Invariant Shape Object Recognition Using B-Spline, Cardinal Spline, and Genetic Algorithm

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1 Proceedngs of the 5th WSEAS Int. Conf. on Sgnal Processng, Robotcs and Automaton, Madrd, Span, February 5-7, 6 (pp4-45) Invarant Shape Obect Recognton Usng B-Splne, Cardnal Splne, and Genetc Algorthm PISIT PHOKHARATKUL Department of Computer Engneerng, Faculty of Engneerng, Mahdol Unversty Salaya, Phuthamonthon, akhorn Pathom, 737, THAILAD SKUL KAMUACHAI and CHOM KIMPA Faculty of Informaton Technology, Rangst Unversty Muang-Ake, Paholyotn and Road, chom@rangst.rsu.ac.th Patumtan,, THAILAD SUPACHAI PHAIBOO Department of Electrcal Engneerng, Faculty of Engneerng, Mahdol Unversty Salaya, Phuthamonthon, akhorn Pathom, 737, THAILAD Abstract: - Obect recognton s an essental part of the computer vson system. Ths paper proposes a genetc algorthm to search the features of model shapes of the obect from model-base, to dentfy nput shapes of the obect. The domnant ponts are extracted from the edge of bnary mages usng Gaussan flterng. There are two methods to compute the output features. The frst, B-Splne, used the domnants to compute the control ponts. The second, Cardnal Splne computes the data ponts form the domnant ponts. The control ponts, and the data ponts are bult a model shapes for searchng by genetc algorthms to dentfy the nput mages. Then, we are compared the two method. Tranng data composes of orgnal obect, ts translaton, ts rotaton and ts scalng. The recognton results of B-Splne mplementaton are 97% for rotated obect, 94% for rotated and scalng obect. The recognton results wth Cardnal Splne feature are 97% for rotated, 95.% for rotated and scalng obect. Key-Words: - Obect recognton, Centrodal profles, Gaussan flterng, B-Splnes, Cardnal splnes, Genetc algorthm Introducton Obect recognton s an mportant goal for computer vson systems to enable the understandng of mages []. The use of curvature or domnant ponts [-5] on an unknown obect boundary has been proven to be an effectve means for recognton of obect shapes. Most of the current obect recognton nvolves matchng the nput mage wth a set of predefned models of obect. If the mages are nvarant to varous fluctuatons of nput mage, ths leads to the problem of recognton. It s necessary to use many of the known rotated obects precompled, creatng a model database, and ths database to large to use. In ths research, n order to solve the problem as mentoned above, we use Gaussan flterng whch are extracts the domnant ponts from the edge of bnary mages. Then we use the B-Splne or Cardnal Splne to compute the control ponts or data ponts for creatng the model shapes. The matchng process uses the data from tranng database to measure the smlarty between the unknown mages wth random data from the tranng database whch determne by genetc algorthm. The research shows the effectveness of the B-Splne and Cardnal Splne to buld the database and the selectng ponts usng the GA for matchng. The detal of recognton procedure wll be llustrated n the followng sectons. Centrodal Profle Representaton The centrodal profle s characterzed by an ordered sequence that represents the dstance from the dgtzed boundary of the obect to ts centrod as a functon of dstance along the boundary. A smple obect s shown n fgure (a) and ts correspondng centrod profle s llustrated n Fg. (b). The centrod (X c, Y c ) s estmated usng the followng formula:

