Shape-Sable Region Bonday Exacion via Affine Mophological Scale Space (AMSS) Peos Kapsalas School of Elecical & Compe Engineeing, aional Technical Univesiy of Ahens 9, Ioon Polyechnio s., 5773 Ahens, Geece +30-0-773039 pkaps@image.na.g Sefanos Kollias School of Elecical & Compe Engineeing, aional Technical Univesiy of Ahens 9, Ioon Polyechnio s., 5773 Ahens, Geece +30-0-77488 sefanos@cs.na.g ABSTRACT In his pape we pesen a new appoach owads he exacion of affine image egions based on deecing shape-sable bondaies fom a mli-scale image epesenaion. We consc an affine mophological scale space (AMSS) epesenaion [], which pefoms anisoopic diffsion while peseving bondaies and being invaian o affine ansfomaions. We exac he ansiion bondaies of he diffsiviy velociy map and ack hei evolion a each level of he scale-space. We hen deemine he sabiliy of he bonday shape hogh a minimizaion pocess ove diffeen scales. Unlike mos sae of he a deecos which se he Gassian scale space fo mli-scale image epesenaion, o appoach is ininsically affine invaian. We evalae o deeco by measing epeaabiliy of egions in ansfomed images of he same scene and compaing i o he sae-of-he-a egion deecos [].. ITRODUCTIO In many objec ecogniion asks, wihin-class changes in pose, lighing, colo, and exe can case consideable vaiaion in local inensiies. Conseqenly, local inensiy no longe povides a sable deecion ce. As sch, inensiy-based inees opeaos (e.g., Hais, Kadi [3][4]) and he objec ecogniion sysems based on hem ofen fail o idenify disciminaive feaes. An alenaive o local inensiy ces is o cape semi-local scal ces sch as edges and cvilinea shapes [5]. These scal ces end o be moe obs o inensiy, colo, and pose vaiaions. As sch, hey povide he basis fo a moe sable inees opeao, which in n impoves objec ecogniion accacy. This pape poposes a egion deeco based on affine image epesenaion. The mehod inodces a new egion exacion scheme ha explois cvilinea sces o eliably deec salien aeas. The poposed Shape Sable Region Bondaies (SSRB) deeco idenifies sces of sable shape wihin he affine invaian image epesenaion. Cvilinea sces ae lines (eihe cved o saigh) sch as oads in aeial o saellie images o blood vessels in medical scans. These cvilinea sces can be deeced ove a ange of viewpoins, scales, and illminaion changes. We develop a pocess ha deecs scal egions efficienly and obsly acoss he levels of he Affine Mophological Scale Space (AMSS). The basic idea of he appoach is o exploi opology of ansiion bondaies beween neighboing image sces. In ode o povide sfficien deeminaion of hese egions we se a mahemaical fomalizaion ha ilizes he fndamenal popey of he AMSS which associaes scale-space diffsiviy velociy.o bonday occence. Ina-egion smoohing is favoed owads ine-egion smoohing which means ha poins close o ineegion bondaies ae evolved wih highe velociies. The basic idea of he appoach is o ack he evolion of significan image sces acoss he pyamid scales and selec he sces of inees in ems of shape sabiliy cieia. Ths, he ansiion bondaies beween neighboing image sces ae indicaed by locaing he maxima of diffsiviy velociy. Sbseqenly, shape feaes of he exaced bondaies ae evalaed. Scale selecion is associaed o finding shape sable sces, and he sabiliy is deemined hogh he minimizaion of Eclidean disance egading sces shape feaes along conseqen pyamid levels. This wok makes wo conibions. Fis, we develop a new opeao based on mophological epesenaion fo esimaing ansiion bondaies beween diffeen sces while we also ilise scale space popeies o enhance bondaies conneciviy. Second, we inodce an exended definiion of sce sabiliy which is based on esimaing he vaiaion of shape feaes. The lae conibion is employed in ode o ake advanage of he mophological scale space epesenaion ha we have embodied in he exacion scheme and which in n especs image sces, wiho disbing hei shape. Secion pesens elaed wok, while he poposed mehod is descibed in Secion 3. An expeimenal sdy is pesened in Secion 4, compaing o appoach o he bes sae-of-he-a mehods. Conclsions and descipion of fhe wok ae given in Secion 5.. RELATED WORK Inees opeaos can ypically be classified ino wo caegoies: inensiy-based deecos and sce-based deecos []. Inensiy-based deecos depend on analyzing local diffeenial
