Object Localization by Subspace Clustering of Local Descriptors

Transcription

1 Object Localzaton by Subspace Clusterng of Local Descrptors C. Bouveyron 1, J. Kannala 2, C. Schmd 1 and S. Grard 1 1 INRIA Rhône-Alpes, 655 avenue de l Europe, Sant-Ismer, France 2 Machne Vson Group, dept. of Electrcal and Informaton Engneerng, Unversty of Oulu, Fnland Abstract. Ths paper presents a probablstc approach for object localzaton whch combnes subspace clusterng wth the selecton of dscrmnatve clusters. Clusterng s often a key step n object recognton and s penalzed by the hgh dmensonalty of the descrptors. Indeed, local descrptors, such as SIFT, whch have shown ecellent results n recognton, are hgh-dmensonal and lve n dfferent low-dmensonal subspaces. We therefore use a subspace clusterng method called Hgh-Dmensonal Data Clusterng (HDDC) whch overcomes the curse of dmensonalty. Furthermore, n many cases only a few of the clusters are useful to dscrmnate the object. We, thus, evaluate the dscrmnatve capacty of clusters and use t to compute the probablty that a local descrptor belongs to the object. Epermental results demonstrate the effectveness of our probablstc approach for object localzaton and show that subspace clusterng gves better results compared to standard clusterng methods. Furthermore, our approach outperforms estng results for the Pascal 2005 dataset. 1 Introducton Object localzaton s one of the most challengng problems n computer vson. Earler approaches characterze the objects by ther global appearance and are not robust to occluson, clutter and geometrc transformatons. To avod these problems, recent methods use local mage descrptors. Many of these approaches form clusters of local descrptors as an ntal step; n most cases clusterng s acheved wth k-means or EMbased clusterng methods. Agarwal and Roth [1] determne the spatal relatons between clusters and use a Sparse Network of Wndows classfer. Dorko and Schmd [2] select dscrmnant clusters based on the lkelhood rato and use the most dscrmnatve ones for recognton. Lebe and Schele [3] learn the spatal dstrbuton of the clusters and use votng for recognton. Bag-of-keypont methods [4,5] represent an mage by a hstogram of cluster labels and learn a Support Vector Machne classfer. Svc et al. [6] combne a bag-of-keypont representaton wth probablstc latent semantc analyss to dscover topcs n an unlabeled dataset. Opelt et al. [7] use AdaBoost to select the most dscrmnant features. However, vsual descrptors used n object recognton are often hgh-dmensonal and ths penalzes classfcaton methods and consequently recognton. Indeed, clusterng methods based on the Gaussan Mture Model (GMM) [8] show a dsappontng behavor when the sze of the tranng dataset s too small compared to the number

2 2 C. Bouveyron, J. Kannala, C. Schmd and S. Grard of parameters to estmate. To avod overfttng, t s therefore necessary to fnd a balance between the number of parameters to estmate and the generalty of the model. Many methods use global dmensonalty reducton and then apply a standard clusterng method. Dmenson reducton technques are ether based on feature etracton or feature selecton. Feature etracton bulds new varables whch carry a large part of the global nformaton. The most popular method s Prncpal Component Analyss (PCA) [9], a lnear technque. Recently, many non-lnear methods have been proposed, such as Kernel PCA [10]. Feature selecton, on the other hand, fnds an approprate subset of the orgnal varables to represent the data [11]. Global dmenson reducton s often advantageous n terms of performance, but loses nformaton whch could be dscrmnant,.e., clusters often le n dfferent subspaces of the orgnal feature space and a global approach cannot capture ths. It s also possble to use a parsmonous model [12] whch reduces the number of parameters to estmate by fng some parameters to be common wthn or between classes. These methods do not solve the problem of hgh dmensonalty because clusters usually le n dfferent subspaces and many dmensons are rrelevant. Recent methods determne the subspaces for each cluster. Many subspace clusterng methods use heurstc search technques to fnd the subspaces. They are usually based on grd search methods and fnd dense clusterable subspaces [13]. The approach mture of Probablstc Prncpal Component Analyzers [14] proposes a latent varable model and derves an EM based method to cluster hgh-dmensonal data. A smlar model s used n [15] n the supervsed framework. The model of these methods can be vewed as a mture of constraned Gaussan denstes wth class-specfc subspaces. An unfed approach for subspace clusterng n the Gaussan mture model framework was proposed n [16]. Ths method, called Hgh Dmensonal Data Clusterng (HDDC), ncludes the prevous approaches and nvolves addtonal regularzatons as n parsmonous models. In ths paper, we propose a probablstc framework for object localzaton combnng subspace clusterng wth the selecton of the dscrmnatve clusters. The frst step of our approach s to cluster the local descrptors usng HDDC [16] whch s not penalzed by the hgh-dmensonalty of the descrptors. Snce only a few of the learned clusters are useful to dscrmnate the object, we then determne the dscrmnatve score of each cluster wth postve and negatve eamples of the category. Ths score s based on a mamum lkelhood formulaton. By combnng ths nformaton wth the posteror probabltes of the clusters, we fnally compute the object probablty for each vsual descrptor. These probabltes are then used for object localzaton,.e., localzaton assumes that ponts wth hgher probabltes are more lkely to belong to the object. We evaluate our approach on two recently proposed object datasets [7,17]. We frst compare HDDC to standard clusterng methods wthn our probablstc recognton framework. Eperments show that results wth HDDC are consstently better than wth other clusterng methods. We then compare our probablstc approach to the state of the art results and show that t outperforms estng results for object localzaton. Ths paper s organzed as follows. Secton 2 presents the EM-based clusterng method HDDC,.e., the estmaton of the parameters and of the ntrnsc dmensons of the subspaces. In Secton 3, we descrbe the probablstc object localzaton frame-