2 Proceedngs of the 5th WSEAS Int. Conf. on Sgnal Processng, Robotcs and Automaton, Madrd, Span, February 5-7, 6 (pp4-45) X Y c c x y () () where s the number of the boundary ponts n an obect. ext, the dstances d (),,, from centrod to the boundary ponts {x, y,, }, are computed startng from an arbtrary poston of the boundary and trackng the boundary n a counterclockwse drecton. Usng as dstance measure the Eucldean norm we have: d() (a) (b) pxel d () ( x x ) + ( y y ),,,. c c (3) d() After, the dstance functon s calculated by convolvng the dstance functon of the boundary pont d () wth the Gaussan flterng [3] : (c) pxel g t σ, ( t σ ) e π σ (4) d() In ths paper, we selected the scale-space flterng σ3. The ponts of local maxma and mnma are determned from the smooth dstance functon are llustrated n Fg. (d) and are assgned as the reference ponts (Fg. (e)) to break the boundary of the shape as boundary ponts. ext, we dvde a half of ponts between these reference ponts. If the ponts that are dvded have lengths over % of the number of boundary ponts, pont dvson begn agan as llustrated n Fg. (f). Thus, the B-splnes control ponts of obect are llustrated Fg. (g), and as features present of obect. (e) (d) ( (f) pxel 3 B-Splnes Representaton B-splnes are pecewse polynomal curves that are guded by a set of ponts called the control ponts (CPs). The CPs are blended wth a set of functons called the blendng functons. Any pont on the curve segment s gven by a parametrc from as P n ( u ) v ( u ), k (5) wth u as the parameter, v,,, n are the n+ control ponts, and,k (u),,,,n are the (k-)th degree blendng functons. They can be evaluated recursvely from (g) Fg..A smple obect and boundary representatons: (a)a clpper; (b) centrodal representaton; (c)smooth usng Gaussan flter; (d-e) local maxma and mnma;(f) reference ponts of obect; (g) control ponts.

3 Proceedngs of the 5th WSEAS Int. Conf. on Sgnal Processng, Robotcs and Automaton, Madrd, Span, February 5-7, 6 (pp4-45) where, f o r t <u<t +, (u), otherwse (6),k (u) +, (7) ( u t ), k ( u ) ( t t ) + k ( t + k u ) +, k ( u ) ( t t ) + k +,, k,3,4,. 4 Cardnal Splnes Representaton The prncple of the Cardnal splnes s based on calculaton wth 4 ponts that are together, ponts, that defne the begnnng and the end, and other pont that defne the slope. The curve P k and P k+ s defned by P k P and k P P through the k k parameter t whch s called the tenson parameter. Ths parameter controls the shape of the curve. P k- P k P(u) P k+ The blendng functons are non-zero only for an nterval gven by the degree of the polynomal. Cubc polynomals are most often preferred because they also preserve contnuty of curvature at the pont on the curve. Snce the CPs are regeneratve, they yeld a large compresson of the boundary data. Scale, translaton and rotaton of the shape result n smlar transformaton of the CPs. Consder fgure whch shows a pecewse curve oned wth curvature contnuty,.e. cubc polynomal. For the segment the blendng functons that take non-zero values are, respectvely, -,4 (u),,4 (u), +,4 (u), +,4 (u). P + + u P u - Fg.. pecewse contnuous curve. We let the parameter u take on values between and for each of the spans and let the ponts, p () p for,, n- and p n- () p n. (9) For closed curves, v v n+, v n and the B-splne equatons can be reformulated n a matrx [] form as, 4. v p 4. v p /6. (). 4 v n p n P k+ Fg.3. pont of cardnal splne When set p k-, p k, p k+ and p k+ are control pont. Any pont on the curve segment s gven by a parametrc form as P(u) P k- A(u)+ P k B(u)+ P k+ C(u)+ P k+ U(u) () When A(u) -Su 3 + Su -Su B(u) (-S)u 3 + (S-3)u + C(u) (S-)u 3 + (3-S)u +Su D(u) Su 3 -Su U (poston pont of pcture between P k and P k+ )/5 When S (.-t)/. ; < t < Ths paper t s. 5 Shape Representaton The boundary ponts from the centrodal profle of the obect represented by a set of ponts p s s chosen on the boundary of the obect from whch the computed ponts. As we dscussed n ths Secton, control ponts are extracted from the boundary ponts. The centrod was used as the central reference pont, and the dstance between each control pont and the centrod s computed. The ten length maxma are selected stored n a prvleged segment. In the followng, we assume prvleged segments that are both the model, and the nput (scene) descrpton. These are gven the form: ( l, θ I, p ), for,,.., where l s the length between