geomey o inensiy paens o find poins o egions ha saisfy some niqeness and sabiliy cieia. The Hais-affine and Hessian-affine deecos [3][6][7] compe maximm deeminans of he second momen maix and he Hessian maix especively acoss scale space and hen apply Laplacian-based chaaceisic scale selecion[8]and second-momen-maix-based shape adapaion [9]. Maximally Sable Exemal Regions (MSER) [] ses a heshold selecion pocess o deec sable egions ha ae eihe bighe o dake han he sonding egion. Shif Invaian Feae Tansfom [] (SIFT) (i.e., he Diffeence of Gassians (DoG) exema deeco sed by Lowe in []) finds local exema acoss hee consecive diffeence-of- Gassian scales and hen emoves spios deecions via a DoGesponse heshold followed by a Hais-like meic o eliminae edge deecions. Kadi s salien egion deeco [4] calclaes he enopy of he pobabiliy densiy fncion (PDF) of inensiy vales ove vaios scales o find egions wih enopy exema. Ohe inensiy-based deecos inclde SUSA (aconym of he mehod defined by he em Smalles Univale Segmen Assimilaing cles) [4] [][3], Inensiy (exema-)based Regions (IBR) [][5], and he wok of Moavec[][5]and Beade [][6]. Sce-based deecos depend on scal image feaes sch as lines, edges, cves, ec. o define inees poins o egions. Ealy sce-based deecos analyze vaios D cves sch as he cvae pimal skech o B-splines exaced fom edges, idges, oghs, ec. and hen seleced high cvae poins, line o cve inesecions, cones, ends, bmps, and dens as inees poins [][3]. Tyelaa s Edge-Based Region (EBR) deeco [9] fis a paallelogam defined by Hais cone poin and poins on wo adjacen edge conos (exaced by he Canny deeco). Scale-Invaian Shape Feaes (SISF) deecs cicles a diffeen locaions and scales by evalaing salien convex aangemens of canny edges based on a mease ha maximizes how well a cicle is sppoed by sonding edges. 3. SHAPE STABLE REGIO BOUDARY As discssed above, we aim a deecing covaian egions along he mli-scale epesenaion. The fis diffeence wih he ohe sae-of-he-a mehods is ha we conside a ly affine invaian scale-space insead of adaping he linea scale-space. The affine invaian scale space is defined hogh he following paial diffeenial eqaion pesened below: D cv 3 () 0,. () 0 The implied noaion in he above eqaion is: D denoes he gadien and cv denoes he cvae of he level. The evolion scheme is based on diffsive inepeaion of he eqaion. Indeed, if ξ is ni veco sch ha 0 and he second deivaive of in he diecion ξ we have:. This fomlaion yields an anisoopic opeaion, in he sense ha diffsion akes place only in he ξ diecion depending on he gadien (compae wih he isoopic diffsion i.e., he hea eqaion). Eqaion () can be ewien as 3 3 whee 3 denoes he speed of diffsion. The lae evolion em is consideed hee as he diffsiviy velociy and i is sed o discen adjacen sces wihin he same image. Exploiing he mahemaical popeies of he diffsiviy velociy opeao we can conclde ha i highlighs egions belonging o ansiion bondaies while smoohing ina-egion sces. The opeabiliy of o Shape-Sable-Region-Bonday exacion appoach can be smmaized hogh he following seps:. The AMSS Scale Space epesenaion is consced.. The Diffsiviy Velociy Map is exaced a each sage of he Scale-Space (egions of high velociy levels coespond o ansiion bondaies) 3. Boken bondaies ae esolved by a win hesholding scheme which consides he velociy diecion in adjacen poins. Accoding o he anisoopic diffsion heoy, each image poin P is evolved wih a velociy faco nomal o he angen a he specific poin. Ths, velociy vecos a wo adjacen poins of he same cve fom an angle of 0 0. Based on he above popey we esolve conneciviy isses by consideing he minimizaion of he velociies inenal vecos a wo adjacen image locaions. 