Face Recognition using Supervised & Unsupervised Techniques

Transcription

1 Natoal Uversty of Sgapore EE5907-Patter recogto-2 NAIONAL UNIVERSIY OF SINGAPORE EE5907 Patter Recogto Project Part-2 Face Recogto usg Supervsed & Usupervsed echques SUBMIED BY: SUDEN NAME: harapa Reddy Gar Ob Reddy SUDEN NUMBER: A A -ID: PROF: Dr. Shucheg Ya Ob Reddy A A

2 Natoal Uversty of Sgapore EE5907-Patter recogto-2 Abstract hs project maly focuses o feature dmesoalty reducto techques lke PA, NMF (usupervsed) ad LDA (supervsed). hese are studed thoroughly ad mplemeted o Yale exteded face database the face recogto s carred out by usg smplest supervsed classfer earest eghbour (NN). Smplfed Yale exteded face database B havg 244 mages of 38 huma subjects early 64 mages per subject, s cosdered to do the expermets Mat lab ad the results are aalysed. Itroducto I recet years face recogto has receved more atteto from research due to the scope for umerable real tme applcatos based o huma face recogto. A complete patter recogto system cossts of: ) a sesor that gathers the observatos to be classfed or descrbed, ) a feature extracto mechasm that computes umerc or symbolc formato from the observatos, ) Feature dmesoalty s reduced v) a classfcato or descrpto scheme that does the actual job of classfyg or descrbg observatos, based o the extracted features. here are may databases avalable to solve patter recogto problem out of these Yale exteded face database B s chose to aalyse the dmesoalty reducto techques performace. About Feature s Each mage vector s a two dmesoal vector of 32x32, X ϵ { } S s the total space of the extracted data set ad each vector whch s more coveetly represeted oe dmesoal as x024, X ϵ { } elemets s the pxel value the mage. Due to varats such as vewg agles, llumato, facal expresso ad so o, the facal feature vector obtaed ca have radom varatos. Gve two smplfed databases oe s YaleB_32x32.mat ad the other s corrected llumato YaleB_32x32_corrected.mat supportable mat lab. Data set s dvded to p=20 ad p=50 splts wth each splt havg some trag ad test samples. otal samples or subjects are 38 ad the umber of mages data set s 244 mages each sample has got approxmately 64 mages. Reducg the dmeso of the features ad the classfy the gve test samples wth 0% error rate s the objectve. Supervsed learg: s the mache learg task of geeralzg a fucto from supervsed trag data. Usupervsed Learg: s a class of problems whch oe seeks to determe how the data s orgazed. Nearest Neghbour lassfer: hs classfer works o the bass of appearace, by comparg wth all the mages avalable ts trag set ad gets the label of the sample whose dfferece s less. hs dfferece betwee two face mage vectors or trag ad a test sample s calculated by Eucldea dstace. NN classfer s also called -NN classfer whch s a case of K-NN classfer wth k=. Let the test samples are Y ϵ { } x024 ad the trag samples are X ϵ { } x024 Eucldea dstace betwee a test ad trag sample face mage s foud by the below formula Ob Reddy A A 2

3 Natoal Uversty of Sgapore EE5907-Patter recogto-2 he process followed mplemetg -NN or Nearest eghbour classfer Each sample wth the data set has a class label the set, lass = {c,...,c }. he test sample earest eghbour the trag set s the foud by fdg Eucldea dstace betwee the test sample ad all the trag samples. he closest trag sample label s the assged to the test sample.. Normalzed the data set to uty. Dmesoalty reducto s to make the hgher dmesoal feature space to low dmesoal whch makes easy to classfy the data computatoally. 2. Prcpal compoet aalyss (PA): PA removes the uwated formato ad precsely decomposes the face structure to orthogoal (ucorrelated) compoets kow as Ege faces. hs method learly projects data to low dmesoal feature space. hs retas as much as possble varato preset the orgal data. Steps followed mplemetato of PA Normalze the data set to uty. Mea of trag samples features s calculated. Subtract the mea from every trag mage vector. alculate the covarace matrx. alculate Ege values ad Ege vectors. S x x x x k k Sort the Ege values descedg order ad the sort Ege vectors accordgly. Reduce the trag data set to the dmeso whch s requred by choosg that may sorted prcpal compoets. Reduce the test data set by cosderg the Ege vectors of the trag set. lassfy the reduced dmeso ( to 00) test samples usg the Nearest Neghbour classfer. Plot the results. x x s the mea. var[ z ] a Sa k k Ege Faces for frst 5 splts p=50 are as show below ad the performace of PA wth NN classfer s also show below. Ob Reddy A A 3