3 Lecture Notes n Computer Scence 3 work. Epermental results for our approach are presented n Secton 4. We conclude the paper n Secton 5. 2 Hgh-Dmensonal Data Clusterng Ths secton presents the clusterng method HDDC [16]. Clusterng dvdes a gven dataset { 1,..., n } of n data ponts nto k homogeneous groups. Popular clusterng technques use Gaussan Mture Models (GMM). The data { 1,..., n } R p are then modeled wth the densty f(, θ) = k =1 π φ(, θ ), where φ s a mult-varate normal densty wth parameter θ = {µ, Σ } and π are mng proportons. Ths model estmates the full covarance matrces and therefore the number of parameters s very large n hgh dmensons. However, due to the empty space phenomenon we can assume that hgh-dmensonal data lve n subspaces wth a dmensonalty lower than the dmensonalty of the orgnal space. We therefore propose to work n low-dmensonal class-specfc subspaces n order to adapt classfcaton to hgh-dmensonal data and to lmt the number of parameters to estmate. Here, we wll present the parameterzaton of GMM desgned for hgh-dmensonal data and then detal the EM-based technque HDDC. 2.1 Gaussan Mture Models for Hgh-Dmensonal Data We assume that class condtonal denstes are Gaussan N(µ, Σ ) wth means µ and covarance matrces Σ, = 1,..., k. Let Q be the orthogonal matr of egenvectors of Σ, then = Q t Σ Q s a dagonal matr contanng the egenvalues of Σ. We further assume that s dvded nto two blocks: 9 a 1 0 =... 0 ; d 0 a d 9 = b 0 0. >=.. (p d ) 0 b >; where a j > b, j = 1,..., d. The class specfc subspace E s generated by the d frst egenvectors correspondng to the egenvalues a j wth µ E. Outsde ths subspace, the varance s modeled by a sngle parameter b. Fnally, let P () = Q t Q ( µ ) + µ be the projecton of on E, where Q s made of the d frst columns of Q supplemented by zeros. Fgure 1 summarzes these notatons. The mture model presented above wll be n the followng referred to by [a j b Q d ]. By fng some parameters to be common wthn or between classes, we obtan partcular models whch correspond to dfferent regularzatons. For eample, f we f the frst d egenvalues to be common wthn each class, we obtan the more restrcted model [a b Q d ]. Ths model s n many cases more robust,.e., the assumpton that the matr contans only two egenvalues a and b seems to be an effcent way to regularze the estmaton of. In ths paper, we focus on the models [a j b Q d ], [a j bq d ], [a b Q d ], [a bq d ] and [abq d ].

