Multiclass Road Sign Detection using Multiplicative Kernel

Transcription

1 Proceeding of the Croatian Computer Viion Workhop, Year 1 Multicla Road Sign Detection uing Multiplicative Kernel Valentina Zadrija Mireo d. d. Zagreb, Croatia valentina.zadrija@mireo.hr Siniša Šegvić Faculty of Electrical Engineering and Computing Univerity of Zagreb Zagreb, Croatia inia.egvic@fer.hr Abtract We conider the problem of multicla road ign detection uing a claification function with multiplicative kernel compried from two kernel. We how that problem of detection and within-foreground claification can be jointly olved by uing one kernel to meaure object-background difference and another one to account for within-cla variation. The main idea behind thi approach i that road ign from different foreground variation can hare feature that dicriminate them from background. The claification function training i accomplihed uing SVM, thu feature haring i obtained through upport vector haring. Training yield a family of linear detector, where each detector correpond to a pecific foreground training ample. The redundancy among detector i alleviated uing k- medoid clutering. Finally, we report detection and claification reult on a et of road ign image obtained from a camera on a moving vehicle. Keyword multicla object detection; object claification; road ign; SVM; multiplicative kernel; feature haring; clutering I. INTRODUCTION Road ign detection and claification i an exciting field of computer viion. There are variou application of the road ign detection and claification in driving aitance ytem, autonomou intelligent vehicle and automated traffic inventorie. The latter one i of particular interet to u ince traffic inventorie include periodical on-ite aement carried out by trained afety expert team. Current road condition i then manually compared againt the reference tate in the inventory. In current practice, the proce i tediou, error prone and cotly in term of expert time. Recently, there have been everal attempt to at leat partially automate the proce [1], [2]. Thi paper preent an attempt to partially automate thi proce in term of road ign detection and claification uing the multiplicative kernel. In general, detection and claification are typically two eparate procee. The mot common detection method i liding window approach, where each window in the original image i evaluated by a binary claifier in order to determine whether the window contain an object. When the propective object location are known, claification tage i applied only on the reulting window. One common claification approach Thi work ha been upported by reearch project Vita (EuropeAid/131920/M/ACT/HR) and Reearch Centre for Advanced Cooperative Sytem (EU FP7 #285939). include partitioning the object pace into ubclae and then training a dedicated claifier for each ubcla. Thi approach i known a one-veru-all claification. In thi paper, we focu on detection and claification of ideogram-baed road ign a a one-tage proce. We employ a jointly learned family of linear detector obtained through Support Vector Machine (SVM) learning with multiplicative kernel a preented in [3]. In it original form, SVM i a binary claifier, but multiplicative kernel formulation enable the multicla detection. Multiplicative kernel i defined a a product of two kernel, namely between-cla kernel k x and within-cla kernel k a decribed in Section IV. Betweencla kernel k x i dedicated for detection, i.e. the foregroundbackground claification. Within-cla kernel k i ued for within-foreground claification, i.e. to dicriminate between variou object ubclae. The reult of SVM training i a et of upport vector and correponding weight which are then ued to generate a family of detector. The detector are obtained by tuning within-cla tate into the multiplicative kernel a decribed in Section IV-B. The key point here i that all detector hare the ame upport vector, but weight of pecific upport vector vary depending on the within-cla tate value. We evaluate the decribed approach on a et of predefined road ign ubclae defined in Section III and preent experimental reult in Section V. II. RELATED WORK In recent year, a lot of work ha been propoed in the area of multicla object detection. We will addre the iue from both road ign detection apect a well a general multicla object detection and feature haring. The approach preented in [4] trie to olve multi-view face detection problem. Foreground cla i partitioned into ubclae according to variation in face orientation. For each ubcla, a correponding detector i learned. Thi approach exhibit everal problem when ued with a larger number of ubclae. More pecifically, number of feature, number of fale poitive and the total training time grow linearly with the number of ubclae. Poter Seion 37

