N. Paragios and R. Deriche, "Geodesic Active Regions for Motion Estimation and Tracking," Proc. Int'l Conf. Computer Vision, vol. 2, pp. 688694, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....are used, and testing on some of the same sequences (e.g. the highway and two manwalking sequences) we found that a simpler algorithm as the one here proposed already achieves satisfactory results. On the other hand, the Paragios Deriche technique, including the recently reported extensions [73, 74], are needed for more complicated scenes or longer ones. Note that due to the similarity between frames, our algorithm converges very fast (typically in less than 30 iterations, insuming a few seconds on our PC, of a non optimal explicit implementation) The CONDENSATION algorithm described in ....

N. Paragios and R. Deriche, "Geodesic active regions for motion estimation and tracking," Proc. Int. Conf. Comp. Vision, Greece, September 1999.

.... to refer the reader to the works [10] and [11] for shape recovery using level sets and edge function, and to more recent and related works by [19] 17] and [8] Finally, we would also like to mention [21] and [12] on shape reconstruction from unorganized points, and to the recent works [15] and [16], where a probability based geodesic active region model combined with classical gradient based active contour techniques is proposed. 2 Description of the model Let C be the evolving curve. We denote by c 1 and c 2 two constants, representing the averages of u 0 inside and outside the curve ....

Paragios, N., and Deriche, R.: Geodesic Active Regions for Motion Estimation and Tracking. INRIA Research Report 3631 (1999).

....active contours [3] are driven towards the edges of an image. The evolution equation is then computed from a criterion that only includes a local information on the boundary of the object to segment. The key idea of region based active contours, firstly proposed by [4 7] and further developed by [8 13], is to introduce a global information on the different regions to segment, in addition to the boundary based information, to make the active contour evolve. However, it is not trivial to compute the evolution equation of the active contour that will make it evolve towards a minimum of a criterion ....

.... Some of these works do not compute the theoretical expression of the velocity vector of the active contour but they choose the displacement that will make the criterion decrease [7, 9] Other works propose the computation of the velocity vector by reducing the whole problem to boundary integrals [6, 8] or by using the level set method [10, 11] They then use the Euler Lagrange equations to compute the evolution equation. However, the information on the different regions, that we call here descriptor of the corresponding region, is generally globally attached to the region. Indeed this case ....

Paragios, N., Deriche, R.: Geodesic active regions for motion estimation and tracking. In: Int. Conf. on Computer Vision, Corfu Greece (1999)

....of moving objects. Variational approaches have been implemented by Kornprobst and al. 6] and motionbased segmentation using Markov Random Fields has been introduced by Odobez and al. 11] Active contours, previously studied in [2,3,7] have been applied to the detection of moving objects in [8,12]. In [12] motion estimation and segmentation are performed jointly using a statistical model. A purely motion based method is proposed in [8] As far as the tracking is concerned, a sufficiently good estimation for the velocity vector field must be computed in order to track moving objects. A ....

....objects. Variational approaches have been implemented by Kornprobst and al. 6] and motionbased segmentation using Markov Random Fields has been introduced by Odobez and al. 11] Active contours, previously studied in [2,3,7] have been applied to the detection of moving objects in [8,12] In [12], motion estimation and segmentation are performed jointly using a statistical model. A purely motion based method is proposed in [8] As far as the tracking is concerned, a sufficiently good estimation for the velocity vector field must be computed in order to track moving objects. A survey of ....

N. Paragios, R. Derfiche, "Geodesic active regions for motion estimation and tracking", IEEE Int. Conf. in Computer Vision, Corfu, Greece, 1999.

....of moving objects since they enclose the whole object by a continuous curve, which can be fitted to any shape. In order to use active contours for the segmentation of moving objects, region based information must be incorporated in the evolution equation of an active contour. Previous works [3, 4, 5, 18, 19, 22, 23] proposed a way of integrating region based terms in the evolution equation of an active contour for many different applications. A short survey of these methods is proposed in section 2. Goals and Contributions: Our goal is to elaborate a general framework for region based active contours. Novel ....

