Signature and Lexicon Pruning Techniques

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1 Sgnature and Lexcon Prunng Technques Srnvas Palla, Hansheng Le, Venu Govndaraju Centre for Unfed Bometrcs and Sensors Unversty at Buffalo {spalla2, hle, Abstract Handwrtten word recognton and Sgnature dentfcaton are mportant areas n machne vson that requre extensve exploraton for mproved results. The performance of such systems tend to degrade when the number of choces to be dealt wth ncrease. In case of a lexcon-drven handwrtten word recognzer, the performance degrades when the lexcon sze ncreases [8]. Smlarly, the matchng process s tedous when the number of reference templates ncrease n case of onlne sgnature dentfcaton. For better performance, both n terms of recognton rates and response tme, nteractve models are suggested, whch nvolve feedback process to further enhance the systems. Interactvty s attaned by choce prunng, whch flter out useless entres, thus provdng the system wth a smaller set for further detaled nvestgaton. The paper manly dentfes the necessty for choce prunng and deals wth two specfc cases sgnature prunng and lexcon prunng. 1. Interactvty and choce prunng exctaton wheren certan choces are excted and certan others are hndered based on the feedback gven. The next teraton consders only the excted choces and flters out the unexcted ones. The number of levels of nteractvty can vary dependng on the applcaton. The model has been descrbed n [2] as nteractve actvaton model. Choce prunng s nnately bult nto the nteractve actvaton model. Choce prunng should allow nondsmssal of correct choces. The flterng process has several advantages. In case of handwrtten word recognton, the prunng process results n a smaller lexcon and thus a detaled one-to-one matchng of the mage wth word models s qucker and more effcent. In case of sgnature recognton too, the number of one-toone matches reduces. Another advantage of prunng sgnatures occurs n the case wheren a detaled one-toone fnger prnt matchng s done only on the fngerprnt templates correspondng to pruned sgnature templates. Such a system ncreases the effcency of fngerprnt matchng based on sgnature prunng. The paper deals wth these ssues n the followng manner. Secton 2 deals wth a novel sgnature prunng method based on regresson of quantle samples. Secton 3 deals wth lexcon prunng based on regular expresson matchng. Secton 4 concludes the paper wth a glmpse on future work. 2. Sgnature Prunng Fgure 1. Generc nteractve model Interactve Process s the one, whch uses a feedback to enhance the process performance, and thus generates a better output. The whole process s based on choce Onlne Sgnature s a tme seres data and therefore regresson analyss [6] can be done to study the propertes of onlne data. The smlarty between two sgnatures can be related to a dstance between them, where the dstance s the squared error dstance, whch can be found from smple lnear regresson. Regresson methods are used to quantfy the relatonshp between two varables. Mean regresson analyss does not take the whole data dstrbuton nto consderaton and therefore there s nformaton loss when such methods are used. To Proceedngs of the 9th Int l Workshop on Fronters n Handwrtng Recognton (IWFHR )