2 Proceeding of the Croatian Computer Viion Workhop, Year 1 Fig. 1. Ditribution of ample with repect to road ign ubclae S = {1, 2, 3, 4, 5} for training dataet. Below each ubcla label v, repreentative ubcla member are hown. Road ign hown for ubcla v=1 are informal, i.e. ubcla contain 9 different road ign. Further, author in [5] focu on feature haring uing JointBoot procedure. In contrat to [4], where number of feature grow linearly with the number of ubclae, the author have experimentally hown that the number of feature grow logarithmically with repect to the number of ubclae. Additionally, the author howed that a jointly trained detector require a ignificantly maller number of feature in order to achieve the ame performance a a independent detector. The approach preented in [6] deal with problem of multiview detection uing the o called Vector Booted Tree procedure. At the detection time, the input i examined by a equence of node tarting from the root node. If the input i claified by the detector of current node a a member of the object cla, it i paed to the node children. Otherwie, it i rejected a a background. The drawback of thi approach i that it require the uer to predefine the tree tructure and chooe the poition to plit. Similar to [6], the approach preented in [7] alo employ a claifier tructured in a form of a tree. However, in contrat to [6], the tree claifier i contructed automatically - the node plit are achieved through unupervied clutering. The algorithm i iterative, i.e. at the beginning it tart with an empty tree and training ample which are aigned weight. By adding a node to the tree, the ample weight are modified accordingly. Additionally, if a plit i achieved, parent claifier of all node along the way to the root node are modified. The concept of feature haring i alo explored through hape-baed hierarchical compoitional model [8], [9], [10]. Thee model are ued for object categorization [8], [10], but alo for multi-view detection, [9]. Different object categorie can hare part or appearance. Part on lower hierarchy level are combined into larger part on higher level. In general, part on lower level are hared amongt variou object categorie, while thoe in higher level are more category pecific. Thi i imilar to approach employed in thi paper, however, in thi paper, the feature haring i obtained through a ingle-level upport vector haring. The approach preented in [1] decribe a road ign detection and recognition ytem baed on haring feature. The detection ubytem i a two tage proce compried of color-baed egmentation and SVM hape detection. The recognition ubytem comprie GentleBoot algorithm and Rotation-Scale-Tranlation Invariant template matching. III. PROBLEM DEFINITION In thi paper, we focu on detection and claification of ideogram-baed road ign. The cla of all road ign exhibit variou foreground variation with repect to the ign hape but alo on preence or abence of thick red rim and ideogram type. We aim to jointly train detector to dicriminate road ign from background a well a to produce foreground variation etimate, i.e. ubcla label. We will ue term "foreground variation" and "ubcla" interchangeably in the ret of the paper denoting the ame concept. Fig. 1 depict within-cla road ign ubclae which we aim to etimate. The cla of all road ign i compried out of five variation denoted with label v from S = {1, 2, 3, 4, 5}. Subcla v=1 include triangular warning ign with thick red. A mall ubet of the ubcla member i hown in Fig. 1, i.e. the ubcla contain nine different road ign. Thee ign belong to the category A according to the Vienna Convention [11]. Subcla v=2 contain circular "End of no overtaking zone" ign which belong to the category C of informative ign. On the other hand, member of ubcla v=3 "Priority road" and "End of Priority Road" are rhomb-haped. Subcla v=4 include quare-haped ign which are a ubet of informative category C road ign. Finally, the ubcla v=5 conatin circular "Speed Limit" ign characterized with the thick red rim which belong to the category B of prohibitory ign. We dicu the decribed road-ign variation in our dataet and the motivation for our approach a follow. Firt, we dicu motivation for partitioning road ign into ubclae according to the ditribution hown in Fig. 1. The dataet i extracted from the video recorded with camera mounted on top of a moving vehicle. Video equence are recorded at daytime, at different weather condition [2]. Further, a Fig. 1 how, the ditribution of ign in the dataet i unbalanced, i.e. certain variation like triangular ign are characterized with large number of intance, while ome other have a mall number of occurrence. In particular, the "End of Priority Road" ign hown a a