer animation
Network topology
Personal digital assistant
Function (mathematics)
Lie group
Theorem
Condition number
Right angle
Game theory
Invariant (mathematics)
1:41:38
Pixel
Ferry Corsten
State of matter
Moment (mathematics)
Direction (geometry)
Distribution (mathematics)
Mass
Pointer (computer programming)
Video game
Singleprecision floatingpoint format
Uniqueness quantification
Subtraction
Descriptive statistics
Adventure game
Area
Spacetime
Inheritance (objectoriented programming)
Distribution (mathematics)
Moment (mathematics)
Euler angles
Functional (mathematics)
Process (computing)
Computer animation
Function (mathematics)
Theorem
1:45:00
Point (geometry)
Pixel
Rotation
Transformation (genetics)
Code
Moment (mathematics)
View (database)
Computergenerated imagery
Distribution (mathematics)
Translation (relic)
Insertion loss
Shape (magazine)
Mass
Computer
Rotation
Mathematics
Uniqueness quantification
Pixel
Subtraction
Zentrales Moment
Descriptive statistics
Invariant (mathematics)
Area
Cliquewidth
Distribution (mathematics)
Discrete group
Moment (mathematics)
Predicate (grammar)
Functional (mathematics)
Shape (magazine)
Probability distribution
Summation
Digital photography
Computer animation
Theorem
Coefficient
Reading (process)
Matching (graph theory)
1:49:29
Point (geometry)
Rotation
Transformation (genetics)
Moment (mathematics)
Scaling (geometry)
Scientific modelling
Multiplication sign
Design by contract
Control flow
Translation (relic)
Mass
Event horizon
Computer
Number
Database normalization
Protein folding
Centralizer and normalizer
Data compression
Queue (abstract data type)
Software testing
Subtraction
Zentrales Moment
Invariant (mathematics)
Area
Context awareness
Spacetime
Moment (mathematics)
Variable (mathematics)
Database normalization
Computer animation
Personal digital assistant
Factory (trading post)
Linear map
1:53:03
Rotation
Density functional theory
Divisor
Observational study
Transformation (genetics)
Moment (mathematics)
Distribution (mathematics)
Angle
Shape (magazine)
Heat transfer
Rotation
Goodness of fit
Prototype
Invariant (mathematics)
Video game
Divisor
Algebra
Associative property
Invariant (mathematics)
Linear map
Sine
Distribution (mathematics)
Moment (mathematics)
Transformation (genetics)
Functional (mathematics)
Shape (magazine)
Metric tensor
Maxima and minima
Summation
Probability distribution
Computer animation
Function (mathematics)
Linearization
Linear map
Matrix (mathematics)
Matching (graph theory)
1:55:54
Transformation (genetics)
Moment (mathematics)
Determinism
Control flow
Shape (magazine)
Metric tensor
Matrix (mathematics)
Rotation
Sign (mathematics)
Invariant (mathematics)
Computer configuration
Ranking
Algebra
Invariant (mathematics)
Information
Algebraic number
Moment (mathematics)
Weight
Functional (mathematics)
Shape (magazine)
Metric tensor
Computer animation
Network topology
Function (mathematics)
Mathematics
Factory (trading post)
Linearization
Invariant (mathematics)
Linear map
Data type
Form (programming)
Matching (graph theory)
1:58:28
Linear algebra
Web page
Software engineering
Transformation (genetics)
Dot product
Moment (mathematics)
Multiplication sign
Shape (magazine)
Number
Power (physics)
Centralizer and normalizer
Invariant (mathematics)
Degree (graph theory)
Fluid
Category of being
Algebra
Invariant (mathematics)
Proof theory
Algebraic number
Moment (mathematics)
Weight
Set (mathematics)
Degree (graph theory)
Arithmetic mean
Algebra
Computer animation
Personal digital assistant
Absolute value
Game theory
Invariant (mathematics)
Linear map
2:01:38
Rotation
Numbering scheme
Moment (mathematics)
Characteristic polynomial
Translation (relic)
Shape (magazine)
Distance
Invariant (mathematics)
Vector space
Pairwise comparison
Subtraction
Descriptive statistics
Invariant (mathematics)
Social class
Pairwise comparison
Assembly language
Computer
Algebraic number
Real number
Moment (mathematics)
Vector graphics
System call
Disk readandwrite head
Distance
Calculation
Computer animation
Angle
Stress (mechanics)
Invariant (mathematics)
Sinc function
Matching (graph theory)
Reduction of order
Separation axiom
2:03:56
Polygon
Greatest element
Statistics
Moment (mathematics)
Parametrische Erregung
Scientific modelling
View (database)
Curve
Calculation
Shape (magazine)
Invariant (mathematics)
Type theory
Vector space
Active contour model
Representation (politics)
Genetic programming
Category of being
Subtraction
Invariant (mathematics)
