Combining Feature-based and Model-based Approaches For Robust Ellipse Detection

Transcription

1 Cobining Feature-based and Model-based Approahes For Robust Ellipse Halil Ibrahi Cakir Departent of Coputer Engineering Dulupinar University, Kutahya, Turkey Eail: Burak Benligiray, Cihan Topal Departent of Eletrial and Eletronis Engineering Anadolu University, Eskisehir, Turkey Eail: {burakbenligiray, Abstrat Fast and robust ellipse detetion is a vital step in any iage proessing and oputer vision appliations. Two ain approahes exist for ellipse detetion, i.e., odel-based and feature-based. Model-based ethods require uh ore oputation, but they an perfor better in olusions. Feature-based approahes are fast but ay perfor insuffiient in luttered ases. In this study, we propose an hybrid ethod whih obines both approahes to aelerate the proess without oproising auray. We extrat elliptial ars to narrow down searh spae by obtaining seeds for prospetive ellipses. For eah seed ar, we opute a liited searh region onsisting of hypothetial ellipses that eah an be fored with that seed. Later, we vote the on the edge iage to deterine best hypothesis aong the all, if exists. We tested the proposed algorith on a publi dataset and proising results are obtained opare to state of the art ethods in the literature. I. INTRODUCTION Apparent geoetri features of ertain objets are oonly used for their detetion in oputer vision appliations [1], [2], [3]. Edges and orners are the ost priitive geoetri features. More oplex geoetri features, suh as lines, irles and ellipses an be fored using these priitive features. There are two ain approahes for this augentation, whih are odel-based ethods and feature-based ethods. Model-based ethods have been long studied in the literature and an be suarized as exhaustively fitting odels to lower level features. The seond approah taken by feature-based ethods fors the desired geoetri features as obinations of lower level features. Charateristially, feature-based ethods have a lower proessing tie and are ore robust against noise. Aong the geoetri shapes, ellipses are one of the ost oon geoetri shapes in the nature. Sine a irle s projetion onto a aera iage plane is also an ellipse, enountering ellipses an be quite frequent in real life appliations. Hene they are used as geoetri features in appliations fro a wide array of fields suh as intelligent vehiles [4], ediine [5] and bioetris [6], [7]. An ellipse has 5 degrees of freedo (DoF), whih stands for the enter oordinates x & y, sei-ajor and sei-inor axes a & b, and rotation angle θ. It is onsiderably higher than oon geoetri features. This work is supported by The Sientifi and Tehnologial Researh Counil of Turkey (TUBITAK) and Anadolu University Coission of Sientifi Researh Projets (BAP) under the grant nubers 115E928 and 1505F319, respetively. Therefore, it is one of the hardest one to properly detet in any senarios. Due to its 5 DoF, various shapes suh as retangles an be represented by an ellipse with a reasonable aount of error. This situation both inreases the oputation tie for the searh in high diensional spae and belouds distinguishing of ellipses fro other shapes. Furtherore, for ost appliations, ellipses should be able to be aurately deteted under olusion and in a reasonable proessing tie. Due to these reasons, ellipse detetion is a diffiult proble that requires further iproved solutions. In this study, we propose an hybrid ethod for ellipse detetion. In our ethod, the lower level features that fors the ellipses are ars, whih theselves are fored by edge segents. Eah ar is used as a seed for an ellipse, siilar to a feature-based approah. Then, additional ars fro the sae ellipse are searhed in the iage by altering the seed ellipse s paraeters, whih is siilar to a odel-based approah. Therefore, we redue the searh spae in one diension and perfor voting in a liited area of iage. In this way, we avoid perforing oputationally expensive odel-based voting operation in 5-diensional paraeter spae of the ellipse for the entire iage. Eventually, the obination of odelbased and feature-based approahes yields the advantage of forer, whih is olusion resistane, and the advantages of latter, whih are lower running tie and robustness against noise. II. RELATED WORK The ost