....of regionbased terms is performed using the Green Riemann theorem and the Euler Lagrange equation. The force magnitude is then computed and it leads to the following evolution equation: c Ud D Me gfJ 0 where is the curvature of . Recently, Paragios and Deriche [18] have proposed an extension of the work of Zhu and Yuille by changing the descriptor of the contour in order to incorporate the image gradient as in geodesic active contours [2] In their study, some descriptors are evaluated for texture or moving objects segmentation. Chakraborty et al. 3] have ....

[Article contains additional citation context not shown here]

N. Paragios and R. Deriche. Geodesic active regions for motion estimation and tracking. In International Conference in Computer Vision, Corfu Greece, 1999.

....Let us note an image sequence by the function 0553 where 33 denotes the spatial location of a pixel and the number of the frame in the sequence. The image domain is noted . The segmentation process is supposed to be already performed by one of the algorithms described in [3, 4, 5], giving us video objects for each frame. Then, in order to predict interframe objects, we must first estimate the apparent motion of an object between two frames. 2.1. The level sets functions Let us introduce in this part some important definitions on the level sets functions. The segmentation ....

N. Paragios and R. Deriche, "Geodesic active regions for motion estimation and tracking," in Int. Conf. on Computer Vision, Corfu Greece, 1999.

....driven towards the edges of an image through the minimization of a boundary integral of functions of features depending on edges. Active contours driven by region functionals in addition to boundary function als have appeared later. Introduced by [11] and [38] they have been further developed in [46, 5, 9, 33, 34, 35, 36, 16, 45] and [26, 28] In effect, the use of active contours for the optimization of a criterion including both region and boundary functionals appears to be really powerful. In general, features of the image region to be segmented, tracked, etc. are embedded in region functionals while the boundary ....

....of a curve in a Riemannian space. Local minima are obtained via the steepest descent method. Region functionals have also been introduced. The region information is em bedded in the function f of (2. 2) These functionals have been used for many applications such as moving objects detection [33, 35, 25, 27], image segmentation [5, 16, 7, 34, 35, 45] or classification [46, 39, 36] For example, people have used such statistical features of a region 1 as the mean or the variance: We use these two exples to motivate the introduction of a gener region func tion Jr( f(x, G1 ( G2 ( Gm( ....

[Article contains additional citation context not shown here]

N. Paragios and R. Deriche. Geodesic active regions for motion estimation and tracking. In International Conference on Computer Vision, Corfu Greece, 1999.

....The introduction of such descriptors is interesting for two reasons. First, for a given application like detection of moving objects, various descriptors can be easily tested inside the same theoretical framework. Second, this framework can be applied to other applications [6] Some authors [7, 8, 9, 10] have proposed a way of adding region based terms in the evolution equation of an active contour. These pioneer works are complementary and show the potential of region based approaches. However, they are made for particular applications with particular descriptors. Moreover, all proofs leading to ....

....complementary and show the potential of region based approaches. However, they are made for particular applications with particular descriptors. Moreover, all proofs leading to the evolution equation of the active contour are based on the derivation of the criterion using Euler Lagrange equations [7, 10] and the dynamical scheme is introduced after the computation of the derivative. With such a method, the case of descriptors depending on the evolution of the curve, i.e. depending upon features globally attached to the region, cannot readily be taken into account. In this paper, we introduce a ....

N. Paragios and R. Deriche, "Geodesic active regions for motion estimation and tracking," in ICCV, Corfu Greece, 1999.

....undetectable. Computing the velocity field hence involves regularizing constraints such as its smoothness and other variants. Object tracking remains of great research interest in computer vision. Methods which exploit boundary based information and or region based information have been proposed [9]. Continuous contours, and snake models [2] for example, are used for estimating the motion along the boundaries of an object that is to be tracked. If the information being utilized in the estimation is very local, however, the result is prone to errors. To overcome this problem, geodesic active ....

