在计算机视觉中,形状的表示和相似性衡量是重要且复杂的问题,提出了一种改进的SUSAN(最小一致性区域)拐点检测算法并用于形状表示,同时基于Delaunay三角化给出了一个用于形状相似性衡量的有效算法。首先,对形状的拐点进行Delaunay三角形构造,然后从Delaunay三角网中获得Delaunay图矩阵,最后使用矩阵的谱对拐点进行匹配。在含有1 400幅图像的MPEG-7 CE-Shape-1数据库中的检索实验进一步验证了算法的有效性。Shape representation and similarity measure are important and difficult problems in computer vision and have been extensively studied for decades.This paper presents an enhanced SUSAN(Smallest Univalue Segment Assimilating Nucleus) Corner Detector for shape representation and an effective algorithm to establish shape similarity measure based on Delaunay triangulation.Firstly,delaunay triangulation was constructed among corners of each shape which has been normalized in advance.Secondly,the Delaunay graph matrix was achieved from Delaunay triangulation net.Finally,the corners were matched by using spectrum of the graph matrix.Shape retrieval Experiments have been conducted on the MPEG-7 Core Experiment CE-Shape-1 database of 1 400 images which illustrate good performance of the algorithm.National 985 Project(0000-X07204);National 863 Plan(2006AA01Z129