oon ethod of odel-based ellipse detetion is to apply Hough Transfor (HT) [8]. However, this is not as viable of an approah as deteting lines with HT, as ellipses have 5 degrees of freedo, while lines have only 2. A large degree of freedo results in a far larger paraeter spae to be searhed, hene proportional proessing ties. Iproveents to HT ainly ai to shrink the searh spae. Lei and Wong onstraint the searh to fewer paraeters at start, then ove on to deterine other paraeters of the ellipse [9]. Randoized Hough Transfor is another ethod designed to redue the oplexity of HT [10], whih is used to detet ellipses [11]. Zhang and Liu take edges onvexity inforation into aount while applying HT, whih iproves running tie by reduing the required oputation [6] /16/$ IEEE 2430

2 input iage Ar Searh Region Coputation by Voting list of ellipses Fig. 1: The blok diagra of the proposed algorith. Feature-based odels obine lower level features to for ellipses. The lowest level features to be used are edges. Sine oputing exhaustive obinations of edge pixels is not feasible, RANSAC has been used to find edge pixels that are on the sae ellipses [12]. Higher level features suh as line segents and ars are lower in nuber, hene using the as building bloks of ellipses is preferred by soe studies. Libuda et al. propose a hierarhial ethod, deteting edges, line segents, ars, extended ars and ellipses in this partiular order [13]. In another work, urves are deteted diretly fro the edges, whih are then obined to for ellipses [14]. In ethods that use high level features suh as ars, ellipses tend to be fit to the edges that onstitute these features [15]. In general, ethods that use higher level features report a uh lower proessing tie opared to other ethods. In addition, Geneti Algorith (GA) and its variants are rarely used for ellipse detetion. Yin applies operations whih are speifi to GA and alulate a fitness value [16]. After soe iproveents on andidates, grouping and hoosing higher values result to ellipses on a loal searh phase. Multi-population Geneti Algorith (MPGA) is also used for deteting partial and full ellipses [17]. It works by lustering subpopulations around an ellipse hypothesis. It is opared to Randoized Hough Transfor and another variant Sharing Geneti Algorith. There are also ethods that derive fro feature-based ethods, yet are essentially odel-based. Prasad et al. hoose edge pixels fro the sae ellipse based on their loal urvature, followed by a lower diensional HT searh [18]. Fornaiari et al. propose a seletion strategy for deteted ars [19]. HT is applied to the seleted ars to detet the ellipses. III. PROPOSED METHOD The proposed hybrid ellipse detetion algorith basially ais to restrit the five-diensional searh spae by the inforation aquired fro priitive ar features and follows the steps shown in Fig. 1. In the first step elliptial ar features are extrated fro the iage and eah of the represented by a paraetri ellipse equation. Then, separate searh regions are fored for eah ar by anipulating their paraeters. Searh region of an ar is atually oprised of a nuber of hypotheti ellipses that eah of the an be a valid ellipse for the seed ar with a reasonable aount of error. Afterwards, a voting shee is perfored for eah ar in their own searh regions on the edge iage and nuber of edge pixels are auulated for eah ellipse hypothesis. Finally, the best ellipse hypothesis is found aording to the voting results and a threshold value. In the following subsetions, we explain steps of the proposed algorith in fine detail. A. Ar In the first step of the algorith we extrat elliptial ar segents fro the input iage in a three stage ethod shown in Fig.2. First, we detet edge segents fro the iage eah of the as a onneted hain of pixels [20]. A test iage and deteted edge segents are shown in Fig. 3.a and Fig. 3.b, respetively. One we obtain the edge segents, we find the orners along eah segent with a urvature-based orner detetion algorith (see Fig. 3.) [21]. Then we fit an ellipse to pixel hains lying between two onseutive orners along the edge segents and opute fitting error to deide whether the pixel hain is an elliptial ar or not [22]. If resulted error is saller than a reasonable threshold (i.e. < 2 px), we deterine that the pixel hain is a valid ar. In Fig. 3.d extrated elliptial ars and the their orresponding ellipse results are shown. With the fitting operation we obtain an ellipse equation in oni for (see Eq. 1) to represent the ar and be utilized for oputation of ar speifi searh region. Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0 (1) B. Searh Region Coputation At the beginning, all elliptial ars and their oni equations are extrated fro the input iage. In the seond step, we opute a searh region for eah seed ar to deterine whether that ar an be part of a valid ellipse. A searh region is atually a list of ellipse hypotheses eah of whih an represent the ar with a reasonable aount of fitting error. In this way, instead of perforing oputationally expensive five-diensional voting operation on entire iage, we perfor voting in only one-diension and on a very liited area in the iage. To opute the searh region, we first derive the paraetri equation for eah seed ar fro the oni equation (Eq. 1) obtained fro ellipse fitting in the previous step: (x x ) 2 a 2 + (y y ) 2 b 2 = 1 (2) where (x, y ) is enter oordinates; a and b are sei-ajor and sei-inor axes of the ellipse, respetively [23]. The sae proedure also yields a θ value as the rotation angle of the ellipse around x axis. As shown in Fig. 4, we tune the enter loation, sei-ajor and sei-inor axes so as to derive ellipse hypotheses whih are siilar to the ellipse of seed ar. input iage Edge Segent Corner Ellipse Fitting list of ars error hek Fig. 2: Blok diagra of ar detetion ethod. 2431

3 (a) Input iage. (b) Edge segents in different olors. Fig. 5: Different variations of searh regions with regard to different ar loations. () Deteted orners on edge segents. (d) Ars with orresponding ellipses. Fig. 3: Steps of ar segent detetion proedure seen in Fig. 2 applied on a test iage. To find the ellipse hypotheses, we need to selet one of the axes or both and opute a diretion for the searh region to span through. For this purpose, we deterine the losest axis to seed ar by oputing distanes between ar s end points e i = (x ei, y ei ) and eah verties of axes on ellipse v i = (x vi, y vi ). Eah vertie is siply a point whih is an intersetion of sei-ajor and sei-inor axes and ellipse ontour. For eah end point of ar we get a losest vertie and this vertie appearently shows us whih axis value is to hange in searh region. It is also possible to hange both axis values and it an be seen as an exaple in Fig. 5. After we find out the axis (i.e. sei-ajor or sei-inor or both) where the searh region take plae, we need to deterine the diretion that it spans through. Diretion of searh region is the diretion of vetor where = (x, y ) is the sei-ajor axis sei-inor axis seed ar ellipse enter θ starting ellipse of searh region ending ellipse of searh region original ellipse of ar Fig. 4: Searh region oputed for a single ar. ar s iddle point and = (x, y ) is the enter of ellipse (See Eq. 3). One we deterine the axis and diretion for the searh region, we derive ellipse hypotheses by tuning hosen sei-ajor (a) and sei-inor (b) axes lengths with a ertain ratio (±10%, i.e. between 90% and 110%) of axes with a 1 pixel step ratio. For eah a and b values, we onurrently update the ellipse enter through searh region diretion in order to ake sure that the new ellipse still overlaps seed ar. α i = aros y y x x (3) As a result of tuning axis length, enter oordinates of ellipse hypotheses ust be shifted depending on aount of variation (k). Initial enter point starting fro first ellipse hypothesis is oputed by Eq. 4 and for eah hypothesis k value is inreased by 1 iteratively. x 0 = x + k os α, y 0 = y + k sin α (4) Finally, we obtain the ellipse hypotheses whih onstitutes searh region for voting. C. By Voting After we obtain all seed ars and searh regions, i.e. ellipse hypotheses, we opute a ratio for eah ellipse hypothesis by voting to edge pixels. We opute ellipse ontour points for eah ellipse hypothesis and utilize those point loation to vote on edge iage. For eah hypothesis, we deterine the nuber of overlapping edge pixels and then opute the overlapping ratio by dividing the value by perieter of the hypothesis. To test if an ellipse hypothesis is valid, we set an adaptive threshold whih varies with respet to the hypothesis perieter. In this anner, larger ellipses are to have higher voting ratios to be eleted as valid ellipses. In the experients, we eploy threshold values for voting ratio linearly varying between 0.4 and 0.9 for ellipses that are 100 and 1000 pixels in perieter, respetively. 2432