....of an object that is to be tracked. If the information being utilized in the estimation is very local, however, the result is prone to errors. To overcome this problem, geodesic active regions, a framework which incorporates both boundary based and region based approaches have been proposed in [9]. This technique involves many different steps, in addition to a consistency check with respect to an affine motion following a motion detection. Our goal in this paper is to build on the previously achieved hindsight to develop a simple and efficient tracking algorithm nice adapted to polygonal ....

N. Paragios and R. Deriche. Geodesic active regions for motion estimation and tracking. Tech. Report INRIA 1999.

....to form a moving object. Temporal tracking is done by projecting the gradient minima of each region onto the next frame, and a modified watershed transformation algorithm is used the grow the regions in the next frame. Special care and a region merging algorithm is needed to handle occlusions. In [43], Paragios and Deriche present an a#ne motion estimation and tracking method using Geodesic Active Regions. Initially, boundary based information is recovered from the gradient values of the absolute di#erence frame between the current frame and a background reference frame. Then mobile pixels are ....

Nikos Paragios and Rachid Deriche. Geodesic active regions for motion estimation and tracking. In Proc. Int. Conf. on Computer Vision (ICCV 99), volume 1, pages 688--694, 1999.

....on some of the same Preliminary work 16 sequences (e.g. the highway and two man walking sequences) we found that a simpler algorithm as the one here proposed already achieves satisfactory results. On the other hand, the Paragios Deriche technique, including the recently reported extensions [73, 74], are needed for more complicated scenes or longer ones. Note that due to the similarity between frames, our algorithm converges very fast (typically in less than 30 iterations, insuming a few seconds on our PC, of a non optimal explicit implementation) The CONDENSATION algorithm described in ....

N. Paragios and R. Deriche, "Geodesic active regions for motion estimation and tracking, " Proc. Int. Conf. Comp. Vision, Greece, September 1999.

....of the object colors will be considered, although the texture distribution can be integrated into the same framework. 4 Tracking Algorithm We assume in the sequel the support of two modules which should provide (a) detection and localization in the initial frame of the objects to track (targets) [21, 23], and (b) periodic analysis of each object to account for possible updates of the target models due to significant changes in color [22] 4.1 Color Representation Target Model Let fx i g i=1: n be the pixel locations of the target model, centered at 0. We define a function b : R 2 f1 : ....

N. Paragios, R. Deriche, "Geodesic Active Regions for Motion Estimation and Tracking," IEEE Int'l Conf. Comp. Vis., Kerkyra, Greece, 688--674, 1999.

....of the object colors will be considered, although the texture distribution can be integrated into the same framework. 4 Tracking Algorithm We assume in the sequel the support of two modules which should provide (a) detection and localization in the initial frame of the objects to track (targets) [21,23], and (b) periodic analysis of each object to accountfor possible updates of the target models due to significant changes in color [22] 4.1 Color Representation Target Model Let fx i g i=1: n be the pixel locations of the target model, centered at 0. We define a function b : R 2 ....

N. Paragios, R. Deriche, "Geodesic Active Regions for Motion Estimation and Tracking," IEEE Int'l Conf. Comp. Vis., Kerkyra, Greece, 688--674, 1999.

....described before, and we end the paper by a brief concluding section. Before describing our model, we would like to refer the reader to the following related works: 27] and [25] on active contours, 29] and [14] on shape reconstruction from unorganized points, and finally to recent works [21] and [22], where a probability based CHAN AND VESE: ACTIVE CONTOURS WITHOUT EDGES 3 geodesic active region model combined with classical gradient based active contour techniques is proposed. II. Description of the model Our model is the minimization of an energy basedsegmentation. Let us first explain ....

....necessarily arround the objects to be detected. We validated our model by various numerical results. ACKNOWLEDGEMENTS The authors would like to thank Jean Michel Morel and Guillermo Sapiro for suggesting us the refferences on Kanisza s work ( 12] and Paragios Deriche work respectively ( 21] [22]) to Michael J. Black and Steve Ruuth for valuable conversations, and especially to Stanley Osher for the very usefull discussions in the level set collective . ....