part of the ubcla v=3 in Fig. 1 ha only nine intance in training dataet. In the approach where we build a ingle detector for a particular ubcla, it i clear that detector trained with only nine ample would have very poor detection rate. However, the "End of Priority Road" ign hare the ame hape a the "Priority Road" ign. If we were to group them into a ingle ubcla, we could exploit foreground-variation feature haring. Other heterogeneou ubclae are deigned with the ame motivation. Note that the ubcla v=5 i alo a heterogeneou ubcla, i.e. it contain variou peed limit ign which hare the thick red rim and the zero digit, ince the peed limit are uually multiple of ten. Second, according to the ubclae defined in Fig. 1, oberve that ign belonging to different ubclae alo hare imilaritie. For example, the "End of no overtaking zone" (ubcla v=2) ign and "End of Priority Road" (ubcla v=3) both hare the ame ditinctive croover mark. Thi imilarity could improve dicrimination capability of both ign with repect to the background cla. Thi ugget that if we olve detection and claification problem for all ubclae together, we could benefit from within-cla feature haring. Poter Seion 38

3 Proceeding of the Croatian Computer Viion Workhop, Year 1 Therefore, due to the decribed characteritic of the dataet ditribution, a well a the nature of ign imilaritie, we decided to employ a method preented in [3] where a claification function i learned jointly for all within-cla variation. The aim of thi approach i to form the claification function which could exploit the fact that different variation hare feature againt background, but at the ame time provide within-cla dicrimination. IV. DETECTION AND CLASSIFICATION APPROACH The overall road ign detection and claification proce i hown in Fig. 2. The detailed decription i a follow. For a given feature vector x n computed for an image patch, the goal i to decide whether it repreent an intance of a road ign cla and, if o, to produce the correponding ubcla etimate v from S = {1, 2, 3, 4, 5}. Let x i denote feature vector of the i-th road ign training ample belonging to the ubcla with label v i. The feature vector are given a HOG feature [15]. According to the above defined parameter, the claification function C(x, i defined a follow: Fig. 2. Training and detector contruction outline the claification function. In thi way, we achieve the withincla feature haring a well a the within-cla dicrimination. 0, x i foreground from theame ubcla a x (, ) i A. Claification Function Training C x i 0, otherwie Thi correpond to the non-parametric approach preented in [3]. The parametric approach [3] i impler, however, it require each ubcla v to be decribed with a pecific parameter. The role of parameter i to decribe member of the ubcla in a unique way. In multiview domain, the parameter typically correpond to the view angle or object poe. However, in the road ign domain the ubclae are heterogeneou and cannot be decribed with a ingle parameter. For thi reaon, the claification function employ the foreground ample feature vector x i in order to decribe a pecific ubcla. Since the road ign ubclae are deigned with the goal that ign within the ubcla are imilar, it i to be expected that they will alo exhibit imilar feature vector value x i. SV Parameter denote the Lagrange multiplier of the -th upport vector [12], x the particular upport vector, x i the i-th foreground training ample, while k (x, x i ) denote the withincla kernel and k x (x, x i ) the between-cla kernel. In addition, the product of firt two term in equation (2) can be ummarized into a ingle term '(, which denote the weight of the -th upport vector x for foreground ample x i : i '( k ( x, x ) into (2) and (3) A a reult, the upport vector for which the within-cla kernel k yield higher value will have a larger influence on i x The claification function (2) training i achieved uing SVM. The training ample take form of tuple (x,. Each foreground training ample x i aigned it correponding ample index i. Background training ample x are obtained from image patche without road ign. Each background training ample x can be aociated with any index of a foreground training ample in order to form a valid tuple. More pecifically, background ample x i a negative with repect to all foreground ample. The number of uch combination i huge and correpond to #( NB) #( NF) The parameter #(NB) correpond to the total number of background and #(NF) to the total number of foreground training ample. Due to combinatorial complexity, including all negative ample in SVM training would not be practical. In order to atify requirement of within-cla feature Therefore, the boottrap training i employed a a hard haring againt the background cla, a well a within-cla