Uniqueness quantification
Spline (mathematics)
Element (mathematics)
Moment (mathematics)
Polygon
Vector graphics
Calculation
Computer animation
Database
Function (mathematics)
Element (mathematics)
Representation (politics)
Data type
Form (programming)
2:06:08
Moment (mathematics)
Distribution (mathematics)
Information retrieval
Goodness of fit
Invariant (mathematics)
Average
Database
Alphabet (computer science)
Vector space
Energy level
Multimedia
Subtraction
Invariant (mathematics)
Physical system
Moment (mathematics)
Perturbation theory
Cartesian coordinate system
Vector graphics
Functional (mathematics)
Probability distribution
Computer animation
Alphabet (computer science)
Information retrieval
Universe (mathematics)
Information systems
Game theory
Invariant (mathematics)
Identical particles
Physical system
Local ring
2:09:27
Query language
Pixel
Group action
Musical ensemble
Multiplication sign
Visual system
Boom (sailing)
Insertion loss
Shape (magazine)
Disk readandwrite head
Weight
Web 2.0
Video game
Mathematics
Hypermedia
Descriptive statistics
Physical system
Area
Boss Corporation
Simulation
Software developer
Gradient
Moment (mathematics)
Basis (linear algebra)
Bit
Process (computing)
Lattice (order)
Network topology
Order (biology)
Website
Procedural programming
Whiteboard
Video game console
Ranking
Figurate number
Uniform space
Resultant
Point (geometry)
Divisor
Computergenerated imagery
Event horizon
Computer icon
Power (physics)
Number
Crosscorrelation
Population density
Database
Operator (mathematics)
Reduction of order
Authorization
Computerassisted translation
Metropolitan area network
Addition
Information
Computer
Physical law
Correlation and dependence
Shape (magazine)
Table (information)
Similarity (geometry)
Word
Voting
Computer animation
Game theory
Pressure
Invariant (mathematics)
Local ring
2:13:11
Uniform resource locator
Query language
Computer animation
Database
Computergenerated imagery
Visual system
Price index
Binary code
Process (computing)
Matching (graph theory)
Representation (politics)
Abstraction
2:15:24
Standard deviation
Query language
Direction (geometry)
Gradient
Computergenerated imagery
Point (geometry)
Calculation
Price index
Image resolution
Computer animation
Pixel
Abstraction
Local ring
2:17:29
Query language
Direction (geometry)
Point (geometry)
Computergenerated imagery
Visual system
Price index
Maxima and minima
Summation
Number
Computer animation
Crosscorrelation
Energy level
Block (periodic table)
Pairwise comparison
Pixel
Local ring
2:19:40
Query language
Direction (geometry)
Computergenerated imagery
Visual system
Calculation
Correlation and dependence
Matching (graph theory)
Counting
Similarity (geometry)
Summation
Information retrieval
Computer animation
Database
Crosscorrelation
IRIST
Block (periodic table)
Pixel
2:21:39
Query language
Moment (mathematics)
Computergenerated imagery
Visual system
Shape (magazine)
Emulation
Area
Information retrieval
Chain
Invariant (mathematics)
Computer animation
Database
Moving average
Code
2:23:43
Information retrieval
Computer animation
Lecture/Conference
Information
Metadata
Formal Metadata
Title  Chain Codes, Area based Retrieva, Moment Invariants, Query by Visual example (05.05.2011) 
Title of Series  Multimedia Databases 
Part Number  5 
Number of Parts  14 
Author 
Balke, WolfTilo

Contributors 
Homoceanu, Silviu

License 
CC Attribution  NonCommercial 3.0 Germany: You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal and noncommercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
DOI  10.5446/336 
Publisher  Technische Universität Braunschweig, Institut für Informationssysteme 
Release Date  2011 
Language  English 
Producer 
Technische Universität Braunschweig

Production Year  2011 
Production Place  Braunschweig 
Content Metadata
Subject Area  Information technology 
Abstract  In this course, we examine the aspects regarding building multimedia database systems and give an insight into the used techniques. The course deals with contentspecific 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, PrecisionRecall Analysis  Semantic content of imagecontent search  Image representation, lowlevel and highlevel features  Texture features, randomfield 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, MPEG7  Extraction of lowand highlevel features  Integration of features and efficient similarity comparison  Indexing over inverted file index, indexing Gemini, R * trees 