4 4 C. Bouveyron, J. Kannala, C. Schmd and S. Grard E P () d(, E ) E X µ d(µ, P ()) P () Fg. 1. The specfc subspace E of the th mture component. 2.2 EM Estmaton of the Model Parameters The parameters of a GMM are usually estmated by the EM algorthm whch repeats teratvely epectaton (E) and mamzaton (M) steps. In ths secton, we present the EM estmaton of the parameters for the subspace GMM. The E-step computes, at teraton q, for each component = 1,..., k and for each j ). Usng the Bayes formula and the parameterzaton of the model [a j b Q d ], the probablty t (q) j can be epressed as follows (the proof of the followng result s avalable n [16]): data pont j = 1,..., n, the condtonal probablty t (q) j t (q) j = π (q 1) k l=1 π(q 1) l φ( j, θ (q 1) ) φ( j, θ (q 1) l ) = 1/ k l=1 = P( j C (q 1) ( ) 1 ep 2 (K ( j ) K l ( j )), where K () = 2 log(π φ(, θ )) s called the cost functon and s defned by: K () = µ P () 2 A + 1 d P () 2 + log(a j )+(p d )log(b ) 2 log(π ), b where. A s a norm on E such that 2 A = t A wth A = Q 1 t Q. We can observe that K () s manly based on two dstances: the dstance between the projecton of on E and the mean of the class and the dstance between the observaton and the subspace E. Ths cost functon favours the assgnment of a new observaton to the class for whch t s close to the subspace and for whch ts projecton on the class subspace s close to the mean of the class. The varance terms a j and b balance the mportance of both dstances. For eample, f the data are very nosy,.e., b s large, t s natural to weght the dstance P () 2 by 1/b n order to take nto account the large varance n E. The M-step mamzes at teraton q the condtonal lkelhood and uses the followng update formulas. The proportons, the means and the covarance matrces of the j=1

5 Lecture Notes n Computer Scence 5 mture are classcally estmated by: ˆπ (q) n = n(q) n, ˆµ(q) j=1 = t(q) j j, n (q) ˆΣ(q) = 1 n t (q) n (q) j=1 j ( j ˆµ (q) )( j ˆµ (q) ) t. where n (q) = n j=1 t(q) j. The ML estmators of model parameters are n closed form for the models consdered n ths paper. Proofs of the followng results are gven n [16]. Subspace E : the d frst columns of Q are estmated by the egenvectors assocated wth the d largest egenvalues λ j of ˆΣ. Model [a j b Q d ]: the estmator of a j s â j = λ j and the estmator of b s: ˆb = 1 (p d ) Tr( ˆΣ d ) j=1 λ j. (1) Model [a j bq d ]: the estmator of a j s â j = λ j and the estmator of b s: 1 k ˆb = (p ξ) Tr(Ŵ) d ˆπ λ j, (2) where ξ = k =1 ˆπ d and Ŵ = k =1 ˆπ ˆΣ s the estmated wthn-covarance matr. Model [a b Q d ]: the estmator of b s gven by (1) and the estmator of a s: =1 j=1 â = 1 d λ j. (3) d Model [a bq d ]: the estmators of a and b are respectvely gven by (3) and (2). Model [abq d ]: the estmator of b s gven by (2) and the estmator of a s: j=1 â = 1 ξ k d ˆπ λ j. (4) =1 j=1 2.3 Intrnsc Dmenson Estmaton Wthn the M step, we also have to estmate the ntrnsc dmenson of each classspecfc subspace. Ths s a dffcult problem wth no eact soluton. Our approach s based on the egenvalues of the class condtonal covarance matr Σ of the class C. The jth egenvalue of Σ corresponds to the fracton of the full varance carred by the jth egenvector of Σ. We estmate the class specfc dmenson d, = 1,..., k, wth the emprcal method scree-test of Cattell [18] whch analyzes the dfferences between successve egenvalues n order to fnd a break n the scree. The selected dmenson s the one for whch the subsequent dfferences are smaller than a threshold. In our eperments the value used for ths threshold was 0.2 tmes the mamum dfference. The resultng average value for dmensons d was appromately 10 n the eperments presented n Secton 4.