4 Proceedngs of the 5th WSEAS Int. Conf. on Sgnal Processng, Robotcs and Automaton, Madrd, Span, February 5-7, 6 (pp4-45) control pont and centrod, θ s the control pont orentaton measured relatve to the horzontal axs, and p s the poston of the control pont from the control ponts segment. (l l,θ,p ) (l,θ,p ) ( l l,θ,p ) (x,y ) (x,y ) (x,y ) Prvleged Segment Fg. 4. Shape descrpton. Control Pont Segment Fgure 4 shows examples of the shape descrpton of the model shapes and nput shapes. From fgure 4, control ponts are stored n a control pont segment. The number of control ponts nvolved n these descrpton ranges between 8 and 4. Genetc algorthms (GAs)[6,7,8] are general purpose search technques based on prncples nspred from the genetc, and evoluton mechansms observed n natural systems, and populatons of lvng begns. A GA s usually mplemented accordng to the followng steps: 5. Chromosome Representaton In ths paper, a bnary strng bult from the matchng model shape, the prvleged of the model shape, and the prvleged of the nput shape represents the chromosome. Each part s encoded nto a four-bt representaton, resultng n a chromosome wth bts. A populaton of chromosomes was employed n the algorthm. Example: The followng s an example ndvdual: [( ), ( ),...] Ths ndvdual to the frst feature of the frst model shape mapped the thrd feature of the nput shapes. 5. Ftness Functon The model poston was defned by a transformaton T, the product of a rotaton, a scalng, and a translaton. The transformaton T descrbed by a parameter vector v (k.cosθ, k.snθ, tx, ty), such as the mage (x*, y*) of an arbtrary pont (x, y) of the model descrpton was gven by the set of equatons x* tx+x.k.cosθ - y.k.snθ (a) y* ty+x.k.snθ + y.k.cosθ. (b) Ftness was calculated by testng the compatblty of the nput shapes features, and the correspondng model shape feature. The dfference between nput shapes I feature, and model feature M was measured by mean of a dfference functon d r, as defned below: d r ( X I X ) + ( Y Y I ), (3) where X I, Y s the I th feature of the nput I shape and (X, Y) was calculated usng the followng formula: X tx + X. s.cosθ y. s. snθ (4a) Y ty + X. s.snθ + y. s. cosθ (4b) and ( l ) ( ) s / l (5a) θ θ θ (5b) tx X s ( X cos θ Y snθ ) (5c) ty Y s ( X sn θ + Y cos θ ) (5d) where (X, Y ) s the th feature of the M th model shape. Ftness functon was calculated usng the followng formula: Ftness ( reman n r ( ) d r + ( unassgned nput or model features )) (6) 6 Expermental In the experments, we tested ths proposed method to the nvarant obects recognton. The obect shapes were represented by the computed ponts, whch were computed by the B-Splne or Cardnal Splne. The shape of obect was composed the length dstances between the centrod and computed ponts, the angles of computed pont orentaton, and the coordnate of computed ponts respectvely. The learnng set conssts of 5 reference obects (Fg.) that have 3x3 pxels. The parameters of all model shapes were stored n the database. In the recognton stage, the genetc algorthm searches models n the database to select a model that has the best-match sequence wth nput mage. The feature of the purposed method conssts of bt strngs. The populaton sze s, and the number of selected strngs for mutaton probablty for each bt was.33. The number of terated generatons was

5 Proceedngs of the 5th WSEAS Int. Conf. on Sgnal Processng, Robotcs and Automaton, Madrd, Span, February 5-7, 6 (pp4-45) 5, wth a suffcent number for obtanng the soluton. The proposed methodology was used to nvarant obect recognton, such as the examples n fgure. The nput mage that has dfferent orentaton was captured by dgtal camera. The system was tested wth obects that have 7 dfferent rotatons (totalng 5 mages of obects), 4 dfferent szes (totalng 6 mages of obects), and 3 dfferent rotatons and szes (totalng 48 mages of obects),. These obects were obtaned under the same llumnaton condtons. Fg.7 Example of scaled obects. (a) b) b) ( ( (c) (d) (e) (f) Fg. 8 Example of both scaled and rotated obects. 6. The B-Splne recognton results are shown n Table. (g) (h) () ( ) (k) (l) (m) (n) (o) Fg.5 Example of Reference obects. Fg.6 Example of rotated obects. Tables : Recognton accuracy (%). Rotated Scaled Rotated and Obect Obects Obects scaled obects a 94 b 94 c 75 8 d 7 8 e f g h k l m n 97 o 97 Average