negative mining technique. In boottrap training, only #(NB) dicrimination, the claification function C(x, i repreented negative are initially included in training. Thee ample are a a product of two kernel: aigned foreground ample indice in a random fahion. After each training round, all negative ample are evaluated by the C( x, k ( x, x ) k ( x, x) claification function (2). Fale poitive are added to the negative et and the SVM training i repeated. Thi i an iterative proce which converge when there are no more fale poitive to add. B. Individual Detector Contruction C(x, i learned a a function of a foreground variation parameter i, rather than learning eparate detector for each i. Individual detector w(x, are obtained from the claification function by plugging in pecific foreground ample value x i w(x, '( kx( x, x) SV Poter Seion 39

4 Proceeding of the Croatian Computer Viion Workhop, Year 1 Note that with fixed foreground variation i and known et of upport vector x, we can precompute the within-cla kernel value k (x, x i ) and conequently upport vector weight '(. Therefore, the within-cla kernel k i not evaluated at detection time. Rather, at detection time, we only evaluate the between-cla kernel k x. Thi fact affect our choice for withincla and between-cla kernel. Firt, we dicu within-cla kernel k. Road ign ubclae are difficult to eparate and i therefore important for k to be able to eparate nonlinear problem. Therefore, Gauian RBF kernel wa choen for that purpoe w(x, SV yield the bet ilhouette value. ' T ( ) ( x x) w( x V. EXPERIMENTAL RESULTS In thi way, the detection i achieved by applying a imple dot product between the image patch and the detector weight denoted a w(. Note that all detector hare the ame et of upport vector. In thi way, feature haring among variou detector i achieved. C. Detection Approach In the detection proce, we employ the well known liding window technique. Each window i evaluated by a family of linear detector w(x, contructed according to (7). From all detector repone, the one with maximum value i choen a a reult. If thi value i poitive, the window i claified a a road ign belonging to the ubcla of x i. Otherwie, the window i dicarded a a background. Note that thi i imilar to the k-nearet neighbor (k-nn) method, with parameter k=1, i.e. the object i imply aigned to the cla of the nearet neighbor elected among all detector [13]. However, in the 1-NN approach, the number of evaluated detector i ignificant, i.e. correpond to the number of foreground ample #(NF). Evaluating all #(NF) detector at the detection tage would make the detection extremely low. In addition, ince foreground ample belonging to the ame ubcla are imilar, there may be redundancy among detector. In order to identify a repreentative et from a family of total #(NF) detector, we ue the k-medoid clutering technique. The k-medoid technique i choen due to it implicity and alo becaue it i le prone to outlier influence than, for intance, k-mean method. Clutering yield a et of k < #(NF) medoid which are then ued in the detection phae. In clutering, each detector w(x, i repreented with a vector of it upport vector weight: ' ' ' 1 2 SV i '( (, (,, ( ) where '(, {1,..., SV} denote the particular upport weight defined with (3), while SV denote total number of upport vector. A a ditance meaure, we ued Dit ( i, j) defined a follow: T ' ( ' ( j) Dit ( i, j) 1 ' ( ' ( j) The appropriate number of medoid k i choen in an k ( x, xi ) exp( D( x, xi )) iterative proce, where we decreae number of medoid gradually and meaure the clutering quality. Initially, the where D(x,x i ) denote Euclidian ditance and target number of medoid, i.e. cluter center k i et to 50% of correponding parameter. Due to the fact that RBF i evaluated only during training and detector contruction, thi choice doen't impoe performance penalty during detection. the initial number of detector, i.e. foreground ample. Thi number wa choen by a rule of thumb. Then, we apply clutering according to the choen number of medoid k. In order to meaure clutering quality, we compute correponding Secondly, ince the between-cla kernel k x i evaluated ilhouette value [14]. The ilhouette value provide an etimate during detection, it i important for k x to be fat. Therefore, we of how the well obtained medoid repreent the data in their choe linear kernel for that purpoe. By ubtituting the linear kernel formulation k x (x,x i ) = x T correponding cluter. In each iteration, the target number of i x into (5) we obtain the final cluter i decreaed by a certain factor and the above proce form of our detector: i repeated. Final clutering outline i choen a the one which In thi ection, we decribe the evaluation of the above decribed method according to