姜青山

洪志令

魏昕路

Xiamen University Institutional Repository

第 25卷　第 4期2007年 12月　　　　广西师范大学学报:自然科学版Jou rna l o f Guangx iN o rm a lU n iv e rsity: N atura l S cience Ed ition　　　　V o .l 25　N o. 4Dec. 2007R ece ived date: 2007-04-30Foundation item: N a tiona l 985 P ro ject ( 0000-X 07204); N at ion al 863 P lan ( 2006AA 01Z 129)Corre spond ing author: JIANG Q ing-shan( 1962— ), m a le, bo rn in Q uebec, C anada, P ro fesso r o f X iam en U nive rsity. E-m a il: qjiang@ xm u. edu. cnSh ape Rep resen ta tion and S im ilar ity M easu re Basedon De launay T riangu lationHONG Zhi-ling1, JIANG Q ing-shan2,WEIX in-lu2( 1. Depar tm ent o f C om pu te r S cience, X iam en U n ive rsity, X iam en 361005, Ch in a;2. S choo l o f So ftw are, X iam en U n iv e rsity, X iam en 361005, Ch ina )Abstract: Shape repre sen ta tion and sim ilar ity m easu re are im po r tan t and d ifficu lt p rob lem s in com pu te r v is ionand h ave been ex ten siv e ly stud ied fo r decades. Th is pape r p resen ts an enhanced SU SAN ( Sm a lle st U n iva lueSegm ent A ss im ila ting N ucleus ) C o rne r De te cto r fo r shape repre sen ta tion and an e ffec tiv e a lg o r ithm toe stab lish shape sim ilar ity m ea sure based on De launay tr iangu lation. F irs tly, de launay tr iangula tion w ascon structed am ong co rner s o f each shape w h ich ha s been no rm a lized in advance. Second ly, the De launayg raph m a tr ix w as ach ieved from De launay tr iangu la tion net. F ina lly, the co rne rs w e re m a tched by usingspectrum o f the g raph m a tr ix. Shape re triev al E xpe rim en ts have been conducted on the M PEG -7 Co reExper im en t CE-Sh ape-1 database o f 1 400 im ages w h ich illu stra te g ood pe rfo rm ance o f the a lg o r ithm.Keywords: shape repre sen ta tion; shape s im ila r ity m easu re; SUSAN ; de launay tr iangu la tion; g raph spec trumCLC number: T P 391　　　D ocum ent code: A　　　A rtic le ID: 1001-6600( 2007) 04-0261-04Shape rep resenta t ion and shape sim ilar ity m ea su re in im age s a re necessa ry com ponen t o f any usefu lim age ret rieva l sy stem. T he re is a va riety o f techniques tha t has been propo sed in the litera tu re fo r shaperep resenta t ion[ 1～ 3]. Co rner is one o f the most w idely used in a ll shape rep re sen tat ion m e thods. H ow todetect co rne rs in an im age is a cla ssica l p rob lem and m any de tecto rs have been p ropo sed[4, 5 ]. Sm ith andB rady[4 ]in t rodu ced a straigh tfo rw a rd m e thod ca lled SU SAN by ex tract ing the po r tion o f fea tu rene ighbo rhoods tha t is o f sim ilar in tensity v a lues. SU SAN is no t sensit iv e to no ise and the accuracy andspeed o f the alg o rithm a re reasonab le, bu t ou r expe rim en ts show th at the resu lt is st ill no t sat isf ied andthere a re room s fo r im provem en t. T h is paper presen ts an enhan ced SU SAN fo r co rner detect ion.A f ter co rne r de tect ion, co rne r m atch ing is a com pu ta t ional ly intensive task. A numbe r o fappro aches have been propo sed to addre ss the theo re t ica l and applied issues o f co rne r m a tch ing[ 6]. Inth is paper, w em a tch co rners be tw een tw o im ages b ased onD e launay T riangu la t ions. B ased onD e launayT riangu lat ions, som e shape sim ila rity m easure m e thods have been propo sed. In [ 2 ], featu re po in th istog ram w h ich com pu ted by coun ting the tw o largest in terio r ang les o f each indiv idua l D e launayt riang le is used fo r sim ilar ity m easu re. T he d istan ce be tw een tw o shapes is then sim p ly the L 2-distancebe tw een the h istog ram s. In [7 ], it first ob ta in the sim ilar tr iang le pa irs, and then ex tend the ir edgescircu la rly un t il al lm atch ing co rne rs a re t riangu lated andm ism a tch ing co rners are disca rded.1　Enhanced SU SAN co rner detecto rIn [4 ], Sm ith and B rady in t rodu ced a straigh tfo rw a rd m e thod ca lled SU SAN. G iven a dig ita lim age, the U SAN areaw ill reach a m in im um w hen the nucleus lies on a co rner po in t. W e presen t a newco rner de tec tion a lgo r ithm by im p rov ing the SU SAN co rner detecto r in the fo llow ing th ree aspec ts.F irst, w e lim it the search space fo r co rne rs candidates so th at the a lgo r ithm becom es m o re ef ficien t.Second, w e adop t an adapt ive th resho ld st ra teg y based on lo ca l br igh tness in stead o f one th resho ld fo rthe w ho le im age. T hird, w e rem ove the fa lse o r the am b iguous co rne rs acco rd ing to a co rne rcon tr ibu tion m easurem e thod.Based on fact tha t a co rner is an end o f an edge, w e on ly need to search fo r co rners f rom po ints onedges in stead o fw ho le im age. T herefo re, the alg o rithm first pe rfo rm s edge detect ion by