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# Mathematical Formulae Recognition

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#### Automatisierte Medienanalyse

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Chen ladies and gentlemen I like to tell you how we recognized online mathematical formula using the glamorous so here the outline of the local modulates the problems of the revolt our contribution I describe briefly How do you grammars
can be used and what is the basic idea behind as of show you something from the implementation W what is our future plan outshone the true short demonstration that the plant preseason questions don't hesitate to interrupt me during the talk openly with reporters questions so this also modulated from this your ethical point of view not from the practical use of my view of this ,comma and particle
emissions and I'm interested in the relation between statistical commissioned a structural 1 solely mathematical formulae used boy for us on which we can play and reason idea children this is the kind of people work on it so we can compare the results the others see you soon beaches theoretical background is described in our book with the promise of Schlesinger which was published the cooler he doesn't do and its application or application only two-dimensional grammar school images Wallstreet topical value grew from being these officials defended the 2005 In this work I will beauty at all only previous work which was published in the International Conference on the Internet is in recognition in September last year when we show me how to recognize the mathematical formulae indeed offline case which means if there is a scanned document and how can you from the scandal in this report I'm going to put men on the online version in which there is a public Europe tablet on which you can draw of strokes as an input and so this is what this here what is the problem of mathematical formulae recognition so let's take a simple formula like this 1 and if we know what is the but body operators which will
apply different and bosses a binary operation which divides the formula into .period problems here the 2nd 1 for that fraction this 1 is a follower which is then again divided into In a binary operation to minors be sold each formula a duration trees the corresponding generation and our aim is to create this derivation real particularly from for offline and online merchants the usual approach may offline version also an on-line is still starter is the is the symbol detection and their
recognition and having the symbols than doing the structural analysis Our case we really don't be things have basically in wanted which allows to go over the main problem which is the main problem is if the civil authority and I strongly then there is basically no good way to recover from Helen but it
doesn't make sense the spectral analysis violent environment in our case to the take several possible options and he traveled there in the structural analysis there are a lot of ambiguities in the so if you will of U.S. office scanning the skies resolve so in this case the expected
interpretation of this 1 but maybe you know that I can medical possible confusion so Bloomberg In problem this is related to the
mathematical formulae however the Google promises Schlesinger has been working on similar problem in the area of the command analysis for all the time and he was the 1st author of the book I mentioned and they tried to electric schematic diagrams successfully and they also tried to sheet music recognition using the structural recognition using structural construction so we I'm just reporting about to be formula so what is the topic of this is recognition of all the on-line strokes and
basically the approach which replied Well 40 offline formulae mentioned it briefly late morning theoretical part of was adopted what we needed to have also adopted new myself for elementary symbol detection and the representation of it there had to be designed and the passing of rhythm which creates the derivation for you have to be modified because the indication of wine formulae .period was the bounding boxes and to hear some orders structures need to be represented representative of all the strokes and the proximity in to space so the on-line cases attempt to detect all sorts of strokes that can form a symbol and to in and
then rank them according to the plausibility and take a few possible options over that to speed up the process and make it simple being too you probably the take into account some of simplification assumptions and the simplification assumption is that once symbol can be In the current implementation composed only all 4 strokes and we don't consider all the strokes which are available but only those which are in the proximity so which is there is some kind of neighborhood than its neighbors the the chosen candidates .period an unrelated by DOC are In this case for OCR to the for on-line symbols and they are assigned to labels and then because of our processes optimization which minimizes some penalties to the penalties are assigned to each of the 2 nations so there is the example just briefly look at the these commerical street between here and of course this can have various interpretations this part because it's disconnected can be interpreted as if W also interpreted this as Peru ruled this along this line can be also a fractional line can be also a minus sign and this ambiguity sodden disambiguated in the passing process so we have to keep all the interpretations the beginning so now I'll give you a last the Swiss Life's sought to slide introduction alters the structure construction which is the basic theoretical
background over the approach the idea is that for each each constructed as the region in all which has grown from scratch and the it terminals in the offline case I individual pixels and in the on-line case these are strokes and some kind of area related to those it don't strokes it's still a little more complicated so are just so that the people of this and the duration of such a region is basically maiden degenerative made by applying the production rules of the appropriate grammar and to these rules have some penalties assigned so basically the duration can be assigned a panel the some of these penalties corresponding duly particle regions then summoned to leave on a global penalty later on and the final interpretive interpretation is the areas the region 2 strokes in the online case which covered all available in each and which has been minimal penalties so this is the case from the off-line because it's easier to do show so let I have region and is as this 1 which is ruled which is