N. Paragios and R. Deriche, Geodesic Active Regions for Motion Estimation and Tracking, INRIA RR-3631, March 1999.

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N. Paragios and R. Deriche. Geodesic Active Regions for Motion Estimation and Tracking. Research Report 3631, INRIA, France, 3631 1999. http://www.inria.fr/rapports/sophia/RR-3631.html.

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N. Paragios and R. Deriche. Geodesic Active regions for Motion Estimation and Tracking. In IEEE International Conference on Computer Vision, pages688--674( Corfu, Greece, 1999.

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N. Paragios, R. Deriche, Geodesic active regions for motion estimation and tracking, in: IEEE Int. Conf. in Computer Vision, 1999, pp. 688--674.

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N. Paragios and R. Deriche. Geodesic Active regions for Motion Estimation and Tracking. In IEEE ICCV, pages6,es Corfu, Greece, 1999.

....segmentation classification cases. 3. GEODESIC ACTIVE REGIONS The Geodesic Active Region model has been initially introduced in [19, 21] for supervised texture segmentation, has been extended to deal with the un supervised image segmentation case in [22] and has been successfully exploited in [20] to provide an elegant solution to the motion estimation and the tracking problem. R R B A (a) b) c) d) FIG. 1. Geodesic Active Region Model: a) the input, b) the boundary based information, c) the region based information corresponding to hypothesis h A , the information is ....

....set methods, where a coupled multi phase propagation is considered to impose the idea of mutually exclusive propagating curves. Some experimental results obtained with proposed framework are shown in [fig. 6) while more details can be found in [19, 21] 5.3. Motion Estimation and Tracking In [20] a general motion estimation and tracking framework is proposed derived from the Geodesic Active Region model that i. Deals simultaneously with the motion estimation and tracking problem, ii. Makes use in a generic form of different boundary and region based tracking modules, iii. Deals with ....

[Article contains additional citation context not shown here]

N. Paragios and R. Deriche. Geodesic Active regions for Motion Estimation and Tracking. In IEEE International Conference on Computer Vision, pages 688--674, Corfu, Greece, 1999.

....for real indoor and outdoor video surveillance sequences [fig. 2) 1 . The main drawback of the model is the cases of occlusion where the output of our model is a single curve for both objects. This can be confronted by incorporating other tracking modules like optical flow based features [16] as well geometric based features (object representations) Summarizing, we presented new ideas concerning the integration of boundary based and region based approaches for tracking. The main contribution of this work consists of creating a tracking model that integrates different type (boundary ....

N. Paragios and R. Deriche. Geodesic Active Regions for Motion Estimation and Tracking. Research Report 3631, INRIA, France, 1999. http://www.inria.fr/rapports/sophia/RR-3631.html.

....of this work, we would like to incorporate a multi phase level set propagation which will permit us to deal with the occlusion cases. Besides, for the time being we try to extend our method for cases with a mobile observer (work in progress) An extended version of this paper can be found in [19]. Various experimental results (in MPEG format) including the ones shown in this article, can be found at: http: www.inria.fr robotvis personnel nparagio demos http: www.inria.fr robotvis personnel der der eng.html responds to the total iteration number, while the Y axis, to the mean square ....

N. Paragios and R. Deriche. Geodesic Active Regions for Motion Estimation and Tracking. Research Report 3631, INRIA, France, 3631 1999. http://www.inria.fr/rapports/sophia/RR-3631.html.

....approxime assez correctement un grand nombre de situations r#elles (mouvement induit par un objet dont la profondeur est relativement petite par rapport # la distance # la cam#ra etc. A(x; y) Ax(x; y) Ay (x; y) a0 a1 a2 b0 b1 b2 1 x y # 4. 5 Int#gration des modules Comme dans [17, 19, 20], nous fusionnons les dioe#rents modules, en d#nissant une #nergie totale associ#e au mod#le r#gion active g#od#sique pour le suivi et l estimation du mouvement comme: E( P(R) A) ff EB ( P(R) fi ED( P(R) fl E I ( P(R) ffi EC ( P(R) A) o# fEB ; ED ; E I ; EC g sont les #nergies ....