the foreground variation ditribution preented in Section III. In our experiment, we ued three dijoint dataet, decribed below [2]. A we already treed, the ditribution hown in Fig. 1 i unbalanced, i.e. ubcla v=1 contain at leat three time more ample that other clae. In uch unbalanced dataet, there i a poibility for pecific road ign variation with maller number of ample to be treated a a noie, e.g. ubcla v=3. In order to tet thi hypothei, we experimented with the number of ample per cla. Namely, we oberved detection performance for N POS =200, 300 and 400 ample per ubcla. For the ubclae with the number of ample lower than N POS, we imply ue all the ample for the ubcla, e.g. ubclae v=2, v=3 and N POS =400. The training ample are extracted randomly from training dataet pool compriing 2153 road ign. Negative dataet contain 4000 image patche extracted randomly from image of background outdoor cene. In order to monitor clutering performance, we ue the tet dataet compried out of 3000 cropped image. Detail of the tet dataet are given in Section V-B. A. Training Approach The training of detector i achieved a decribed in Section IV. A feature, we ued HOG vector [15] computed from training image cropped and caled to 24 x 24 pixel. Cell ize i et to 4 pixel, where each cell i normalized within a block of four cell. In order to increae performance, we ue block overlapping with block tride et to ize of ingle cell. The training i achieved uing SVMlight [16] with multiplicative kernel. In contrat to [3], where parameter of the RBF kernel Poter Seion 40

5 Proceeding of the Croatian Computer Viion Workhop, Year 1 (a) Fig. 3. Example of a detection and claification: (a) correct claification, (b) correct claification and fale poitive. (6) i et to a fixed value, we perform cro validation on training dataet in each boottrapping round in order to obtain the bet value. We compared both training approache and the one with optimized value yield a lower number of upport vector. Thi ugget a better mapping in the tranformed feature pace. More pecifically, with training et compried out of 1325 poitive ample and 4000 negative ample, the training with the fixed value yield a et of 857 upport vector. On the other hand, the training with the optimized decreae the number of upport vector for 10%. The training yield a family of #(NF) detector. The #(NF) correpond to the number of foreground training ample which depend on the number of training ample per ubcla N POS, Table I. Due to performance reaon, we ue k-medoid clutering in order to elect a repreentative et of detector from total #(NF) detector. The clutering i implemented in Matlab according to the Partitioning Around Medoid method [17]. In each clutering iteration, we monitor the ilhouette value and the validation reult on the tet dataet compried out of cropped image. Note that thi dataet i dijoint from tet dataet ued for detection. Interetingly, better ilhouette value correpond to a maller number fale negative obtained from validation on tet data. The reult of clutering are ummarized in Table I. depending on the N POS and #(NF). Reulting number of detector k correpond approximately to 30% of total training ample #(NF). Lower k value lead to poor validation reult and mall ilhouette value. B. Detection and Claification Reult The tet dataet for detection evaluation contain 1038 image in 720x576 reolution. From the total 1038 image, we elected 200 image and ued them for performance evaluation. In thee image, there were 214 phyical road ign. Table II. how the detection and foreground etimation reult for the three cae tudie. We report the detection rate D, the claification rate C, the fale poitive rate FP and the fale poitive rate per image FP/I. D i defined a a number of detected ign with repect to the total number of ign, while C and FP correpond to the number of correct claification and fale detection with repect to the total number of ign, repectively. FP/I correpond to the number of fale detection with repect to the number of image. Column denoted with ign how difference in above metric with repect to configuration denoted by N POS =200. We tarted the experiment with N POS =200 ample per ubcla. Thi configuration achieve overall detection rate of (b) 90% with fale poitive rate of 43%. Next, N POS =300 achieve 4% rie in detection rate giving total 94%, and 3% rie in claification rate, i.e. 93%. However, it i characterized with a large fale poitive rate of 55%. In liding window detection, ome computer viion librarie like OpenCV [18] employ fale poitive detection policy where an object mut exhibit at leat n detection in order to be accounted a a reult. Thi i undertandable, ince liding window technique exhibit multiple repone around ingle object. In thi work, we