F. Heitz, P. Perez, and P. Bouthemy. Multiscale minimization of global energy functions in some visual recovery problems. CVGIP: Image Understanding, 59:125--134, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... for the optimal estimates for such models is computationally demanding, requiring methods such as simulated annealing for their solution or leading to suboptimal methods such as iterated conditional mode (ICM) 36] These problems have led a variety of authors to consider MR algorithms and models [48, 14, 135, 40, 144, 179, 180, 42, 59, 53, 58]. We will describe how some of these methods fall directly into the framework on which we focus and how others relate to it. 2.6 Multisensor Fusion for Groundwater Hydrology As we mentioned in Section 1, one of the motivations for using multiresolution methods comes from applications in which ....

....coarser 2x2 blocks, this fine scale detail could then be used to correct for the erroneous averaging at the coarser scale, allowing new, coarser scale estimates to be computed. This is exactly what the fine to coarse multigrid correction step does. In a number of other MRF estimation algorithms [135, 40, 145, 257, 144, 140, 195, 126] the full multigrid structure is not used, and only coarse to fine operations are performed. In some of these (e.g, see [40, 145, 144, 140] the problems that are solved at coarser scales correspond exactly to the original problems but with a constrained set of allowed reconstructions (e.g. ....

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F. Heitz, P. Perez, and P. Bouthemy. Multiscale minimization of global energy functions in some visual recovery problems. Comput. Vision Graphics and Image Process., 59(1):125--134, January 1994.

....If the number of objects is large, e.g. in the case of large images, the proposed approach is computationally demanding, even if comparatively e#cient optimization techniques like DA are used. In order to arrive at improved running times for the PDC algorithm, a multi scale optimization scheme [6] [11] is applied. The idea of multi scale optimization is to lower the computational complexity by decreasing the number of considered entities in the object space. In most application domains for image segmentation it is a natural assumption, that neighboring image sites contain identical, or at ....

F. Heitz, P. Perez, and P. Bouthemy. Multiscale minimization of global energy functions in some visual recovery problems. CVGIP: Image Understanding, 59(1):125-- 134, 1994.

....satisfactory results. What we expect from multigrid implementations is to reduce neighborhood connectivity of the monogrid MRF model at comparable results and the ratio of number of operations iteration ratio. Multiscale model The following multiscale model has been introduced by Perez et al. in [15]. Now, we are giving only a very short description of this model, but still to be able to understand its main idea. In this model, we have a top down strategy from coarser representation of the image to ner scales (we used 2 # 2 sites to build up a coarser block) Optimization is started on the ....

Heitz, F, Perez, P. & Bouthemy, P. (1994) Multiscale minimization of global energy functions in some visual recovery problems. CVGIP: Image Understanding, 59(1): 125134.

....have a long history in the literature. Important examples include the seminal paper by Geman and Geman [1] on simulated annealing, approaches for suboptimal Markov Random Field (MRF) minimization like the ICM algorithm [2] the highest con dence rst heuristic [3] multi scale approaches [4], and other approximations [5, 6] A further important class of approaches comprises continuation methods like Leclers partitioning approach [7] the graduated non convexity strategy by Blake and Zisserman [8] and various deterministic (approximate) versions of the annealing approach in ....

F. Heitz, P. Perez, and P. Bouthemy. Multiscale minimization of global energy functions in some visual recovery problems. Comp. Vis. Graph. Image Proc.: IU, 59(1):125-134, 1994.

....computer vision and image analysis have been expressed as global optimization problems. The general issue is to nd the global minimum of an objective (also called cost or energy) function which describes the interaction between the di erent variables modeling the image features in a given problem [8]. In particular, a common framework for image registration consists in minimizing a cost function that expresses the pixel or voxel similarity of the images to be aligned [14] The purpose of image registration (also called image matching) is to geometrically align one image (the oating or ....

.... nally every voxel in the MRI images. The same number of populations is generated on the four rst resolutions and only one population on the nal resolution. Multigrid matching is usually motivated by the signi cant computational gain obtained in the registration. As noticed by several authors [8], multigrid algorithms are also far less sensitive to local minima in the cost function than single resolution optimization schemes. It has indeed been conjectured that multigrid analysis may, to a certain extent, smooth the landscape of the objective function to minimize. This yields fast ....

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F. Heitz, P. Perez, and P. Bouthemy. Multiscale minimization of global energy functions in some visual recovery problems. Comput. Vis. Graphics Image Proc. Image Understanding, 59(1):125134, 1994.

....a novel approach to the global optimization of the quality measures commonly used by most texture segmentation models. The achieved processing times are small enough to meet the real time constraints e.g. in autonomous robotics 1 . Our algorithm relies on the concept of multiscale optimization [17]. The available image neighborhood information is used to signi cantly accelerate computation by exploiting the fact, that with high probability nearby image locations belong to the same segment. The optimization problem is rede ned on di erent scales such that the original cost function is ....