4 Natoal Uversty of Sgapore EE5907-Patter recogto-2 Observato: As we see the performace of NN classfer o the PA reduced dmesoalty data as the dmeso creases the performace creased. 3. Noegatve Matrx Factorzato (NMF): NMF s smpler algorthm compared to PA sce t reduces the computatoal complexty. A mportat costrat of NMF s the o-egatveess of base mages matrx ad ecodg; oly allowg addtve combato of o-egatve parts. Steps followed mplemetato of NMF are Italze the radom w ad h vectors. Apply NMF update rule utl the mea square s less tha the specfed or the maxmum umber of teratos are reached. Reduce the dmesoalty of trag sample by multplyg the bases vector wth the trag data set. No classfcato s doe oly dsplayg the bases mage vectors. Base mages for p=50 ad splt are show below V WH 2 s t W H WH, m.. 0, 0. For the three rus of NMF for the same splt results dfferet base mages every tme. Reaso behd the chage the base mages s because of the talsato of the base mages ad ecodg matrces wth dfferet radom umbers. 4. Lear Dscrmat Aalyss (LDA): LDA s a supervsed techque reducg dmesoalty of the hgher dmesoal feature space. he objectve of LDA s to fd out the optmal trasformato matrx so the rato of betwee class scatter matrx ad wth class scatter matrx reaches to ts maxmum. Oe dffculty face recogto usg LDA fsher faces s that the wth class scatter matrx s sgular. o solve ths very small umber s added to the dagoal elemets or we ca frst do PA dmesoalty reducto o that LDA has to be doe. Steps followed mplemetato of LDA ompute each class mea of 38. ompute each class covarace ad sum all class covarace to get Wth lass scatter. ompute global mea of the avalable trag sample set. Ob Reddy A A 4

5 Natoal Uversty of Sgapore EE5907-Patter recogto-2 ompute betwee class scatter ompute Ege vectors for wthclass-* betwee class matrces Sort the Ege vectors descedg order. Depedg o the dmeso requremet choose that may Ege vectors the multply wth the trag ad test samples. lassfy the est samples usg NN classfer. lass covarace Wth lass Scatter Betwee class Scatter S x m x m xx mm. x S S S, s the class umber. W P N S P m m m m B PP 2, j x m m m m j j j. Fgure: shows Performace of NN classfer o LDA reduced dmeso data. Observato: As we see NN classfcato wth LDA has gve better results compared to the PA. Eve for lesser dmeso (reduced) the classfer has performed very well. LDA out performs PA classfyg the data reaso behd ths s PA fds the most accurate data represetato a lower dmesoal space ad projects data the drectos of maxmum varace whereas Fsher Lear Dscrmat project to a le whch preserves drecto useful for data classfcato. he drectos of maxmum varace PA may be useless for classfcatos whereas, LDA projected drectos are much useful for classfcato. LDA performs very well whe sample gve s large. 5. Gaussa Mxture Model Itally assumg the class mea as Gaussa model. Usg the Geeratve mxture model EM method we are estmatg the meas of all 38 classes ad the we are comparg wth actual meas of the 38 subjects. After comparg the estmated wth actual meas t seems that they are almost smlar. Refereces. Lecture Sldes 2. Wk Pages for PA, LDA & GMM 3. EIGENFAES AND FISHERFAES by, Naotosh Seo, Uversty of MaryLad. Ob Reddy A A 5