the composed of all 4 regions no they noted Europe ABC and the and you can see that there a need regions in the offline considerably rectangles the combined by some kind of concatenation knowledge within the production Center if you'd like to come the because of course the problem is complicated and would even be possible single funding dramas context 3
Grandma's completely so in the case of duty dramas it's even more complicated so did here are some simplifying assumptions which allow us to dramatically reduce the complexity to make the whole approach useful practically so the region's Orrick bundles which allowed tool for adjusting the rectangles which which ultimately wanna basically interested in what is inside the EU and in such a case that to conflict-free grammar there can be constructed for which there is a passing algorithm because the generalization of famous people younger possibly on words and complexity is relatively low the polynomial you can see here and an our sizes sold the image which correspond to the so it's practical fees it practically feasible the production rules are very simple soldier on the ground basically the flow of any judgment will be the nation's 1 is
horizontal and 1 vertical combination and then that's it of these simple formulae these simple rules are enough unfortunately for amount article formally A. There is a need for extensions and this extension is supposed
to bring the mutual position all the symbols the beach the ordering Grandma prudent to take into account for instance if you like to have the power and then the notion of a size should be in taken into account and then also the relative positions of the 2 the same problem would be 40 fraction of what a fraction moreover there is some uncertainty because of the the appropriate rectangles so Indy handwritten case
wouldn't be precisely aligned children must be some kind of elasticity specific which is explicitly expressed in terms of mutual constraints between the boxes represented to some parts of the so the implementation of the who is available or something like that politician is done died in the In yellow because
reflected and to a it's it said ball just for the best thing in the verdicts of the momentum is so simple mathematical constructs like numbers and disease come ,comma Munir in binary operators Barbaro power cooperated fractions subscript superscript songs and into integral and of course the mess of things slower in circumstances that are resistant to noise which all show you In late so also my eyes lost like at the 1st World War body experiences the experiences of that
the massive lost their staple 400 formulated this is the precision and which is 88 per cent rich if the OCR terrorism they can intercom let me remind you that you'll see a lot in the public domain tool which is used in applied and if the errors made by the OCR pool are subtracted then the level of 97 per cent the approaches so fast you can see the fraction of a 2nd for a wellbore formula in a marriage beaches so those greater than in the offline case the goal of the year sequence of the stroke that given additional information which makes a which tremendous and so opinionated that's practically useful maybe it might be it might be really applies so future work in his life he tries to do take a book mathematical book and tried to beat the system to be able to call with the problems in the book Olson offline and also an online version this is a project which doesn't have any money so it's like the included project of enthusiasts now I find that people must student the lady she's been there she'll be working on it for the next several months and she would be doing nothing else so hopefully to review progress on area for for a presentation and let me will demonstrations which is the here is the tool which is the job approach
Digital implementation simple user interface and to so for instance
if you will look for formulae like that the start the industry people line ones which were drawn on the tablets stored in some form of which takes into account the the sequence of strokes and if you like to recognize the formula the formula is going to be recognized here is the outcome of the formula what you have here is the duration 3 which tells what rules are applied in both sequence for dead particulary formula and of course the Eureka and these side green boxes show the individual part of the formula and Kennedy can comedy can for instance if filed a show so this is the stroke number 6 for instance he conceded here you can look it up in the the operation created policies that which used and there is a problem because the EU production how to find then I can show you that it can even work for the drawing Inc because I don't have a problem with missile is a simple way help draw by miles long tried to and it's not fair my handwriting is playing for someone else's life but let me try to show it is for this study on so I think I'm gonna Mister Chairman few questions about this fact in a the friend so so well some problems in all of this is relatively complicated issue so it's 1 way is to assign a monumental and that's the reason we have relatively small amount of production roles and the 2nd approach is cold during the during the learning process so you be training set which is available offline too to assigned penalties and this is the problem he recalled an article would differences actually working on the but income and again it's 1 of the city's penalties are created and the and that call on a phone for the channel team not only also for symbols sofa and if if you like to see the more detailed description of how the penalties are described the look at the bigger paper paper 2 thousand 740 offline formulae and on the beach he can each have had exactly it's so complicated process and like regulated simple the there is no you it's the most common area it's more the there was a destructive sometimes for instance specially fractions and their roots in our implementation if you will not material tried to make some of the year so for instance if you if you drop tonight it doesn't it doesn't remember triggered longtime leftovers from his courage so that all may discourage them anything like that so then the authority only outcomes would it doesn't recognize my skirt or a dozen other people made history too but they could that will get out of the doesn't it is not able to in the context this symbol but if there are problems of this sort that it's the main problems which are not based on it all depending that it is the arriving water-dependent playing the stroke gets into your mind and your final .period we still a no more aggression the question is is counted on the amount of it's 1 the wrong from Uncle the policyholders and other days the