4 TABLE I: Average tiing results of eah algorith. Algorith Basa Prasad Libuda Proposed Tiing (s) (a) Deteted ar segents. (b) Separate searh regions for ars. threshold values are 0.83 for Prasad, 0.01 for Libuda and 0.93 for Basa. perforanes as f-easure is shown in Fig. 7. It is obvious that our algorith outperfos others quantitatively. Soe visual results fro the dataset are illustrated in 8. Tiing results for eah algorith an be seen in Table. I. Algoriths exhibit various tiing results fro long running to real-tie. As it is seen that our algorith and Libuda are in a opetition by perforing very lose tiing in illiseonds. Note that all experients are perfored on a laptop oputer with an Intel i GHz proessor and 8 GB of RAM. () Voting result for one ar. (d) Deteted ellipses after voting. Fig. 6: Ellipse detetion proess for the input iage. In () a voting result is seen with the olor legend for voting ratios. IV. EXPERIMENTAL RESULTS In our experients, we used an annotated real dataset and opared our ethod with three popular odel-based and feature-based ethods [18], [13], [24] naed Prasad, Libuda and Basa respetively. The dataset is naed Sartphone whih reently proposed in [19]. It has 629 fraes in 640x480 resolution and alost eah frae is hallenging for detetion of real elliptial objets. All of the are used for oparison and the oparison etri to quantify the detetion perforane is the overlap ratio alulation entioned in [18]. Eah algorith was tested under fixed ellipse validation threshold value that yields the best perforane for this dataset. These F-Measure Basa Prasad Libuda Proposed Fig. 7: Quantitative detetion perforane oparison for eah algorith. Eah bar represents average F-Measure value per iage. V. CONCLUSION In this study, we propose an ellipse detetion algorith whih ais to obine advantages of feature-based and odel-based approahes. The algorith starts in feature-based anner by extrating edge segents, orners and elliptial ars fro the input iage, respetively. After the ars are obtained, they are used as seeds for detetion of ellipses and the algorith oputes ar-speifi searh region based on the inforation inferred fro eah ar. A searh region is atually a group of ellipse hypotheses eah of whih an represent the seed ar with a reasonable aount of proxiity. Searh regions are then utilized to perfor voting on the edge iage for the ar that the region is derived fro. During the voting, edge pixels are auulated for eah ellipse hypothesis to perfor oparison. Finally, at ost one ellipse is seleted aong the hypotheses if it an auulate enough nuber of pixels. The proposed ethod an utilize very priitive features that annot be for an ar but still belong to an ellipse by using nearby ars as seeds. In this way the algorith both saves exessive oputation tie, and handles luttered situations where ellipses have lutters. We perfor extensive experients with a publily available dataset and obtain better auray results opare to existing ethods in the literature. The proposed ethod gives also proising results in ters of oputation tie. REFERENCES [1] A. Laurentini, The visual hull onept for silhouette-based iage understanding, Pattern Analysis and Mahine Intelligene, IEEE Transations on, vol. 16, no. 2, pp , [2] A.C. Berg, T.L. Berg, and J. Malik, Shape athing and objet reognition using low distortion orrespondenes, in Coputer Vision and Pattern Reognition, CVPR IEEE Coputer Soiety Conferene on, 2005, vol. 1, pp vol. 1. [3] F. Jianping, D.K.Y. Yau, A.K. Elagarid, and W.G. Aref, Autoati iage segentation by integrating olor-edge extration and seeded region growing, Iage Proessing, IEEE Transations on, vol. 10, no. 10, pp , [4] A. Soetedjo and K. Yaada, Fast and robust traffi sign detetion, in Systes, Man and Cybernetis, 2005 IEEE International Conferene on, 2005, vol. 2, pp [5] W. Lu and J. Tan, of inoplete ellipse in iages with strong noise by iterative randoized hough transfor (irht), Pattern Reognition, vol. 41, no. 4, pp ,

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