COHEN I.: Nonlinear variational method for optical flow computation. In Proc. of the Eighth Scandinavian Conference on Image Analysis (1993), pp. 523--530. 2  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... c Springer Verlag Berlin Heidelberg 2002 Alvarez et al. tothe preOk0H of occlusions and discontinuitie9 Inorde toeyk5HO9 the optical flowmore accurate4H one have toeH4kB5y1#4 take into accountthe proble of occlusions and discontinuitieB Se the following works,mostlybase on variational approache [20,19,10,24,15,14,22,13,5,18,11,3,31].Due tothe fact thatthe functional to be minimise isge0HH4y1#O0 convek some focusingstrateHHk0 beBOMk the meM d in a multi re#kOOkye schek or aline9 scaley1#kO have beB succey1#HHO9ye4y toreH#9 the risk to ge trappe insome irre50 ant minima [20,4,3] The me4 dpreHM te he isinspire from this kind ....

I. Cohen. Nonlinear variational method for optical flowcomputation. In Scandi navi Conference on Image , volume 1, pages 523--530, 1993.

....(applications in medical images analysis) Here, a vector field models the pixels motion between the two images and a PDE is used to describe its evolution until it converges to the expected image transformation (Fig.1. 7) Interesting survey and references on this subject can be found in [5, 3, 6, 11, 13, 15, 17, 18, 49, 56, 67, 74, 94, 98, 109, 117, 124, 151, 172, 183, 192]. a) Direct superposing of two MRI images of the brain (b) Superposing after image registration [49] Figure 1.7: Image registration, treated as the evolution of a displacement field. Shape from Shading : This new and challenging problem consists in reconstructing a 3D representation of an ....

I. Cohen. Nonlinear variational method for optical flow computation. In Scandinavian Conference on Image Analysis, volume 1, pages 523--530, 1993.

....motions with missing data. 1 Introduction Tracking algorithms have been recently performed to determine 2D motion and deformations of complex shapes in image sequences. The representation and processing of deformations has many potential applications, for instance in biomedical image analysis [7, 16] or in human computer interaction [5, 20, 10] Deformable models have been introduced to incorporate geometric information about shapes and their variations and motion [5, 16] Active contour models attempt to extract regions of interest throughout the sequence and accurately delineate the shapes ....

.... (Kalman filter) and optimization of the deformable contour points under an affine motion constraint [5, 1] or propose a modal analysis of the physical motion of the dynamic contour [9] An alternative approach consists in using a dense optical flow field to displace the deformable contour points [7] ; in some cases, the information given by optical flow measurements computed along the deformable contour only is required to constrain the deformable contour optimization accordingly [3] Another class of approach addresses the problem of tracking a region surrounding the feature of interest [1, ....

I. COHEN. -- A nonlinear variational method for optical flow computation. -- In Proc. Scandinavian. Conf. Image Analysis, pages 523--530, Tromso, Norway, May 1993.

.... [23, 32] and it has first been used for image smoothing with simultaneous edge enhancement [26] Later on, close connections to regularization methods have been discovered [29] and related nonlinear methods have also entered computer vision fields such as motion analysis in image sequences [8] or interactive segmentation [4, 20] In this paper we shall learn about the basic ideas behind these methods, but also about their theoretical foundation and their adequate numerical realization. In this context we will also discuss the specific requirements for adequate numerical schemes in ....

....where (x, y) ## denotes the location and z # [0, Z] is the time. We are looking for the optic flow field # u(x,y,z) v(x,y,z) # which describes the correspondence of image structures at di#erent times. Variational methods constitute one possibility to solve the optic flow problem; see e.g. [8, 14, 22, 37]. In [38] a method is considered which is based on the following two assumptions: 1. Image structures do not change their grey value over time. Therefore, along their path (x(z) y(z) one obtains (19) 0 = df(x(z) y(z) z) dz = f x u f y v f z . 2. As second assumption we impose a ....

Cohen I., Nonlinear variational method for optical flow computation, In Proc. Eighth Scandinavian Conference on Image Analysis, Vol. 1, Troms, Norway, pp. 523--530, May 1993.

....vision [6] and it requires to be supplemented with additional regularizing assumptions. The regularization by Horn and Schunck [13] assumes that the optical flow field is smooth. Much research has been done to modify the Horn and Schunck approach in order to permit discontinuous flow fields; see [7, 8, 18, 21 24, 28] and the references therein. An important improvement in this direction has been achieved by Nagel and Enkelmann [21] in 1986. They consider the following minimization problem: ENE (h) Z R 2 (I 1 (x Gamma u(x; y) y Gamma v(x; y) Gamma I 2 (x; y) 2 dx (3) C Z R 2 trace i (rh) T ....

I. Cohen, Nonlinear variational method for optical flow computation, Proc. Eighth Scandinavian Conf. on Image Analysis (SCIA '93, Troms, May 25--28, 1993), Vol. 1, 523--530, 1993.