....randomized to avoid arti cial patterns due to coarse graining. Coarse grained cost functions of uniform algebraic structure on all resolution levels are derived for all clustering variants. We like to emphasize that this uniformity was not achieved in previous multiscale optimization approaches [17, 21, 22, 23, 24] and enables highly ecient optimization across scale. 2 Previous Work This contribution mainly focuses on deriving ecient optimization algorithms for cost function based image segmentation. It thus is applicable and helpful for all cluster based unsupervised texture segmentation schemes [1, 2, ....

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F. Heitz, P. Perez, and P. Bouthemy, \Multiscale minimization of global energy functions in some visual recovery problems," CVGIP: Image Understanding, vol. 59, no. 1, pp. 125-134, 1994.

....29, 58] Hierarchical methods are also used here in order not to get trapped in some local minima. # Energy based: A last kind of approach which does not suoeer any of the shortcomings presented above, consists of solving the correspondence problem in a minimization and regularization formulation [6, 8, 24, 45, 46, 51, 59]. An iterative solution of the discrete version of the associated EulerLagrange equation is then used in order to estimate depth. For instance, in [46] the authors propose a method to directly compute the depth map Z(x; y) as the minimum of the following energy: S(Z) ZZ (I l (x; y) Gamma I ....

F. Heitz, P. P#rez, and P. Bouthemy. Multiscale minimization of global energy functions in some visual recovery problems. CVGIP : Image Understanding, 59(1):125134, January 1994.

....the iterations, we use a focusing strategy based on a linear scalespace. Experimental results on both synthetic and real images are presented to illustrate the capabilities of this PDE and scale space based method. 1 Introduction Energy based methods have been extensively used in the last years [4, 5, 6, 8, 9, 11, 12] for estimating the disparity map between images. The goal Address: Edicio de Inform#tica y Sistemas, Campus Universitario de Tara. SP 35017 Las Palmas, Spain. E mail: lalvarez dis.ulpgc.es y Address: 2004 Route des Lucioles. F06902 Sophia Antipolis, France. E mail: ....

F. Heitz, P. P#rez, and P. Bouthemy, Multiscale minimization of global energy functions in some visual recovery problems. CVGIP : Image Understanding 59, 1994, 125134.

....Hierarchical methods are also used here in order not to get trapped in some local minimum. Energy based: A last kind of approach which does not su er from any of the shortcomings presented above, consists of solving the correspondence problem in a minimization and regularization formulation [7, 9, 11, 12, 17, 23, 40, 41, 42, 46, 53]. An iterative solution of the discrete version of the associated Euler Lagrange equation is then used in order to estimate disparity or depth. For instance, in [42] a variational approach for solving the stereo problem was proposed using the classical quadratic Tikhonov regularization term in ....

F. Heitz, P. Perez, and P. Bouthemy, Multiscale minimization of global energy functions in some visual recovery problems. CVGIP : Image Understanding 59, 1994, 125-134. 18 ALVAREZ, DERICHE, S  ANCHEZ, AND WEICKERT

....accelerate the optimization of the likelihood by maximizing over a suitable nested sequence of subspaces in a coarse to fine manner, where each subspace has a greatly reduced number of class assignment variables. This 6 strategy is formalized by the concept of multiscale optimization [HPB94,NP93,PB98] which in essence leads to cost functions redefined on a coarsened version of the original image. In contrast to most multi resolution optimization schemes the original cost function is optimized at all grids, only the configuration space is reduced by variable tying. We first sketch the general ....

F. Heitz, P. Perez, and P. Bouthemy. Multiscale minimization of global energy functions in some visual recovery problems. CVGIP: Image Understanding, 59(1):125--134, 1994.

....a smooth operation to the objective function that reduces the risk of converging to local minima. The main idea consists in defining a consistent coarse to fine multi grid contour propagation by using contours which are constrained to be piecewise constant over smaller and smaller pixel subsets [11]. The objective (0) 1) 2) 3) Fig. 5. Segmentation for the woman image [fig. 2.a) Multi phase Curve Propagation. A random initialization step is used with a large number of spoiled regions. The initial regions are the same for all hypothesis. 1) Region 1 (black pants) 2) Region 2 ....

F. Heitz, P. Perez, and P. Bouthemy. Multiscale minimization of global energy functions in some visual recovery problems. CVGIP: Image Understanding, 59:125-- 134, 1994.

....formulated as a continuous valued tomographic reconstruction problem with the number of points equal to the number of classes. Finally, we extend our reconstruction method to a multiresolution algorithm. Multiresolution techniques achieve performance improvements in a variety of imaging problems [31, 32] including image segmentation [33, 34] and continuous valued tomographic reconstruction [35] Multiresolution algorithms reconstruct the image at different resolutions, typically progressing from coarse to fine scale. The coarse scale solutions serve as initialization or prior information for ....

F. Heitz, P. Perez, and P. Bouthemy, "Multiscale minimization of global energy functions in some visual recovery problems," Comput. Vision Graphics and Image Process. 59, 125--134 (1994).