2 properly quantfy the whole relatonshp between two data dstrbutons, t has been shown n lterature that quantle regresson can yeld better results [4,5] Quantle samples Quantle samples are values that splt the data populaton nto dfferent proportons. To summarze a vector of numerc values, the general approach s to represent the vector usng the mean value. However, the mean does not always provde the best representaton of the whole vector. If the data values are skewed such that there are very few hgh values but a large number of small values, the mean s senstve to hgh values. Such a data can be summarzed by usng not just one mean but by usng dfferent quantles. smlarty can be assessed by takng the quantle values from dfferent data populatons and then plottng the quantles of one dstrbuton aganst the other. Once the ponts are formed, a smple lnear regresson s done so as to get the best fttng lne through these ponts. If the two data populatons belong to the same dstrbuton, then ther quantle-quantle plot s a straght lne. So the squared error dstance gves how smlar the two dstrbutons are. The two dstrbutons can also be tme seres data. Based on ths dea, sgnature prunng s done as follows. For every user, a reference sgnature s taken. The reference sgnature s selected from the tranng samples (5 samples are taken durng user regstraton). The reference sgnature s the one that has the least dstance from all the other sgnatures. The dstance here s the least square error dstance found after smple lnear regresson through quantle samples. If only the x-y coordnates are taken to represent a user sgnature, the sgnature s frst made scale and translaton nvarant. Ths s done as follows: X X mn( X) = max( X ) mn( X ) Y mn( Y) Y = max( Y ) mn( Y ) Fgure 2. 25% - 50% - 75% Quantles A p% quantle s defned as the value that splts the data nto proportons of p/100 and (100-p)/100. For example, a 25% sample quantle splts the data nto ¼ and ¾ whle a 50% quantle splts the data populaton nto two halves. The latter s equal to the more popular medan of the dstrbuton. By takng nto account all the quantles nstead of medan, the nnate skew ness n the data populaton can be accounted for. The fgure 2 s a plot of the X-data values for varous Users sgnatures. The fgure shows 25%, 50% and 75% quantles of each X-data populaton Smple lnear regre sson of quantles Quantle regresson as descrbed n [4] s an extenson of classcal least squares estmaton of condtonal mean models to the estmaton of an ensemble of models for several condtonal quantle functons. Data dstrbuton Once the sgnatures are normalzed, the dstance between them can be found from the X-data and Y-data quantles (fg 3). Let the quantle dstance (qdst) be defned as the sum of the squared resduals after smple lnear regresson through the quantle Vs quantle plot, obtaned by plottng the quantles of one populaton aganst the other. Gven two sgnatures S 1 <X 1, Y 1 > and S 2 <X 2, Y 2 >, the dstance between them s gven by: d = qdst ( X 1, X x 2) d = qdst( Y, Y ) y 1 2 d = d x d y 2.3. Prunng process For every regstered user, the reference sgnature s stored. When a test sgnature s gven, the dstance of the test sgnature wth every reference sgnature s taken. The reference sgnatures are sorted accordng to ther dstance from the test sgnature and the top n sgnatures are fltered for further consderaton whle other sgnatures are dscarded. The choce of n s made based on the experments wth a set of test sgnatures pertanng to varous users. The test dataset conssted of 40 users wth 19 sgnatures per user for a total of 760 sgnatures. One reference sgnature per user s already set asde and does not consttute the test dataset. Proceedngs of the 9th Int l Workshop on Fronters n Handwrtng Recognton (IWFHR )

3 Fgure 3. Quantle Quantle plots The prunng results are shown n table 1. The correct sgnature template s always wthn the pruned results when n=5. Also 86% of the tme, the correct sgnature s the one wth least quantle dstance ( d = d x d y ). So by takng top 5 sgnatures, t s ensured that there are no false dsmssals. No forgeres are consdered here, snce the man dea s to prune correct templates and pass t to the actual recognzer. So even f a forgery s gven, t s for the later stage to deal wth t. Prunng only ensures that false dsmssals don t occur. Table 1. Results of prunng on sgnature dataset Total Top Top Top Top Top Sgnatures Lexcon Prunng The word mage can be consdered as havng three parts man body, ascenders and descenders. Accordngly, we have four lnes to segment the word mage. These are the ascender lne, the half lne, the base lne and the descender lne. Once the mage features are extracted, we can fnd whether the mage contans ascenders or descenders. Based on ths nformaton, the lexcon can be pruned so that a one to one match s done only wth the pruned lexcon entres. Ths wll mnmze the comparson tme and at the same tme ncreases accuracy Reference lnes Gven a word mage, the reference lnes of the mage are found. The reference lnes are found accordng to the algorthm descrbed n [3]. The basc dea s to construct horzontal runs from the mage. Once the horzontal runs are found, the center of mass of the mage s found. A regresson lne s drawn through all the horzontal runs below the center of mass, whch have no neghbors below. Ths s an approxmaton for the base lne. Now consder only those horzontal runs (wth no neghbors below) wthn a small dstance from the approxmated baselne and do a smple lnear regresson to get the fnal baselne. The horzontal runs whch are mnma and maxma help determne the descender lne and ascender lne. The half lne corresponds to maxma near to base lne. Proceedngs of the 9th Int l Workshop on Fronters n Handwrtng Recognton (IWFHR )