....are ignored by a blind smoothing. This deficiency results in a bad estimation nearby these border lines. A great deal of studies has been dedicated to this specific problem of discontinuity preserving regularization in computing optical flow (and in computer vision in general) See for instance [10, 13, 15, 24, 37, 40, 41]. Adopting a more global viewpoint, M. J. Black points out in [5] that all the different problems we have just evoked can be seen as deviations from the data model and from the prior model respectively. Though different in nature, they can hopefully be located and treated 1 Any occurrence of ....

I. COHEN. Nonlinear variational method for optical flow computation. In Proc. Scand. Conf. Image Analysis, pages 1:523--530, Tromso, Norway, May 1993.

....that the optic flow field is smooth. However, since many natural image sequences are better described in terms of piecewise smooth flow fields with discontinuities in between, much research has been done to modify the Horn and Schunck approach in order to permit such discontinuous flow fields; see [4, 6, 10, 11, 12, 15, 18] and the references therein. The work to be presented here is in line with this research. We investigate a modification of Horn and Schunck s energy functional which replaces the quadratic smoothness constraint by a novel nonquadratic one. Energy minimization is performed by applying gradient ....

....and Section 3 describes our modification. The basic ideas behind the numerical approximation are described in Section 4, and Section 5 illustrates the potential of our approach by appying it to natural test images. The paper is concluded with a summary in Section 6. Related work. Isaac Cohen [4] pioneered the field of investigating nonquadratic smoothness constraints for optic flow calculations. His L 1 minimization is related to total variation denoising strategies as introduced by Rudin et al. 16] A method identical to Cohen s approach has been studied later on by Kumar et al. ....

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I. Cohen, Nonlinear variational method for optical flow computation, Proc. Eighth Scandinavian Conf. on Image Analysis (SCIA '93, Troms, May 25--28, 1993), Vol. 1, 523--530, 1993.

....are ignored by a blind smoothing. This deficiency results in a bad estimation nearby these border lines. A great deal of studies has been dedicated to this specific problem of discontinuity preserving regularization in computing optical flow (and in computer vision in general) See for instance [10, 13, 15, 24, 37, 40, 41]. Adopting a more global viewpoint, M. J. Black points out in [5] that all the different problems we have just evoked can be seen as deviations from the data model and from the prior model respectively. Though different in nature, they can hopefully be located and treated 1 Any occurrence of ....

I. COHEN. Nonlinear variational method for optical flow computation. In Proc. Scand. Conf. Image Analysis, pages 1:523--530, Tromso, Norway, May 1993.

No context found.

Isaac Cohen. Nonlinear variational method for optical flow computation. In Proceedings of the 8th Scandinavian Conference on Image Analysis, pages 523--530, Tromso, Norway, June 1993. IAPR.

....[38] minimizing Z q u 2 x u 2 y . This gives the evolution equation similar to (98) u t = x ( u x q u 2 x u 2 y ) y ( u y q u 2 x u 2 y ) 100) This is solved using a totally explicit scheme. A similar approach is used for optical flow computation in [39], but the scheme is semi explicit. This means that the non linear part 1 p u 2 x u 2 y is explicit while the partial differential equation solved is similar to (99) This could be interpreted as solving an auxiliary problem where this nonlinear term is not time dependent. Note that in ....

Isaac Cohen. Nonlinear variational method for optical flow computation. In Proceedings of the 8th Scandinavian Conference on Image Analysis, pages 523--530, Tromso, Norway, June 1993. IAPR.

.... Segmentation for ultrasound images was presented as an application of the balloon model in [3] Temporal tracking in a time sequence of ultrasound images was studied in [6, 7] The tracking is helped by a Kalman filter in the Kalman snakes [8] Other references can be found in the book [9] In [10, 11], the initialization at each step is given by the previous solution deformed by prediction in the direction of the local flow obtained by optical flow analysis of the sequence of images. Our goal is to follow the deformation of a wall by including in the energy of the model the knowledge of its ....

Isaac Cohen. Nonlinear variational method for optical flow computation. In Proceedings of the 8th Scandinavian Conference on Image Analysis, pages 523--530, Tromso, Norway, June 1993. IAPR.

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COHEN I.: Nonlinear variational method for optical flow computation. In Proc. of the Eighth Scandinavian Conference on Image Analysis (1993), pp. 523--530. 2

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COHEN I.: Nonlinear variational method for optical flow computation. In Proc. of the Eighth Scandinavian Conference on Image Analysis (1993), pp. 523--530.

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I. Cohen. Nonlinear variational method for optical flow computation. In Proc. Eighth Scandinavian Conference on Image Analysis, volume 1, pages 523-530, Troms, Norway, May 1993.

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I. Cohen. Nonlinear variational method for optical flow computation. In Proc. Eighth Scandinavian Conference on Image Analysis, volume 1, pages 523--530, Troms, Norway, May 1993.

No context found.

I. Cohen. Nonlinear variational method for optical flow computation. In Scandinavian Conference on Image Analysis, volume 1, pages 523--530, 1993.

No context found.

I. Cohen. Nonlinear variational method for optical flow computation. In Scandinavian Conference on Image Analysis, volume 1, pages 523--530, 1993.

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