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F. Heitz, P. Prez, P. Bouthemy. Multiscale minimization of global energy functions in some visual recovery problems. CVGIP : Image Understanding, 59(1):125-134, January 1994.

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F. Heitz, P. Prez, P. Bouthemy. Multiscale minimization of global energy functions in some visual recovery problems. CVGIP : Image Understanding, 59(1):125-134, January 1994.

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F. Heitz, P. Perez, and P. Bouthemy. Multiscale minimization of global energy functions in some visual recovery problems. Comput. Vis. Graphics Image Proc. Image Understanding, 59(1):125134, 1994.

....concerns the subsampling of MRF s. The general properties of several subsampling schemes are examined. It is shown that most standard subsampling schemes lead Alternate approaches, involving various kind of coarsening operators on a single resolution model, have also been developed recently [7] [19], 20] 27] 34] 36] 37] These approaches are not subject to a loss of locality and hence will not be considered in this paper. to a loss of locality. Examples of subsampling schemes which preserve a local Markov property are also presented. The statistical properties of MRF models defined on ....

F. Heitz, P. P'erez, and P. Bouthemy, "Multiscale minimization of global energy functions in some visual recovery problems," CVGIP: Image Understanding, vol. 59, no. 1, pp. 125-134, 1994.

....is available. Deterministic approaches converge to configurations corresponding to local minima of the global energy function. On the other hand, 2 E. Memin, F. Heitz and F. Charot it is known that multigrid methods can significantly improve the convergence rate of iterative relaxation schemes [6, 22, 37]. The major drawback of relaxation algorithms is the amount of computation required to update the image. For real world applications the computation time quickly becomes prohibitive on workstations. On the other hand, in low level vision, the global energy functions usually adopted decompose into ....

....relaxation converges to a local minimum of the energy function, but this loss of optimality may be compensated for by an appropriate initial guess. When a relevant initial guess is not available, the solution at convergence may however be far from the optimum and lead to poor performances [17, 22, 25, 27]. A now very popular non linear deterministic relaxation scheme, known as the Iterated Conditional Mode (ICM) algorithm, has been proposed by Besag in 1986 [4] ICM basically corresponds to non linear Gauss Seidel 6 E. Memin, F. Heitz and F. Charot function SR( e; U(o; e) result e 2 Omega ....

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F. HEITZ, P. PEREZ, and P. BOUTHEMY. -- Multiscale minimization of global energy functions in some visual recovery problems. -- CVGIP : Image Understanding, Vol. 59, No 1, January 1994.

....algorithms remains the amount of computation required to update the image. For real world applications the computation time quickly becomes prohibitive on workstations. Several efficient approaches have been proposed to alleviate this computational burden. Among them, multigrid techniques [7, 23, 43]. have shown to significantly improve the convergence rate of linear and non linear relaxation schemes. It is also well known that the computations involved by these algorithms are regular and local, and lead naturally to massive data parallelism, which is well suited for parallel processing on ....

....[6] can often be used instead, when a good initial guess is available. Deterministic approaches converge to configurations corresponding to local minima of the global energy function. They may be combined with multigrid methods to improve the convergence rate of iterative relaxation schemes [7, 23, 43]. The major drawback of relaxation algorithms is the amount of computation required to update the image. For real world applications the computation time quickly becomes prohibitive on workstations. On the other hand, in low level vision, RR n2184 4 E. M emin, F. Heitz and F. Charot the global ....

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F. HEITZ, P. PEREZ, and P. BOUTHEMY. -- Multiscale minimization of global energy functions in some visual recovery problems. -- CVGIP : Image Understanding, Vol. 59, No 1: pages 125--134, January 1994.

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F. Heitz, P. Perez, and P. Bouthemy. Multiscale minimization of global energy functions in some visual recovery problems. CVGIP: Image Understanding, 59:125--134, 1994.

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F. Heitz, P.Perez, and P. Bouthemy. Multiscale minimization of global energy functions in some visual recovery problems. CVGIP: Image Understanding, 59:125-- 134, 1994.

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F. Heitz, P. Pe rez, P. Bouthemy, Multiscale minimization of global energy functions in some visual recovery problems, CVGIP: Image Understanding 59 (1994) 125---134.

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F. Heitz, P. Perez, and P. Bouthemy. Multiscale minimization of global energy functions in some visual recovery problems. Comp. Vis. Graph. Image Proc.: IU, 59(1):125--134, 1994.

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F. Heitz, P. Perez, and P. Bouthemy, "Multiscale Minimization of Global Energy Functions in Some Visual Recovery Problems," CVGIP-Image Understanding, vol. 59, no. 1, pp. 125-134, 1994.

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F. Heitz, P. Perez, and P. Bouthemy. Multiscale minimization of global energy functions in some visual recovery problems. Computer Vision and Image Understanding, 59#1#:125#134, 1994.

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F. Heitz, P. P'erez, P. Bouthemy, "Multiscale minimization of global energy function in some visual recovery problems", CVGIP: Image Understanding, vol. 59, no. 1, 1994. 23

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