4 Fgure 4. Orgnal mage ndcates that a symbol appears one or more tmes. For example, a regular expresson nd(n)*(a) + (n)*a ndcates that the word starts wth a normal character, followed by a descender, followed by zero or more occurrences of a normal character, followed by one or more occurrences of an ascender, followed by zero or more occurrences of a normal character, followed by an ascender. A word matchng the regular expresson s symbol. As an other example, a regular expresson a(n)*(d) + n*an corresponds to buffalo but not Amherst snce the regular expresson ndcates that there s at least one character whch s a descender Prunng process Fgure 5. Reference lnes Once the reference lnes are detected, the presence or absence of ascenders and descenders can be found. For ths purpose the mage s converted nto a block adjacency graph from the horzontal runs. A graph wth nodes and edges correspondng to the mage s generated from the BAG. The graph representaton along wth the reference lnes ad n the generaton of a regular expresson correspondng to the mage. Gven a word mage, the reference lnes are detected and the graph s generated. From ths nformaton, a regular expresson correspondng to the word s generated. Every entry of the lexcon s checked aganst the regular expresson based on a fast regular expresson - matchng algorthm. Only those words matchng the regular expresson are consdered for further nvestgaton. The prunng process s customzed for a partcular word recognzer [1] that uses the reference lnes and graph representaton for mage feature extracton. So the prunng process s just a part of the mage feature extracton process wth only an addtonal regular expresson matchng [7] nvolved. Fgure 6. Graph Representaton of Image 3.2. Regular expresson match prunng Gven a word mage, a regular expresson pertanng to that word can be formed. Ascender-Descender detecton s trval, gven a graph representaton and reference lnes. The regular expresson s formed usng three basc symbols <a, d, n>. Here a stands for ascender, d stands for descender and n stands for any character. Now a regular expresson s formed based on these symbols for a partcular mage and lexcon entres, whch match the regular expresson, are only consdered for further matchng. A Legal regular expresson [7] contans symbols wth ther occurrence ndcator. A * ndcates that the symbol appears zero or more tmes. A + Fgure 7. Regular expresson based prunng 4. Conclusons The sgnature prunng and lexcon prunng processes, when ntegrated wth the actual recognzer make the whole system more robust. Any recognzer nvolvng a one to one match mechansm wll beneft from such a feedback. Proceedngs of the 9th Int l Workshop on Fronters n Handwrtng Recognton (IWFHR )

5 The feedback can also be n a dfferent form. An alternatve approach nvolves bnnng where n the feedback s the bn dentfer whch contans templates to be matched. Sgnature bnnng can be qute useful n bometrcs when a large fngerprnt database s used. Sgnature dentfes the bn and a fngerprnt matchng s done only wth correspondng templates belongng to that bn. Study of varous other knds of feedback methods and faster prunng and bnnng technques are promsng areas where further work can be done. References [1] H. Xue, V Govndaraju. Stochastc Model Combnng Dscrete Symbols and Contnuous Attrbutes and ts Applcaton to Handwrtten Recognton. Internatonal Journal of Document Analyss and Recognton [2003]. [2] Marcus Taft. Readng and the Mental Lexcon, Essays n Cogntve Psychology. [3] Slavk, V Govndaraju. An Overvew of Run-Length Encodng of Handwrtten Word Images. Buffalo tech Reports [2000]. [4] Koenker Roger, Kevn F. Hallock. Quantle Regresson. Journal of Economc Perspectves, 15(4), Fall, [5] Kemng Yu, Zud Lu, Julan Stander. Quantle Regresson: Applcatons and Current Research Areas. Journal of the Royal Statstcal Socety: Seres D (The Statstcan), Volume 52 Issue 3 [2003]. [6] F. Mosteller and J.W. Tukey. Data Analyss and Regresson A Second Course n Statstcs. Addson-Wesley, [7] John E. Hopcroft, Rajeev Motwan, Jeffrey D. Ullman. Introducton to Automata Theory, Languages and Computaton. Addson-Wesley [8] H. Xue, V Govndaraju. On the dependence of handwrtten word recognzers on lexcons. IEEE transactons on pattern analyss and machne ntellgence, December 2002 (Vol 24 No 12). Proceedngs of the 9th Int l Workshop on Fronters n Handwrtng Recognton (IWFHR )

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