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104
Color TV: Total Variation Methods for Restoration of Vector Valued Images
 IEEE Trans. Image Processing
, 1996
"... We propose a new definition of the total variation norm for vector valued functions which can be applied to restore color and other vector valued images. The new TV norm has the desirable properties of (i) not penalizing discontinuities (edges) in the image, (ii) rotationally invariant in the image ..."
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Cited by 111 (13 self)
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We propose a new definition of the total variation norm for vector valued functions which can be applied to restore color and other vector valued images. The new TV norm has the desirable properties of (i) not penalizing discontinuities (edges) in the image, (ii) rotationally invariant in the image space, and (iii) reduces to the usual TV norm in the scalar case. Some numerical experiments on denoising simple color images in RGB color space are presented. 1 Introduction During gathering and transfer of image data some noise and blur is usually introduced into the image. Several reconstruction methods based on the total variation (TV) norm have been proposed and studied for intensity (gray scale) images, see [9, 14, 21, 26, 29]. Since these methods have been successful in reducing noise and blur without smearing sharp edges for intensity images, it is natural to extend the TV norm to handle color and other vector valued images. Why do we need color restoration? It can be argued that si...
Inverse Kinematics Positioning Using Nonlinear Programming for Highly Articulated Figures
 ACM Transactions on Graphics
, 1994
"... An articulated figure is often modeled as a set of rigid segments connected with joints. Its configuration can be altered by varying the joint angles. Although it is straightforward to compute figure configurations given joint angles (forward kinematics), it is not so to find the joint angles for ..."
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Cited by 101 (9 self)
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An articulated figure is often modeled as a set of rigid segments connected with joints. Its configuration can be altered by varying the joint angles. Although it is straightforward to compute figure configurations given joint angles (forward kinematics), it is not so to find the joint angles for a desired configuration (inverse kinematics). Since the inverse kinematics problem is of special importance to an animator wishing to set a figure to a posture satisfying a set of positioning constraints, researchers have proposed many approaches. But when we try to follow these approaches in an interactive animation system where the object to operate on is as highly articulated as a realistic human figure, they fail in either generality or performance, and so a new approach is fostered. Our approach is based on nonlinear programming techniques. It has been used for several years in the spatial constraint system in the Jack TM human figure simulation software developed at the Compute...
Radioptimization  Goal Based Rendering
 In Computer Graphics Proceedings, Annual Conference Series
, 1993
"... This paper presents a method for designing the illumination in an environment using optimization techniques applied to a radiosity based image synthesis system. An optimization of lighting parameters is performed based on user specified constraints and objectives for the illumination of the envir ..."
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Cited by 42 (0 self)
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This paper presents a method for designing the illumination in an environment using optimization techniques applied to a radiosity based image synthesis system. An optimization of lighting parameters is performed based on user specified constraints and objectives for the illumination of the environment. The system solves for the "best" possible settings for: light source emissivities, element reflectivities, and spot light directionality parameters so that the design goals, suchastominimize energy or to give the the room an impression of privacy, are met. The system absorbs much of the burden for searching the design space allowing the user to focus on the goals of the illumination design rather than the intricate details of a complete lighting specification. A software implementation is described and some results of using the system are reported.
Learning compatibility coefficients for relaxation labeling processes
 IEEE Trans. Pattern Anal. Machine Intell
, 1994
"... AbstractRelaxation labeling processes have been widely used in many different domains including image processing, pattern recognition, and artificial intelligence. They are iterative procedures that aim at reducing local ambiguities and achieving global consistency through a parallel exploitation o ..."
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Cited by 39 (5 self)
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AbstractRelaxation labeling processes have been widely used in many different domains including image processing, pattern recognition, and artificial intelligence. They are iterative procedures that aim at reducing local ambiguities and achieving global consistency through a parallel exploitation of contextual information, which is quantitatively expressed in terms of a set of “compatibility coefficients. ” The problem of determining compatibility coefficients has received a considerable attention in the past and many heuristic, statisticalbased methods have been suggested. In this paper, we propose a rather different viewpoint to solve this problem: we derive them attempting to optimize the performance of the relaxation algorithm over a sample of training data; no statistical interpretation is given: compatibility coefficients are simply interpreted as real numbers, for which performance is optimal. Experimental results over a novel application of relaxation are given, which prove the effectiveness of the proposed approach. Index Terms Compatibility coefficients, constraint satisfaction, gradient projection, learning, neural networks, nonlinear
A Computational Algorithm for Minimizing Total Variation in Image Restoration
 IEEE Trans. Image Processing
, 1996
"... A reliable and efficient computational algorithm for restoring blurred and noisy images is proposed. The restoration process is based on the minimal total variation principle introduced by Rudin et al [1], [2], [3]. For discrete images, the proposed algorithm minimizes a piecewise linear l 1 functio ..."
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Cited by 34 (1 self)
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A reliable and efficient computational algorithm for restoring blurred and noisy images is proposed. The restoration process is based on the minimal total variation principle introduced by Rudin et al [1], [2], [3]. For discrete images, the proposed algorithm minimizes a piecewise linear l 1 function (a measure of total variation) subject to a single 2norm inequality constraint (a measure of data fit). The algorithm starts by finding a feasible point for the inequality constraint using a (partial) conjugate gradient method. This corresponds to a deblurring process. Noise and other artifacts are removed by a subsequent total variation minimization process. The use of the linear l 1 objective function for the total variation measurement leads to a simplier computational algorithm. Both the steepest descent and an affine scaling Newton method are considered for solving this constrained piecewise linear l 1 minimization problem. The resulting algorithm, when viewed as an image restoratio...