6 6 C. Bouveyron, J. Kannala, C. Schmd and S. Grard 3 A Probablstc Framework for Object Localzaton In ths secton, we present a probablstc framework for object localzaton whch computes for each local descrptor j of an mage the probablty P( j O j ) that j belongs to a gven object O. It s then easy to precsely locate the object by consderng only the local descrptors wth hgh probabltes P( j O j ). We frst etract a set of local nvarant descrptors usng the Harrs-Laplace detector [19] and the SIFT descrptor [20]. The dmenson of the obtaned SIFT features s 128. An nterest pont and ts correspondng descrptor are n the followng referred to by j. 3.1 Tranng Durng tranng we determne the dscrmnatve clusters of local descrptors. We frst cluster local features and then dentfy dscrmnatve clusters. Tranng can be ether supervsed or weakly supervsed. In the weakly supervsed scenaro the postve descrptors nclude descrptors from the background, as only the mage s labeled as postve. Clusterng. Descrptors of the tranng mages are organzed n k groups usng the clusterng method HDDC. From a theoretcal pont of vew, the descrptors j of an mage are realzatons of a random varable X R p wth the followng densty f() = k =1 π φ(, θ ) = τf O () + (1 τ)f B (), where f O and f B are respectvely the denstes of descrptors of the object and of the background and τ denotes the pror probablty P(O). The parameter τ s equal to k =1 R π, where R = P(C O). The densty f can thus be rewrtten as follows: f() = k R π φ(, θ ) + =1 } {{ } Object k (1 R )π φ(, θ ). =1 } {{ } Background The clusterng method HDDC provdes the estmators of parameters π and θ, = 1,..., k and t thus remans to estmate parameters R, = 1,..., k. Identfcaton of dscrmnatve clusters. Ths step ams to dentfy dscrmnatve clusters by computng estmators of parameters R. Postve descrptors are denoted by P and negatve ones by N. The condtonal ML estmate of R = {R 1,..., R k } satsfes: ˆR = argma P( j O j ) P( j B j ) R. j P The epresson of the gradent s: R = j P Ψ j < R, Ψ j > j N j N Ψ j 1 < R, Ψ j >, where Ψ j = {Ψ j } =1,...,k and Ψ j = P( j C j ) whch are provded by HDDC. The ML estmate of R does not have an eplct formulaton and t requres an teratve

7 Lecture Notes n Computer Scence 7 optmzaton method to fnd ˆR. We observed that the classcal gradent method converges towards a soluton very close to the least square estmator ˆR LS = (Ψ t Ψ) 1 Ψ t Φ, where Φ j = P( j O j ). In our eperments, we use ths least square estmator of R n order to reduce computaton tme. We assume for ths estmaton that j P, P( j O j ) = 1 and j N, P( j O j ) = 0. Thus, R s a measure for the dscrmnatve capacty of the class C for the object O. 3.2 Object Localzaton Durng recognton we compute the probablty for each local descrptor of a test mage to belong to the object. Usng these probabltes, t s then possble to locate the object n a test mage,.e., the descrptors of an mage wth a hgh probablty to belong to the object gve a strong ndcaton for the presence of an object. Usng the Bayes formula we obtan the posteror probablty of an descrptor j to belongs to the object O: P( j O j ) = k R P( j C j ), (5) =1 where the posteror probablty P( j C j ) s gven by HDDC. The object can then be located n a test mage by usng the ponts wth the hghest probabltes P( j O j ). For comparson wth estng methods we determne the boundng bo wth a very smple technque. We compute the mean and varance of the pont coordnates weghted by ther posteror probabltes gven by (5). The mean s then the center of the bo and a default boundng bo s scaled by the varance. 4 Eperments and Comparsons In ths secton, we frst compare HDDC to standard clusterng technques wthn our probablstc localzaton framework on the Graz dataset [7]. We then compare our approach to the results on the Pascal 2005 dataset [17]. 4.1 Evaluaton of the Clusterng Approach In the followng, we compare HDDC to the several standard clusterng methods wthn our probablstc localzaton framework: dagonal Gaussan mture model (Dagonal GMM), sphercal Gaussan mture model (Sphercal GMM), and data reducton wth PCA combned wth a dagonal Gaussan mture model (PCA + dag. GMM). The dagonal GMM has a covarance matr defned by Σ = dag(σ 1,..., σ p ) and the sphercal GMM s characterzed by Σ = σ Id. In all cases, the parameters are estmated wth the EM algorthm. The ntalzaton of the EM estmaton was obtaned usng k-means and was eactly the same for both HDDC and the standard methods. For ths evaluaton, we use the bcycle category of the Graz dataset whch s conssts of 200 tranng mages and 100 test mages. We determned 40 clusters wth each clusterng method n a weakly supervsed settng.

