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11
Deterministic edgepreserving regularization in computed imaging
 IEEE Trans. Image Processing
, 1997
"... Abstract—Many image processing problems are ill posed and must be regularized. Usually, a roughness penalty is imposed on the solution. The difficulty is to avoid the smoothing of edges, which are very important attributes of the image. In this paper, we first give conditions for the design of such ..."
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Cited by 245 (22 self)
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Abstract—Many image processing problems are ill posed and must be regularized. Usually, a roughness penalty is imposed on the solution. The difficulty is to avoid the smoothing of edges, which are very important attributes of the image. In this paper, we first give conditions for the design of such an edgepreserving regularization. Under these conditions, we show that it is possible to introduce an auxiliary variable whose role is twofold. First, it marks the discontinuities and ensures their preservation from smoothing. Second, it makes the criterion halfquadratic. The optimization is then easier. We propose a deterministic strategy, based on alternate minimizations on the image and the auxiliary variable. This leads to the definition of an original reconstruction algorithm, called ARTUR. Some theoretical properties of ARTUR are discussed. Experimental results illustrate the behavior of the algorithm. These results are shown in the field of tomography, but this method can be applied in a large number of applications in image processing. I.
Reliable Estimation of Dense Optical Flow Fields with Large Displacements
, 2001
"... In this paper we show that a classic optical ow technique by Nagel and Enkelmann (1986) can be regarded as an early anisotropic diusion method with a diusion tensor. We introduce three improvements into the model formulation that (i) avoid inconsistencies caused by centering the brightness term and ..."
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Cited by 105 (13 self)
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In this paper we show that a classic optical ow technique by Nagel and Enkelmann (1986) can be regarded as an early anisotropic diusion method with a diusion tensor. We introduce three improvements into the model formulation that (i) avoid inconsistencies caused by centering the brightness term and the smoothness term in dierent images, (ii) use a linear scalespace focusing strategy from coarse to ne scales for avoiding convergence to physically irrelevant local minima, and (iii) create an energy functional that is invariant under linear brightness changes. Applying a gradient descent method to the resulting energy functional leads to a system of diusion{reaction equations. We prove that this system has a unique solution under realistic assumptions on the initial data, and we present an ecient linear implicit numerical scheme in detail. Our method creates ow elds with 100 % density over the entire image domain, it is robust under a large range of parameter variations, and it c...
Dense Estimation and ObjectBased Segmentation of the Optical Flow with Robust Techniques
, 1998
"... In this paper we address the issue of recovering and segmenting the apparent velocity field in sequences of images. As for motion estimation, we minimize an objective function involving two robust terms. The first one cautiously captures the optical flow constraint, while the second (a priori) term ..."
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Cited by 102 (19 self)
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In this paper we address the issue of recovering and segmenting the apparent velocity field in sequences of images. As for motion estimation, we minimize an objective function involving two robust terms. The first one cautiously captures the optical flow constraint, while the second (a priori) term incorporates a discontinuitypreserving smoothness constraint. To cope with the nonconvex minimization problem thus defined, we design an efficient deterministic multigrid procedure. It converges fast toward estimates of good quality, while revealing the large discontinuity structures of flow fields. We then propose an extension of the model by attaching to it a flexible objectbased segmentation device based on deformable closed curves (different families of curve equipped with different kinds of prior can be easily supported). Experimental results on synthetic and natural sequences are presented, including an analysis of sensitivity to parameter tuning. INdex Terms Closed segmenting cu...
A Theoretical Framework for Convex Regularizers in PDEBased Computation of Image Motion
, 2000
"... Many differential methods for the recovery of the optic flow field from an image sequence can be expressed in terms of a variational problem where the optic flow minimizes some energy. Typically, these energy functionals consist of two terms: a data term, which requires e.g. that a brightness consta ..."
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Cited by 84 (21 self)
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Many differential methods for the recovery of the optic flow field from an image sequence can be expressed in terms of a variational problem where the optic flow minimizes some energy. Typically, these energy functionals consist of two terms: a data term, which requires e.g. that a brightness constancy assumption holds, and a regularizer that encourages global or piecewise smoothness of the flow field. In this paper we present a systematic classification of rotation invariant convex regularizers by exploring their connection to diffusion filters for multichannel images. This taxonomy provides a unifying framework for datadriven and flowdriven, isotropic and anisotropic, as well as spatial and spatiotemporal regularizers. While some of these techniques are classic methods from the literature, others are derived here for the first time. We prove that all these methods are wellposed: they posses a unique solution that depends in a continuous way on the initial data. An interesting structural relation between isotropic and anisotropic flowdriven regularizers is identified, and a design criterion is proposed for constructing anisotropic flowdriven regularizers in a simple and direct way from isotropic ones. Its use is illustrated by several examples.
A Theoretical Framework for Convex Regularizers in PDEBased Computation of Image Motion
, 2000
"... Many differential methods for the recovery of the optic flow field from an image sequence can be expressed in terms of a variational problem where the optic flow minimizes some energy. Typically, these energy functionals consist of two terms: a data term, which requires e.g. that a brightness consta ..."