Nonlinear Variational Method for Optical Flow Computation
, 1993
"... We present a new method for optical flow computation based on the minimization of a nonquadratic functional. The solution of the obtained nonlinear di#erential equations is done with a time dependent approach leading to the successive solutions of linear systems. This new method allows to compute o ..."
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Cited by 29 (1 self)
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We present a new method for optical flow computation based on the minimization of a nonquadratic functional. The solution of the obtained nonlinear di#erential equations is done with a time dependent approach leading to the successive solutions of linear systems. This new method allows to compute optical flow fields while insuring a unique solution and preserving the flow discontinuities. This method seems to be more appropriate since it does not enforce the optical flow to be smooth in the boundaries of moving objects and reconstruct the optical flow discontinuities without any specific processing of these points.
The Many Facets of Linear Programming
, 2000
"... . We examine the history of linear programming from computational, geometric, and complexity points of view, looking at simplex, ellipsoid, interiorpoint, and other methods. Key words. linear programming  history  simplex method  ellipsoid method  interiorpoint methods 1. Introduction A ..."
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Cited by 25 (1 self)
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. We examine the history of linear programming from computational, geometric, and complexity points of view, looking at simplex, ellipsoid, interiorpoint, and other methods. Key words. linear programming  history  simplex method  ellipsoid method  interiorpoint methods 1. Introduction At the last Mathematical Programming Symposium in Lausanne, we celebrated the 50th anniversary of the simplex method. Here, we are at or close to several other anniversaries relating to linear programming: the sixtieth of Kantorovich's 1939 paper on "Mathematical Methods in the Organization and Planning of Production" (and the fortieth of its appearance in the Western literature) [55]; the fiftieth of the historic 0th Mathematical Programming Symposium that took place in Chicago in 1949 on Activity Analysis of Production and Allocation [64]; the fortyfifth of Frisch's suggestion of the logarithmic barrier function for linear programming [37]; the twentyfifth of the awarding of the 1975 Nobe...
InexactRestoration Method with Lagrangian Tangent Decrease and New Merit Function for Nonlinear Programming
, 1999
"... . A new InexactRestoration method for Nonlinear Programming is introduced. The iteration of the main algorithm has two phases. In Phase 1, feasibility is explicitly improved and in Phase 2 optimality is improved on a tangent approximation of the constraints. Trust regions are used for reducing the ..."
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Cited by 22 (6 self)
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. A new InexactRestoration method for Nonlinear Programming is introduced. The iteration of the main algorithm has two phases. In Phase 1, feasibility is explicitly improved and in Phase 2 optimality is improved on a tangent approximation of the constraints. Trust regions are used for reducing the step when the trial point is not good enough. The trust region is not centered in the current point, as in many Nonlinear Programming algorithms, but in the intermediate "more feasible" point. Therefore, in this semifeasible approach, the more feasible intermediate point is considered to be essentially better than the current point. This is the first method in which intermediatepointcentered trust regions are combined with the decrease of the Lagrangian in the tangent approximation to the constraints. The merit function used in this paper is also new: it consists of a convex combination of the Lagrangian and the (nonsquared) norm of the constraints. The Euclidean norm is used for simplicity but other norms for measuring infeasibility are admissible. Global convergence theorems are proved, a theoretically justified algorithm for the first phase is introduced and some numerical insight is given. Key Words: Nonlinear Programming, trust regions, GRG methods, SGRA methods, restoration methods, global convergence. 1
InexactRestoration Algorithm for Constrained Optimization
 Journal of Optimization Theory and Applications
, 1999
"... We introduce a new model algorithm for solving nonlinear programming problems. No slack variables are introduced for dealing with inequality constraints. Each iteration of the method proceeds in two phases. In the first phase, feasibility of the current iterate is improved and in second phase the ob ..."
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Cited by 19 (6 self)
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We introduce a new model algorithm for solving nonlinear programming problems. No slack variables are introduced for dealing with inequality constraints. Each iteration of the method proceeds in two phases. In the first phase, feasibility of the current iterate is improved and in second phase the objective function value is reduced in an approximate feasible set. The point that results from the second phase is compared with the current point using a nonsmooth merit function that combines feasibility and optimality. This merit function includes a penalty parameter that changes between different iterations. A suitable updating procedure for this penalty parameter is included by means of which it can be increased or decreased along different iterations. The conditions for feasibility improvement at the first phase and for optimality improvement at the second phase are mild, and largescale implementations of the resulting method are possible. We prove that under suitable conditions, that ...
Optical Flow: A Curve Evolution Approach
 IEEE TRANSACTIONS ON IMAGE PROCESSING
, 1996
"... A novel approach for the computation of optical flow based on an L type minimization is presented. It is shown that the approach has inherent advantages since it does not smooth the flowvelocity across the edges and hence preserves edge information. A numerical approach based on computation o ..."
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Cited by 19 (0 self)
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A novel approach for the computation of optical flow based on an L type minimization is presented. It is shown that the approach has inherent advantages since it does not smooth the flowvelocity across the edges and hence preserves edge information. A numerical approach based on computation of evolving curves is proposed for computing the optical flow field. Computations are carried out on a number of synthetic and real image sequences in order to illustrate the theory as well as the numerical approach.