4. Bonday shape feaes (momens) ae exaced a each sage of he scale-space and a feae veco is consced, ha shold be invaian acoss a ange of geomeical ansfomaions. To achieve his, nomalized momens ae employed in his appoach. Assming ha he shape bonday has been epesened as a shape feae signae z(i), he h momen m and cenal momen μ can be esimaed as: m z i (3) i (4) z i m i Whee is he nmbe of bonday poins. The nomalized momens 3 3 m m and ae invaian o shape anslaion, oaion and scaling 5. The Eclidean disance beween feae vecos of he coesponding aeas is meased. 6. A egion is consideed o be sable when is feae veco does no change significanly along consecive levels of he scale space (he 3 boom sages of he exacion pocess will be efeed o as popagaion sage ) 4 EVALUATIO We fis smmaize he famewok fo evalaing disingished egion epeaabiliy. A descipion of he expeimens and a discssion of he esls follow. (a)
addiion, he egions ae ansfomed o have a nomalised size befoe calclaing he ovelap, o avoid he poblems wih egions of diffeen sizes discssed in []. (b) 4. Expeimens & Discssion The esls of he epeaabiliy and nmbe of coespondences - ess fo he fo gops of six images in he daase ae shown in Figes (a)-(h). Cves coesponding o six mehods ae shown in each gaph. The cves labelled MSER and Hessian-affine coespond o he wo bes pefoming mehods of he six esed in he evalaion of affine covaian egion deecos in [] (c) (a) Gaf Repeaabiliy (b) Wall Repeaabiliy (d) Fige : Pa of he evalaion daase. (a) Viewpoin change, (b) viewpoin change, (c), (d) Zoom + oaion 4. Evalaion Famewok Repeaabiliy meases he exen o which egions deeced in ansfomed images of he same scene ovelap. We se he evalaion famewok pesened in []. The famewok consiss of eigh images, whee each image is sbjeced o five ansfomaions, esling in ses of six images. Examples fom he image ses ae shown in Fige. The homogaphies beween he efeence images and he ohe images fo each se have been comped, allowing he ovelap beween disingished egions in he efeence and anohe image o be evalaed. In [], only ellipical disingished egions ae consideed, as hese ae ininsically podced by fo of he six algoihms esed in []. Fo he ohe algoihms, ellipses appoximaing he egions ae chosen. To be compaible wih he famewok, we also fi ellipses o he edges of he egions podced by he poposed mehods, sing he ellipse fiing algoihm in [9]. Repeaabiliy is meased beween he efeence image and anohe image fom he se. The disingished egions ae deeced in boh images and hose fom he second image ae pojeced ono he efeence image by sing he known homogaphy. Two egions ae said o fom a egion-o-egion coespondence if he ovelap eo is sfficienly small in his pape we se a vale of 0.4 as was done fo he expeimens in []. The ovelap eo is defined as [] R R T H b H (5) R R T whee R H b H is he egion enclosed by he ellipse defined by x T x and H is he homogaphy elaing he images. The epeaabiliy scoe fo a pai of images is he aio beween he nmbe of egion-o-egion coespondences and he smalle nmbe of egions in he pai of images. Only egions locaed in he pa of he scene pesen in boh images ae coned. In (c) Boa Repeaabiliy, (e)gaff Coespodences, (g)boa Coespondences (d) Bak Repeaabiliy (f) Wall Coespodences (h) Bak Coespondences Fige : The epeaabiliy and nmbe of coespondences (a, b, e, f) viewpoin angle vaiaion, (c, d, g, h) vaiaion of scale change As has aleady been poined o in [], diffeen algoihms pefom bee fo diffeen ansfomaions, as can be seen by he epeaabiliy esls fo he MSER and Hessian-affine deecos. The poblem of compaing deecos podcing diffeen densiies of egions is discssed in []. They poin o ha fo deecos ha podce few egions, he hesholds can be se so ha he pefomance is ofen bee han aveage. Fo deecos ha podce many egions, he image may be so cleed wih egions