6 Proceedngs of the 5th WSEAS Int. Conf. on Sgnal Processng, Robotcs and Automaton, Madrd, Span, February 5-7, 6 (pp4-45) 6. The Cardnal-Splne recognton results are shown n Table. Table Recognton accuracy (%). Obect Rotated Obects Scaled Obects Rotated and scaled obects a 93.7 b c 93.7 d e f g h k 93.7 l m n o 95.9 Average Concluson In ths partcular research, we studed nvarant obect recognton usng the control ponts of B- splne and data ponts of Cardnal splne wth genetc algorthms. Genetc Algorthms have been proven to be powerful methods n search, optmzaton and machne learnng. Expermental results show that the genetc algorthm has been successful n shape-matchng experments attempted so far. The algorthm s fast, and explores a relatvely small number of elements of the search space. However, a -D obect can have dfferent shapes dependng upon the poston, orentaton, and sze. The boundary shapes of the obect were composed of the control and data ponts. The method s adusted to be ndependent of translaton, scalng, and rotaton, by usng relatve dstances of computed ponts to the centrod. The advantage of the centrodal profle s reference ponts tend to be a stable pont of reference for the obect. In the case of features beng data ponts, usng cardnal splne extractng drectly from the boundary ponts wthout usng the nverse matrx, the experment shows that ths method s better than usng control ponts of the B-Splne method. To compare other methods, for example the Gaussan Flter [3] whch has a ratng recognton less than the other mentoned, because the number of domnant ponts recognzed by the Gaussan Flter s less. Many of the ponts are lost. As for Convex Factor [4] and the Corner Detector [5] these have a recognton less than the Gaussan Flter. The corner Detector s the fastest of them all, yet has the worst recognton. The man advantages of the Cardnal splne and B- splne recognton system are as follows: Feature ponts stored n a database are between 8-4 features for Cardnal splne and not over 6 features for B-splne; the recognton method was adusted to be ndependent of transformaton such as translaton, scalng, and rotaton; t used prvleged segments to calculate orentaton, scalng, and translaton. References: [] D. Ballard and C. Brown, Computer Vson, Prentce Hall, Englewood Clffs, 98. [] R. Chn, and C. Dyer, Model-Based recognton n robot vson, Compungt.Surveys, Vol. 8, o., 986, pp [3] S. Fotong, P. Phokharatkul, O. Pngern, and C. Kmpan, Invarant Obect Recognton Usng Domnant Ponts and Genetc Algorthms, Proceedngs of the Internatonal Conference on Robotcs, Vson, Informaton and Sgnal Processng, 3, pp [4] P. Phokharatkul, S. Fotong, and C. Kmpan, Obect Recognton Usng Characterstc Component and Genetc Algorthms, IEEE Regon Internatonal Conference on Electrcal and Electronc Technology,, pp [5] S. Fotong, C. Kmpan, and P. Phokharatkul, Invarant Obect Recognton Usng Shape Descrptors and Genetc Algorthms, World Multconference on Systemcs, Cybernetcs and Informatcs, Vol.VI,, pp [6] Endor Ozcan, and Chlukur K.Mohan, Shape recognton usng Genetc algorthms. Proceedng of IEEE Internatonal Conference on Evolutonary Computaton, 966, pp [7] P.W.M. Tsang, A Genetc for Affne Invarant Obect Shape Recognton., Genetc Algorthm n Engneerng System: Innovatons and Applcatons, 995, Conference Publcaton o. 44. [8] D.E. Glodberg, Genetc Algorthms n Search, Optmzaton, and Machne Learnng, Addson Wesley, 989.

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