N. Paragios and R. Deriche. Geodesic Active regions for Motion Estimation and Tracking. In IEEE International Conference on Computer Vision, pages 688674, Corfu, Greece, 1999.

....for real indoor and outdoor video surveillance sequences [fig. 2) 1 . The main drawback of the model is the cases of occlusion where the output of our model is a single curve for both objects. This can be confronted by incorporating other tracking modules like optical flow based features [16] as well geometric based features (object representations) Summarizing, we presented new ideas concerning the integration of boundary based and region based approaches for tracking. The main contribution of this work consists of creating a tracking model that integrates different type (boundary ....

N. Paragios and R. Deriche. Geodesic Active Regions for Motion Estimation and Tracking. Research Report 3631, INRIA, France, 1999. http://www.inria.fr/rapports/sophia/RR-3631.html.

....homogeneity properties, whereas boundary based ones use the non homogeneity of the same data as a guide. In this paper, a unified approach for image segmentation is presented that is based on the propagation of regular curves [4, 5, 23, 24,26] and is exploited from the Geodesic Active Region model [19, 20]. This approach is as an extension of our previous work on supervised texture segmentation [18, 20] This approach is depicted in [fig. 1) and is composed of two stages. The first stage refers to a modeling phase where the observed histogram is approximated using a mixture of Gaussian ....

....implementation issues are addressed in section 5. Finally, conclusions and discussion appear in section 6. 2 Geodesic Active Regions The Geodesic Active Region [15] model was originally proposed in [16] to deal with the problem of supervised texture segmentation and was successfully exploited in [19] to deal with the the motion estimation and tracking problem. This model will be shortly presented for a simple image segmentation case with two hypotheses (hA ; hB ) bi modal) In order to facilitate the notation, let us make some definitions: Let I be the input frame. Let P(R) fRA ; ....

N. Paragios and R. Deriche. Geodesic Active regions for Motion Estimation and Tracking. In IEEE ICCV, pages 688--674, Corfu, Greece, 1999.

....of this work, we would like to incorporate a multi phase level set propagation which will permit us to deal with the occlusion cases. Besides, for the time being we try to extend our method for cases with a mobile observer (work in progress) An extended version of this paper can be found in [19]. Various experimental results (in MPEG format) including the ones shown in this article, can be found at: http: www.inria.fr robotvis personnel nparagio demos http: www.inria.fr robotvis personnel der der eng.html responds to the total iteration number, while the Y axis, to the mean square ....

N. Paragios and R. Deriche. Geodesic Active Regions for Motion Estimation and Tracking. Research Report 3631, INRIA, France, 3631 1999. http://www.inria.fr/rapports/sophia/RR-3631.html.

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N. Paragios and R. Deriche, "Geodesic Active Regions for Motion Estimation and Tracking," Proc. Int'l Conf. Computer Vision, vol. 2, pp. 688694, 1999.

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Paragios, N., Deriche, R., September 1999a. Geodesic active regions for motion estimation and tracking. In: Proceedings of the 7th International Conference on Computer Vision. IEEE Computer Society Press, Los Alamitos, CA, pp. 688--694.

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N. Paragios and R. Deriche, "Geodesic Active Regions for Motion Estimation and Tracking ," 7th IEEE Conference in Computer Vision, Greece, 1999.

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N. Paragios and R. Deriche, "Geodesic active regions for motion estimation and tracking," in ICCV, Corfu Greece, 1999.

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N. Paragios and R. Deriche. Geodesic active regions for motion estimation and tracking. In ICCV, Corfu Greece, 1999.

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N. Paragios and R. Deriche, "Geodesic active regions for motion estimation and tracking". IEEE ICCV, Corfu, Greece, 1999.

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N. Paragios and R. Deriche, "Geodesic active regions for motion estimation and tracking," in ICCV, Corfu Greece, 1999.

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N. Paragios and R. Deriche, "Geodesic Active Regions for Motion Estimation and Tracking," in IEEE Proc. of the Seventh International Conference on Computer Vision (ICCV `99), pp. 688-694, Corfu, Greece, Sept. 1999.

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