didn't experiment with thi property, however we believe that it would decreae fale poitive rate. Finally, the configuration N POS =400 exhibit wore reult with repect to N POS =300. Thi upport our hypothei that the unbalanced dataet N POS =400 treat ubclae with a lower number of ample a a noie giving the lower overall detection rate. Table III. depict D and C rate, a well a the FP rate per pecific ubcla v for configuration N POS =300 and N POS =200, repectively. The ubcla v=1 achieve better reult when a larger number of ample i ued. Thi i undertandable, ince thi ubcla comprie a large number of different road ign. Interetingly, the ubcla v=3 which ha only 98 ample (8% of the total ample for ubcla v=1) achieve detection and claification rate of 100% in all cae tudie. Subclae v=2 and v=4 achieve lower detection and claification rate with repect to other ubclae. Subcla v=2 i circle-haped but lack red rim in order to hare feature with ubcla v=5. On the other hand, ubcla v=4 i rectangle-haped and gain le benefit from feature haring with other ubclae. Subcla v=5 obtain imilar reult for N POS =300 and N POS =200. FP ditribution per ubcla for N POS =200 how that ubcla v=4 exhibit the larget number of fale poitive, i.e. 58%. Example of fale poitive claified a member of ubcla v=4 include building window. On the other hand, N POS =300 yield a rather balanced FP ditribution, where ubclae v=1, 4 and 5 obtain FP rate of approximately 30%. Example of detection and claification are given in Fig. 3a and Fig. 3b. Fig. 3a illutrate an example of a correct claification, where "Speed Limit" ign i claified a a member of ubcla v=5 (orange dotted line), while the "Children" ign i claified a a member of ubcla v=1 (green dotted line). Fig. 3.b illutrate correct claification, a well a two fale poitive. The "Priority Road" ign i correctly claified a a ubcla v=3 (cyan dotted line). The "Weight Limit" ign wa not preent in training data, however, due to imilarity with "Speed Limit" ign, it i claified a a member of ubcla v=5 (orange dotted line). The latter one indicate within-cla feature haring. The triangle-like object i incorrectly claified a a member of ubcla v=1 (green dotted line). VI. CONCLUSION In thi paper, we conidered a road-ign detection technique baed on a multiplicative kernel. One of the major challenge wa a poorly balanced dataet, where triangular warning ign have at leat three time more intance than other ubclae. Our approach i baed on a premie that different ign ubclae hare feature which dicriminate them from background. Therefore, intead of learning a dedicated detector for each ubcla, we trained ingle claification function for all ubclae uing SVM [3]. Individual detector Poter Seion 41

6 Proceeding of the Croatian Computer Viion Workhop, Year 1 TABLE I. CLUSTERING RESULTS N POS #(NF) k TABLE II. DETECTION AND CLASSIFICATION N POS D D C C FP FP FP/I FP/I % - 90% - 45% - 47% % +3% 93% +3% 55% +10% 58% +11% % -1% 90% 0% 43% -2% 45% -3% TABLE III. RESULTS PER SUBCLASS N POS = 300 N POS = 200 v D C FP D C FP 1 100% 100% 34% 91% 91% 15% 2 82% 77% 0% 82% 82% 0% 3 100% 100% 4% 100% 100% 5% 4 88% 82% 31% 76% 71% 58% 5 92% 92% 31% 93% 93% 22% are afterward contructed from a hared et of upport vector. Major benefit of uch approach with repect to eparately trained detector lie in feature haring which enhance the detection rate for ubclae with lower number of ample. In comparion to partition baed approache, thi approach doe not require the training ample to be labeled with ubcla parameter in order to learn claification function. Thi fact ha proven to be ueful for our domain, ince the road ign ubclae are heterogeneou and it i hard to decribe a ubcla with a ingle parameter. Intead, each training ample i labeled with it correponding HOG feature vector. In thi way we obtain #(NF) ubcla parameter and conequently #(NF) detector from the claification function, where #(NF) correpond to the number of foreground ample. However, due to performance iue, we perform clutering in order to obtain a repreentative et of detector from a et of total #(NF) detector. The reduced et of detector i ued in detection. Uing the decribed method, we achieved the bet detection rate of 94% at a relatively high fale poitive rate of 55%. We experimented with different number of ample per ubcla in order to oberve the effect on detection rate. The obtained reult howed that detector trained on a limited number of ample, i.e. 300 ample per cla obtain better detection reult with repect to the larger number of ample. Due to the fact that thi method ha hown promiing reult in road ign domain, in future work we plan to explore it applicability in the domain of multiview vehicle detection. 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