8 8 C. Bouveyron, J. Kannala, C. Schmd and S. Grard Clusterng HDDC [ Q d ] Classcal GMM Result method [a jb ] [a jb] [a b ] [a b] [ab] PCA+dag Dag. Sphe. of [2] Precson Table 1. Object localzaton on Graz: comparson between HDDC and other methods. Precson s computed on segmented mages wth on average 10 detectons per mage (.e., detectons such that P( j O j) > 0.9). All detectons HDDC PCA+dag. GMM Dag. GMM Fg. 2. Object localzaton on Graz: localzaton results dsplayed on groundtruth segmentatons. We dsplay the ponts wth hghest probabltes P( j O j). The same number of ponts s dsplayed for all models (5% of all detectons whch s equal to 12 detectons per mage). The localzaton performance was evaluated usng segmented mages [7]. Table 1 summarzes localzaton performance of the compared methods as well as results presented n [2]. Precson s the number of ponts wthn the object regon wth respect to the total number of selected ponts. We can observe that the HDDC models gve better localzaton results than the other methods. In partcular, the model [a b Q d ] obtans best results,.e., a precson of 92% when consderng ponts wth P( j O j ) > 0.9. We also observe that a global dmenson reducton wth PCA does not mprove the results compared to dagonal GMM. Ths confrms our ntal assumpton that data of dfferent clusters lve n dfferent low-dmensonal subspaces and that a global dmenson reducton technque s not able to take ths nto account. Fgure 2 shows localzaton results on segmented test mages wth the dfferent methods. The left mage shows all nterest ponts detected on the test mages. The boundng boes are computed wth the dsplayed ponts,.e., the ponts wth the hghest probabltes n the case of the three rght most mages. It appears that our localzaton method dentfes precsely the ponts belongng to the object and consequently s able to locate small objects n dfferent postons, poses and scales whereas other methods do not gve an effcent localzaton. 4.2 Comparson to the State of the Art For ths second eperment, we compare our approach to the results on the Pascal vsual object class 2005 dataset [17]. It contans four categores: motorbkes, bcycles, people and cars. It s made of 684 tranng mages and two test sets: test1 and test2. We chose to evaluate our method on the set test2, whch s the more dffcult one and contans 956 mages. Snce the boundng boes of the objects are avalable for all categores we evaluate our method wth supervsed as well as a weakly supervsed tranng data. In the supervsed case only the descrptors located nsde the boundng boes are labeled as postve durng tranng. Here we use 50 clusters for each of the four categores. We

9 Lecture Notes n Computer Scence 9 Clusterng Supervsed Weakly-supervsed method Moto Bke People Car Aver. Moto Bke People Car Aver. HDDC Best of [17] / / / / / Table 2. Average precson (AP) for supervsed and weakly-supervsed localzaton on Pascal test2. The result n talc s the average result of the best method of the Pascal challenge [17]. (a) motorbke (b) car (c) two cars Fg. 3. Supervsed localzaton on Pascal test2: predcted boundng boes are n magenta and true boes n yellow. use the model [a b Q d ] for HDDC, snce the prevous eperment has shown that t s the most effcent model. To compare wth the results of Pascal Challenge [17], we use the localzaton measure average precson (AP) whch s the arthmetc mean of 11 values on the precson-recall curves computed wth ground-truth boundng boes (see [17] for more detals). The localzaton results on Pascal test2 are presented n Table 2 for supervsed and weakly supervsed tranng data. In the supervsed case, Table 2 shows that our probablstc recognton approach performs well compared to the results n the Pascal competton. In partcular, our approach wns two compettons (bcycle and people) and s on average more effcent than the methods of the Pascal challenge. Ths s despte the fact that our approach detects only one boundng bo per mage for each category and ths reduces the performance when multple objects are present, as shown n the rght part of Fgure 3. Notce that our approach has the best overall performance although we do not have any model for the spatal relatonshps of the local features. We can also observe that our weakly-supervsed localzaton results are only slghtly lower than the ones n the supervsed case and on average better than the Pascal results n the supervsed case. Ths means that our approach effcently dentfes dscrmnatve clusters of each object category and ths even n the case of weak supervson. There are no correspondng results for the Pascal Challenge, snce all competng methods used supervsed data. It s promsng that the weakly supervsed approach obtans good localzaton results because the manual annotaton of tranng mages s tme consumng.