Sobe l opera to r.T hen from the edges select po in ts w ho se values o fm easu re a re above a th resho ld as co rner cand ida tes.T he se lection o f the th re sho ld o f b righ tness dif fe rence is a key to pe rfo rm ance o f the SU SANope ra to r because d ifferen t resu lts are ob tained fo r d if feren t th resho lds. In this pape r, w e adopt O tsu[ 8]adap t ive th re sho ld a lgo rithm w h ich dete rm ines the th resho ld b ased on lo ca lb righ tness. O tsu is based ona very sim ple idea: f ind the thresho ld tha tm inim izes the w e igh ted w ith-in class va riance. T h is tu rns ou tto be the sam e as m ax im izing the be tw een-class v ar iance. O tsus ope ra t ion is done direc tly on the g rayleve l h isto g ram, so its v ery fast.A ll o f the local m inimum s are conside red as co rner candidates, includ ing the false co rne rs.Fo llow ing crite rion is used to rem ove them. In gene ra l, aw e ll-def ined co rne r shou ld have a sh arp ang leand tw o re la tiv e long edges. T he pro cess o f rem ov ing fa lse co rners is done acco rd ing to relev ancem easu reR g iven by: R i= (θi×L i×L i+ 1 ) / (L i+ L i+ 1 ). W he reθi is the tu rn ang le at the po in tP i, L i, andL i+ 1 a re the tw o re la t iv e edges w h ich have been no rm a lized w ith respect to the to ta l leng th o f a po ly gona lcurveC. T he h igher the va lue o fR i, the larg er is the con tribu t ion to the shape o f the cu rv e. If the tu rnang leθi and the tw o relat ive edges L i and L i+ 1 a re sm a ll, andR i is be low a th resho ld, the po in t P iw ill bet rea t a s a fa lse co rner, and being rem oved.2　Co rner m a tch ing based on de launay triangu la tionT he propo sed co rne r m a tch ing a lgo rithm is based on De launay T r iang les. T he a lgo rithm f irstconst ructs the De launay T riang les andD elaunay g raph m atrix, and thenm a tches co rners using spect rumo f the g raph m a tr ix.　　Le tX= {p 1, p 2,… , pn } be a set o f po in ts in the tw o d im ensional Eu clidean p lane, nam ely the sites.F ig. 1　Vo rono i d iag ram and de launaytriangu la tionPar t it ion the p lane by labe ling each po in t in the plane to it s neare st. A ll tho se po in ts labe led as p i fo rmthe V o rono i reg ion V (p i ). V (p i ) consists o f all the po in ts xs at least a s clo se to p i to any o ther site[2 ]:V (p i )= { x:|p i- x|≤|p j - x|, j≠ i}.T he se t o f a ll po ints tha t h avem o re than one nea rest site fo rm theV o rono i diag ram V (p ) fo r the seto f site s. T he D elaunay triangu la t ionD (p ) is the em bedd ing o f the dua l g raph o f the V o rono i diag ramV (p ) w here the nodes o fD ( p ) are the site s o f V ( p ), and tw onodes a re connected by an arc if the ir co rre sponding V o rono ipo lyg ons sha re aV o rono i edge. E ach face o fD (p ) is a t riang le, asshow n in fig 1.　　 W ith the D elaunay t riangu la tion, w e con stru ct D e launayg raphm atrix. T he g raph is deno ted byG= (V, E ), w hereV is these t o f co rner nodes, and E V×V is the edge-se t. Fo r the g raphG, w e com pu te the ad jacency m atrix A. T h is is a |V|×|V|m a trix w ho se e lem en t w ith row index i and co lum n index j is262 广西师范大学学报: 自然科学版　　　　　　　　　　　　　　　　第 25卷A ( i, j )=1　　 if( i, j )∈ E0　　 o therw ise.　　 Based on the D elaunay g raph m a trix, the co rner fea tu re can be der iv ed and de scribed as fo llow s.F rom the ad jacency m a tr ix A, w e can ca lcu la te the e ig enva luesλby so lv ing the equa t ion|A -λI|= 0 andthe associated eig envecto rsX by so lv ing the sy stem o f equa t ions AXw= λwXw , w herew is the e ig enm odeindex. W e o rde r the e igenva lue s acco rd ing to the decreasing m agn itude o f the eig enva lues, i. e. |λ1|> |λ2|> … > |λ|V||. T he spect rum F eature fo r the co rne r represen ta tion is const ructed f rom the f irst teno rde red eig enva lues o f the ad jacency m a trix.3　Experim en ta l resu lts3. 1　Corner de tection( a) P lane im age　　　　　 ( b) H a rr is de tec to r　　　 　 ( c) SU SAN de tec to r ( d) Im proved SUSAN de tec to rF ig. 2　E xam ple o f co rne r de tectionW e at tem p tedm any d ifferen t im ages, bu t on ly one sam ple is being depicted here. F ig. 2 show s theco rner detect ion resu lts by H arr is de tecto r[9 ], SU SAN[4 ]and ou r im proved SU SAN a lg o rithm. C o rnersare indicated by sm all circ le. 3 and 4 false co rne rsw ere detected by H arr is and SU SAN de tecto rs, w h ile8 and 3 co rne rs w e re m issed. H ow eve r, no false co rne r w as de tected o r any co rner w as m issed byimp roved SU SAN a lgo r ithm w e propo sed h ere. T ab le 1 show s the com pa risons o f co rne r de tect ion.3. 