ha some ge mached by acciden. The Hessian-affine deeco podces he lages nmbe of coespondences fo each image seqence excep Wall, indicaing ha he densiy of he disingished egions is highe. Fo he viewpoin changes (Fige (a),(b)), he MSER deeco has he highes epeaabiliy. Fo he Gaffii, Bak and Boa images he SSBR algoihm povided good epeaabiliy scoes which ae compaable o MSER ones, while fo he case of he boa seqence, SSBR opefoms MSER. In an effo o explain he chaaceisics of SSBR esponse we shold iniially exploi is poenial o exac eliable sces in images pesening significan edge sces. (gaffii, boa seqence). A fhe isse egads he SSBR invaiance owads viewpoin angle change. The expeimenal esls show ha he mehod povides qie consideable epeaabiliy scoes when lage image sces ae enconeed in he image. One of he dawbacks of he evalaion famewok sed is ha he diffeence in he nmbe of egions (egion densiy) exaced by each algoihm is no aken ino accon, which cold affec he epeaabiliy esls In an effo o povide visal evalaion of o poposed egion exacion appoach we illsae SSBR deeced in some images obained fom he Calech daabase. Fige 3 shows he symmeical deecions is seveal images. We can see ha he deeced egions ae qie accae and disincive, poviding a valable ce fo he deecion and ecogniion of symmeical objecs. hem b poviding qie compaable esls. One of he dawbacks of he evalaion famewok sed is ha he diffeence in he nmbe of egions (egion densiy) exaced by each algoihm is no aken ino accon, which cold affec he epeaabiliy esls. We have so fa sed shape feaes o mease he sabiliy of he exaced egions. Howeve, he deived esls cold be enhanced by e-consideing some ohe image sces chaaceisics sch as egion exen o enopy. A fhe diecion ha cold benefi he exacion of sable egions is o associae egion acking o image evolion as he lae cold be deived by he AMSS evolion law. 5 REFERECES [] Alvaez, L., Gichad, F., Lions, P. L., Moel, J. M., Axioms and Fndamenal Eqaions of Image Pocessing, J. of Ach. Raional Mech. Anal., 3 (993), pp. 99-57. [] Mikolajczyk, K., Tyelaas, T., Schmid, C., Zisseman, A., Maas, J., Schaffalizky, F., Kadi, T., Van Gool, L, 005, A compaison of affine egion deecos. Inenaional Jonal of Compe Vision, (005), 65(/), 43 7 [3] Hais, C., and Sephens, M, 988, A combined cone and edge deeco. Alvey Vision Conf., (988), 47 5 [4] Kadi, T., and Bady, M, 00, Scale, saliency and image descipion, 00, IJCV, 45():83 05,. [5] Sege, C., 998, An nbiased deeco of cvilinea sces.(998), PAMI, 0():3 5. [6] Mikolajczyk, K. and Schmid, C., 00. An affine invaian inees poin deeco, 00,. ECCV, ():8 4, [7] Mikolajczyk K., and Schmid, C., 004, Scale and affine invaian inees poin deecos. IJCV, (004), 60():63 86 [8] Lindebeg, T., 998, Feae deecion wih aomaic scale selecion. (998) IJCV, 30(), 79 6,. Fige 3: Salien egion exacion sing SSBR 5. COCLUSIOS AD FURTHER WORK This pape has pesened a new sce-based inees egion deeco called Shape Sable Region Bondaies (SSBR) and has demonsaed is sccessfl applicaion o seveal asks. The SSBR inees opeao deecs sable egion bondaies wihin he affine mophological scale space epesenaion ha descibes boh edge and cvilinea sces. Anisoopic diffsion popeies o ack he evolion and enhance he conneciviy of shape sable bondaies along wih a new shape sabiliy esimaion scheme ae inodced in his wok. Fhe, SSBR achieves obs deecion acoss mliple scales by selecing sable egions acoss consecive scales. Expeimens measing he epeaabiliy of he exaced egions fo diffeen ypes of image ansfomaions ae pesened. The obained epeaabiliy falls ino he ange of he epeaabiliy of he mos effecive algoihms esed in [], wiho spassing [9] Lindebeg, T., and Gading, J., 997, Shape-adaped smoohing in esimaion of 3-d shape ces fom affine defomaions of local -d bighness sce. (997), Image and Vision Comping, pages 45 434. [0] Bambeg, A., 000, Reliable feae maching acoss widely sepaaed views. (000) CVPR, pages 774 78. [] Maas, J., Chm, O., Uban, M., and Pajdla. T., 004, Robs widebaseline seeo fom maximally sable exemal egions, (004), Image and Vision Comping, (0):76 767. [] Lowe, D. G., 004, Disincive image feaes fom scale-invaian Keypoins, (004), IJCV, 60():9 0. [3] Smih, S., and Bady, J. M,.997, Ssan a new appoach o low level image pocessing, (997),. IJCV, 3(), 45 78 [4] Tyelaas, T., and Gool, L. V., 000, Wide baseline seeo maching based on local, affinely invaian egions., (000), BMVC, pages 4 45. [5] Moavec, H., 977, Towads aomaic visal obsacle avoidance, (977). Inenaional Join Conf. on Aificial Inelligence, page 584. [6] Beade, P., 978, Roaionally invaian image opeaos. (978), ICPR, pages 579 58