10 10 C. Bouveyron, J. Kannala, C. Schmd and S. Grard 5 Concluson The man contrbuton of ths paper s the ntroducton of a probablstc approach for object localzaton whch combnes subspace clusterng wth the selecton of dscrmnatve clusters. Ths approach has the advantage of usng posteror probabltes to weght nterest ponts. We proposed to use the subspace clusterng method called HDDC desgned for hgh-dmensonal data. Epermental results show that HDDC performs better than other Gaussan models for locatng objects n natural mages. Ths s due to the fact that HDDC correctly models the groups n ther subspaces and thus forms more homogeneous groups. In addton, our method performs well also n the weakly-supervsed framework whch s promsng. Fnally, our approach provdes better results than the state of the art methods and that usng only one type of detector and descrptor (Harrs-Laplace+Sft). We beleve that the results could be further mproved usng a combnaton of descrptors as n [2,5]. Also, the localzaton results presented here are based on a very smple spatal model whch can be easly mproved to further ncrease the performance of our approach. References 1. Agarwal, S., Roth, D.: Learnng a sparse representaton for object detecton. In: 7th European Conference on Computer Vson. Volume 4. (2002) Dorko, G., Schmd, C.: Object class recognton usng dscrmnatve local features. Techncal Report 5497, INRIA (2004) 3. Lebe, B., Schele, B.: Interleaved object categorzaton and segmentaton. In: Brtsh Machne Vson Conference, Norwch, England (2003) 4. Wllamowsk, J., Arregu, D., Csurka, G., Dance, C., Fan, L.: Coategorzng nne vsual classes usng local appareance descrptors. In: Internatonal Workshop on Learnng for Adaptable Vsual Systems, Cambrdge, UK (2004) 5. Zhang, J., Marszalek, M., Lazebnk, S., Schmd, C.: Local features and kernels for classfcaton of teture and object categores. Techncal report, INRIA (2005) 6. Svc, J., Russell, B., Efros, A., Zsserman, A., Freeman, W.: Dscoverng objects and ther locaton n mages. In: Internatonal Conference on Computer Vson. (2005) 7. Opelt, A., Fussenegger, M., Pnz, A., Auer, P.: Weak hypotheses and boostng for generc object detecton and recognton. In: European Conference on Computer Vson. Volume 2. (2004) McLachlan, G., Peel, D.: Fnte Mture Models. Wley Interscence, New York (2000) 9. Jollffe, I.: Prncpal Component Analyss. Sprnger-Verlag, New York (1986) 10. Schölkopf, B., Smola, A., Müller, K.: Nonlnear component analyss as a kernel egenvalue problem. Neural Computaton 10 (1998) Guyon, I., Elsseeff, A.: An ntroducton to varable and feature selecton. Journal of Machne Learnng Research 3 (2003) Fraley, C., Raftery, A.: Model-based clusterng, dscrmnant analyss and densty estmaton. Journal of Amercan Statstcal Assocaton 97 (2002) Parsons, L., Haque, E., Lu, H.: Subspace clusterng for hgh dmensonal data: a revew. SIGKDD Eplor. Newsl. 6 (2004) Tppng, M., Bshop, C.: Mtures of probablstc prncpal component analysers. Neural Computaton 11 (1999)

11 Lecture Notes n Computer Scence Moghaddam, B.: Prncpal Manfolds and Probablstc Subspaces for Vsual Recognton. IEEE Trans. on Pattern Analyss and Machne Intellgence 24 (2002) Bouveyron, C., Grard, S., Schmd, C.: Hgh-Dmensonal Data Clusterng. Techncal Report 1083M, LMC-IMAG, Unversté J. Fourer Grenoble 1 (2006) 17. Everngham, M., Zsserman, A., Wllams, C., Gool, L.V., et al.: The 2005 PASCAL vsual object classes challenge. In: Frst PASCAL Challenge Workshop. Sprnger (2006) 18. Cattell, R.: The scree test for the number of factors. Multvarate Behavoral Research 1 (1966) Mkolajczyk, K., Schmd, C.: Scale and affne nvarant nterest pont detectors. Internatonal Journal of Computer Vson 60 (2004) Lowe, D.: Dstnctve mage features from scale-nvarant keyponts. Internatonal Journal of Computer Vson 60 (2004)