2　 Shape image retrievalW e perfo rm sh ape im age re trieva l expe rim ent using the M PEG -7 C o re E xpe rim ent CE-Shape-1da tabase to evalua te the pe rfo rm ance o f DTM a lgo rithm. T he da tabase consists o f 70 dif feren t cla sses o fshapes, each class conta ining 20 sim ilar ob jects, u sual ly ( heav ily ) d isto rted versions o f a sing le baseshape. T hew ho le data se t the re fo re con sists o f 1 400 shapes. E ach im age w as used a s a query, and theret rieva l rate is exp ressed by the Bu lls Eye Pe rcen tag e (BEP): the fract ion o f im ages tha t be long to thesam e cla ss in the top 40m a tches. S ince them ax imum num ber o f co rrectm a tches fo r a sing lequery im ageis 20, the to ta l num ber o f co rrect m a tches is 28 000. T he overall re tr iev al ra te is com pu ted as the rat ioo f the to ta l num ber o f actua l co rrect m atches and the to ta l num ber o f possib le co rrectm atches.Tab. 1　Com par isons of corner de tec tionE valua tions H a rr is SUSAN Im proved SU SANFa lse Co rne rs 3 4 0M iss C o rne rs 8 3 0Tab. 2　 Performance of sim ilar itymeasure sEva lua tions H isto g ram DTMBEP 47 49　　W e com pare ou r m e thod ( sho rt in DTM ) w ith De launay tr iangu la t ion shape rep resenta t ion w ithh istog ram[2 ]( sho r t in H istog ram ). T he ret rieva l perfo rm ance is show n in tab le 2. It is obse rved tha t ou rm ethod ou tpe rfo rm ed by bo th theH istog ram m e thod.4　 C onclus ion sT h is paper p ropo sed an enhanced co rner detecto r based on SU SAN alg o rithm. T h e im p rovem en ts263第 4期　　　　　　　　　洪志令等: 基于 De launay三角化的形状表示与相似性衡量include three aspects. A com pa rison expe rim en ts dem on strated tha t th is enhanced SU SAN g ive s m o reaccu ra te and stab le re su lts.T h is paper also propo sed an alg o rithm to estab lish shape sim i larity m easu re based on D e launayt riangu la tion (DTM ). S ince the spect rum o f De launay g raph m a trix robu st to no ises and can describeshape im ages bet ter, the p roposed a lgo r ithm is robust and ef fec tive in shape im age re trieva l.References:[ 1] M EH TRE B M, KANKANHA LL IM S, LEE W F. Shapem easu res fo r con ten t based im age re trieva l: a com par ison[J ]. Info rm at ion P rocessing & M an agem en t, 1997, 33( 3): 319-337.[ 2] TAO Y, G RO SKY W I. De launay tr iangu lation fo r im age ob je ct index ing: a nove l m e thod fo r shape representa tion[C ] / / P ro ceeding s o f the Seventh SP IE Sym posium on S to rag e and Re tr iev a l fo r Im age and V ideo Da taba sesⅦ .C a lifo rn ia: U niv ers ity o fW ayne S ta te, 1999: 631-942.[ 3] SHAHAB I C, SA FAR M. A n exper im en ta l study o f a lte rnat iv e shape-based im age re triev a l techn iques [ J]. M u ltim ed iaT oo ls and App licat ion s, 2007, 32( 1): 29-48.[ 4] SM ITH S M , BRA DY JM . SUSAN—— a new app roach to low leve l im age p rocessing [ J]. In terna tiona l Journa l o fCom pu ter V ision, 1997, 23( 1): 45-78.[5 ] H E X iao-ch en, YUNG N H. C urva ture sca le space co rner de tec to r w ith adap tiv e thre sho ld and dynam ic reg ion o fsuppo r t [C ] / / P ro ceed ing s o f 17th In te rna tiona l C onference on Pa ttern Recogn ition: V o lum e 2. W ash ing ton DC: IEEECom pu te r Society, 2004: 791-794.[ 6 ] ZHAO Feng, HUANG Q ing-m ing, GAO W en. Im age m a tch ing by m u ltisca le o riented co rner co rre la tion [C ] / /P ro ceed ing o f 7 th A sian Conference on C om puter V ision. H yde rabad, Ind ia: Spr inger, 2006: 928-937.[ 7] ZHOU Dong-x iang, L IG an-hua, L IU Y un-hu i. E ffectiv e co rner m a tch ing ba sed on de launay tr iangula tion [C ] / /IEEEIn terna tiona l Confe rence on Robo tics and A u tom at ion. N ew O rleans, LA: IEEE C om pu te r S oc ie ty, 2004: 2730-2735.[ 8] OT SU N. A thre sho ld se lect ion m ethod from g ray-leve l h istog ram [J ]. IEEE T rans on Sy stem, M an and Cybem eticsSM C-9, 1979: 62-66.[ 9 ] HARR IS C, STEPHEN S M . A com b ined co rne r and edge de tecto r [C ] / /A lv ey V ir ion C on fe rence. M ach ester:U n iv er sity o f M anche ste r, 1987: 147-151.基于 D e launay三角化的形状表示与相似性衡量洪志令1,姜青山2, 魏昕路2( 1. 厦门大学计算机科学系,福建 厦门 361005 ; 2. 厦门大学软件学院,福建 厦门 361005)摘　要: 在计算机视觉中,形状的表示和相似性衡量是重要且复杂的问题,提出了一种改进的 SU SAN (最小一致性区域 )拐点检测算法并用于形状表示, 同时基于 De launay三角化给出了一个用于形状相似性衡量的有效算法。首先,对形状的拐点进行 De laun ay三角形构造,然后从 De launay三角网中获得 De launay图矩阵,最后使用矩阵的谱对拐点进行匹配。在含有 1 400幅图像的M PEG -7CE -Shape-1数据库中的检索实验进一步验证了算法的有效性。关键词: 形状表示; 形状相似性衡量; SU SAN; De launay三角化; 图谱中图分类号: T P391　　　　文献标识码: A　　　　文章编号: 1001-6600( 2007) 04-0261-04(责任编辑　马殷华 )264 广西师范大学学报: 自然科学版　　　　　　　　　　　　　　　　第 25卷

Shape Representation and Similarity Measure Based on Delaunay Triangulation

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Shape Representation and Similarity Measure Based on Delaunay Triangulation

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