don't this is what it's all about I don't know if this is for it to be but there is no longer form at the moment it's all over the world is available this experimental school so it's not you know if you like the white the consented but you will not get anything you have at hand have now gone as you suggest they don't want you to know that nothing have if you think about this and this and that was it it but this is also of course the play which can help and it's possible that we didn't consider it at this moment but the construction of housing because if you have someone thinks and you know who you are operating on the mathematics is based physical don't wonderment that mechanics then you know what kind of formulation can expect and this this can cost constraints the possibility of nations grounded out so it's possible tool is implemented there but this is not our main problem only after fighting is much more basic you can have the house and I don't think it was back at the time of year yes something that would be yeah the main message I wanted to mediate to you is that there is something like the drama and that they are practical that's the main message and that was the reason I was going it was this is what my my interest and now it's useful know so maybe we can do about that but for a time money the commander in the garrison command papers concerning for medical conditions and also the last time using the demand I'm an assistant bishop ,comma you should use this difference and the next 50 years practical experience preparing you with the obvious experience is 1 tool which called which is called Marsh cat I think is the name of the school so this is really about paper prominent harmonization and as hasn't can 90 70 something it's totally anytime on origin the glamor to the but I don't think that I don't think so armistice was how I have you arrive here at home and that it was not so the fact that this the Irish favorite and then also said similar succeeding papers so we should clarify the difference maybe you have a son on Monday practices of his emphasis is also follows the Foshan or development in the bathroom Commission area as you might remember at the beginning of a decent and the seventies structure but recognition was very fashionable among Drexel for kinks so full books and so on and then it died out because people didn't find it was used for a practical case and the other trying some of the others will be either of the question he needed make a comparison another yesterday and the presentation of the you on the other hand ,comma the reason for this he also had harsh have met the above have I'm I have to all of those who may have run out it is apparent did the asthmatic and you have to have feeling position that take 240 sedan anything looked into the cause of the thank you very much
Punkt
Fakultät <Mathematik>
Explosion <Stochastik>
Modul
Kombinatorische Gruppentheorie
Ausdruck <Logik>
Resultante
Nichtlinearer Operator
Bruchrechnung
Mathematik
Statistische Hypothese
Mathematik
Kartesische Koordinaten
Derivation <Algebra>
Endlich erzeugte Gruppe
Physikalische Theorie
Computeranimation
Inverser Limes
Ausdruck <Logik>
Topologie
Statistische Analyse
Bruchrechnung
Explosion <Stochastik>
Dimension 2
Thermodynamisches System
Graphische Statik
Stichprobenfehler
Derivation <Algebra>
Punktspektrum
Analysis
Computeranimation
Topologie
Analysis
Objekt <Kategorie>
Diagramm
Flächeninhalt
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Mathematik
Algebraische Struktur
Analysis
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Teilmenge
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Minimierung
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Raum-Zeit
Physikalische Theorie
Computeranimation
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Algebraische Struktur
Vorzeichen <Mathematik>
Abstand
Indexberechnung
Bruchrechnung
Prozess <Physik>
Rechteck
Vorzeichen <Mathematik>
Grundrechenart
Frequenz
Grundrechenart
Wurzel <Mathematik>
Sortierte Logik
Mereologie
Ordnungsstruktur
Algebraische Struktur
Dämpfung
Flächeninhalt
Rechteck
Derivation <Algebra>
Schlussregel
Biprodukt
Computeranimation
Schlussregel
Erweiterung
Rechteck
Rechteck
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Schlussregel
Kombinator
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Massestrom
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Schlussregel
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Rechteck
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Term
Schlussregel
Physikalisches System
Ausdruck <Logik>
Mereologie
Elastische Deformation
Algebraische Struktur
Term
Leistung <Physik>
Mittelwert
Impuls
Folge <Mathematik>
Prozess <Physik>
t-Test
Zahlenbereich
Geräusch
Nichtlinearer Operator
Stichprobenfehler
Computeranimation
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Arithmetische Folge
Ausdruck <Logik>
Bruchrechnung
Leistung <Physik>
Bruchrechnung
Nichtlinearer Operator
Mathematik
Stichprobenfehler
Physikalisches System
Binärbaum
Variable
Schlussregel
Integral
Integral
Flächeninhalt
Wurzel <Mathematik>
Zahlenbereich
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Prozess <Physik>
Wellenpaket
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Bilinearform
Extrempunkt
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Eins
Ausdruck <Logik>
Unendlichkeit
Deskriptive Statistik
Ausdruck <Logik>
Primzahlzwillinge
Wurzel <Mathematik>
Regulator <Mathematik>
Bruchrechnung
Nichtlinearer Operator
Green-Funktion
Stichprobenfehler
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Biprodukt
Frequenz
Schlussregel
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Sortierte Logik
Mereologie
Mittelwert
Harmonische Analyse
Nebenbedingung
Subtraktion
Ortsoperator
Momentenproblem
Mathematik
Physikalischer Effekt
Stichprobenfehler
Physikalismus
Paarvergleich
Bilinearform
Kombinatorische Gruppentheorie
Computeranimation
Schlussregel
Algebraische Struktur
Flächeninhalt
Einheit <Mathematik>
Ausdruck <Logik>
Mechanismus-Design-Theorie