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Cited by 4 (1 self)
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Many differential methods for the recovery of the optic flow field from an image sequence can be expressed in terms of a variational problem where the optic flow minimizes some energy. Typically, these energy functionals consist of two terms: a data term, which requires e.g. that a brightness constancy assumption holds, and a regularizer that encourages global or piecewise smoothness of the flow field. In this paper we present a systematic classification of rotation invariant convex regularizers by exploring their connection to diffusion filters for multichannel images. This taxonomy provides a unifying framework for datadriven and flowdriven, isotropic and anisotropic, as well as spatial and spatiotemporal regularizers. While some of these techniques are classic methods from the literature, others are derived here for the first time. We prove that all these methods are wellposed: they posses a unique solution that depends in a continuous way on the initial data. An interesting structural relation between isotropic and anisotropic flowdriven regularizers is identified, and a design criterion is proposed for constructing anisotropic flowdriven regularizers in a simple and direct way from isotropic ones. Its use is illustrated by several examples.
Regularized motion estimation using robust entropic functionals
 In International Conference on Image Processing
, 1995
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BoundaryControl Vector (BCV) Motion Field Representation and Estimation By Using A Markov Random Field Model
, 1995
"... A new motion field representation based on the boundarycontrol vector (BCV) scheme for video coding is examined in this work. With this scheme, the motion field is characterized by a set of control vectors and boundary functions. The control vectors are associated with the center points of block ..."
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Cited by 1 (0 self)
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A new motion field representation based on the boundarycontrol vector (BCV) scheme for video coding is examined in this work. With this scheme, the motion field is characterized by a set of control vectors and boundary functions. The control vectors are associated with the center points of blocks to control the overall motion behavior. We use the boundary functions to specify the continuity of the motion field across adjacentblocks. For BCVbased motion field estimation, an optimization framework based on the Markov random field model and maximum aposterior (MAP) criterion is used. The new scheme effectively represents complex motions such as translation, rotation, zooming and deformation and does not require complex scene analysis. Compared with MPEG of similar decoded SNR (signaltonoise ratio) quality, 1565% bit rate saving can be achieved in the proposed scheme with a more pleasant visual quality.
AND
, 1995
"... DFD have to be transmitted to the receiver, a well designed A new motion field representation based on the boundary video coder should balance the bits used in these two control vector (BCV) scheme for video coding is examined in parts. Other factors of consideration in video coder design this work ..."
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DFD have to be transmitted to the receiver, a well designed A new motion field representation based on the boundary video coder should balance the bits used in these two control vector (BCV) scheme for video coding is examined in parts. Other factors of consideration in video coder design this work. With this scheme, the motion field is characterized include computational cost, hardware complexity and the by a set of control vectors and boundary functions. The control domain of applicability. vectors are associated with the center points of blocks to control We can roughly classify existing motion field representathe overall motion behavior. We use the boundary functions tion into blockbased, pelbased, and modelbased categoto specify the continuity of the motion field across adjacent ries. The blockbased representation has been widely used blocks. For BCVbased motion field estimation, an optimization framework based on the Markov random field model and maxi and adopted by several standards such as H.261 [16] and mum a posteriori (MAP) criterion is used. The new scheme MPEG [6]. It divides an image frame into nonoverlapping effectively represents complex motions such as translation, ro blocks, and represents the motion field in each block with tation, zooming, and deformation and does not require complex a translation vector. This representation is generally appli
Dense Estimation and ObjectBased Segmentation of the Optical Flow with Robust Techniques
"... Abstract—In this paper, we address the issue of recovering and segmenting the apparent velocity field in sequences of images. As for motion estimation, we minimize an objective function involving two robust terms. The first one cautiously captures the optical flow constraint, while the second (a pri ..."
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Abstract—In this paper, we address the issue of recovering and segmenting the apparent velocity field in sequences of images. As for motion estimation, we minimize an objective function involving two robust terms. The first one cautiously captures the optical flow constraint, while the second (a priori) term incorporates a discontinuitypreserving smoothness constraint. To cope with the nonconvex minimization problem thus defined, we design an efficient deterministic multigrid procedure. It converges fast toward estimates of good quality, while revealing the large discontinuity structures of flow fields. We then propose an extension of the model by attaching to it a flexible objectbased segmentation device based on deformable closed curves (different families of curve equipped with different kinds of prior can be easily supported). Experimental results on synthetic and natural sequences are presented, including an analysis of sensitivity to parameter tuning. Index Terms—Closed segmenting curve, incremental multiresolution, motion segmentation, multigrid nonconvex minimization, optical flow, robust estimators. I.
Abstract Segmentation of a vector field: Dominant parameter and shape optimization
"... Vector field segmentation methods usually belong to either of three classes: methods which segment regions homogeneous in direction and/or norm, methods which detect discontinuities in the vector field, and region growing or classification methods. The first two classes of method do not allow segmen ..."
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Vector field segmentation methods usually belong to either of three classes: methods which segment regions homogeneous in direction and/or norm, methods which detect discontinuities in the vector field, and region growing or classification methods. The first two classes of method do not allow segmentation of complex vector fields and control of the type of fields to be segmented, respectively. The third class does not directly allow a smooth representation of the segmentation boundaries. In the particular case where the vector field actually represents an optical flow, a fourth class of methods acts as a detector of main motion. The proposed method combines a vector field model and a theoretically founded minimization approach. Compared to existing methods following the same philosophy, it relies on an intuitive, geometric way to define the model while preserving a general point of view adapted to the segmentation of potentially complex vector fields with the condition that they can be described by a finite number of parameters. The energy to be minimized is deduced from the choice of a specific class of field lines, e.g. straight lines or circles, described by the general form of their parametric equations. In that sense, the proposed method is a principled approach for segmenting parametric vector fields. The minimization problem was rewritten into a shape optimization and implemented by splinebased active contours. The algorithm was applied to the segmentation of precomputed optical flow fields given by an external, independent algorithm.