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66
High Accuracy Optical Flow Estimation Based on a Theory for Warping
, 2004
"... We study an energy functional for computing optical flow that combines three assumptions: a brightness constancy assumption, a gradient constancy assumption, and a discontinuitypreserving spatiotemporal smoothness constraint. ..."
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Cited by 299 (37 self)
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We study an energy functional for computing optical flow that combines three assumptions: a brightness constancy assumption, a gradient constancy assumption, and a discontinuitypreserving spatiotemporal smoothness constraint.
VectorValued Image Regularization with PDEs: A Common Framework for Different Applications
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2003
"... We address the problem of vectorvalued image regularization with variational methods and PDE's. From the study of existing formalisms, we propose a unifying framework based on a very local interpretation of the regularization processes. The resulting equations are then specialized into new regulari ..."
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Cited by 115 (7 self)
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We address the problem of vectorvalued image regularization with variational methods and PDE's. From the study of existing formalisms, we propose a unifying framework based on a very local interpretation of the regularization processes. The resulting equations are then specialized into new regularization PDE's and corresponding numerical schemes that respect the local geometry of vectorvalued images. They are finally applied on a wide variety of image processing problems, including color image restoration, inpainting, magnification and flow visualization.
Dense estimation of fluid flows
 IEEE Trans. Pattern Anal. Machine Intell
, 2002
"... AbstractÐIn this paper, we address the problem of estimating and analyzing the motion of fluids in image sequences. Due to the great deal of spatial and temporal distortions that intensity patterns exhibit in images of fluids, the standard techniques from Computer Vision, originally designed for qua ..."
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Cited by 92 (37 self)
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AbstractÐIn this paper, we address the problem of estimating and analyzing the motion of fluids in image sequences. Due to the great deal of spatial and temporal distortions that intensity patterns exhibit in images of fluids, the standard techniques from Computer Vision, originally designed for quasirigid motions with stable salient features, are not well adapted in this context. We thus investigate a dedicated minimizationbased motion estimator. The cost function to be minimized includes a novel data term relyingon an integrated version of the continuity equation of fluid mechanics, which is compatible with large displacements. This term is associated with an original secondorder divcurl regularization which prevents the washing out of the salient vorticity and divergence structures. The performance of the resulting fluid flow estimator is demonstrated on meteorological satellite images. In addition, we show how the sequences of dense motion fields we estimate can be reliably used to reconstruct trajectories and to extract the regions of high vorticity and divergence. Index TermsÐFluid motion, continuity equation, divcurl regularization, nonconvex minimization, trajectories, vorticity, and divergence concentration. 1
Highly accurate optic flow computation with theoretically justified warping
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 2006
"... ..."
Motion competition: a variational approach to piecewise parametric motion segmentation
 Int. J. Comput. Vision
, 2005
"... Abstract. We present a novel variational approach for segmenting the image plane into a set of regions of parametric motion on the basis of two consecutive frames from an image sequence. Our model is based on a conditional probability for the spatiotemporal image gradient, given a particular veloci ..."
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Cited by 54 (8 self)
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Abstract. We present a novel variational approach for segmenting the image plane into a set of regions of parametric motion on the basis of two consecutive frames from an image sequence. Our model is based on a conditional probability for the spatiotemporal image gradient, given a particular velocity model, and on a geometric prior on the estimated motion field favoring motion boundaries of minimal length. Exploiting the Bayesian framework, we derive a cost functional which depends on parametric motion models for each of a set of regions and on the boundary separating these regions. The resulting functional can be interpreted as an extension of the MumfordShah functional from intensity segmentation to motion segmentation. In contrast to most alternative approaches, the problems of segmentation and motion estimation are jointly solved by continuous minimization of a single functional. Minimizing this functional with respect to its dynamic variables results in an eigenvalue problem for the motion parameters and in a gradient descent evolution for the motion discontinuity set. We propose two different representations of this motion boundary: an explicit splinebased implementation which can be applied to the motionbased tracking of a single moving object, and an implicit multiphase level set implementation which allows for the segmentation of an arbitrary number of multiply connected moving objects. Numerical results both for simulated ground truth experiments and for realworld sequences demonstrate the capacity of our approach to segment objects based exclusively on their relative motion.
Symmetrical Dense Optical Flow Estimation with Occlusion Detection
 In ECCV
, 2002
"... Traditional techniques of dense optical flowestimation don't generally yield symmetrical solutions: the results will di#er if they are applied between images I1 and I2 or between images I2 and I1 . In this work, we present a method to recover a dense optical flow field map from two images, while exp ..."
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Cited by 40 (1 self)
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Traditional techniques of dense optical flowestimation don't generally yield symmetrical solutions: the results will di#er if they are applied between images I1 and I2 or between images I2 and I1 . In this work, we present a method to recover a dense optical flow field map from two images, while explicitely taking into account the symmetry across the images as well as possible occlusions and discontinuities in the flow field. The idea is to consider both displacements vectors from I1 to I2 and I2 to I1 and to minimise an energy functional that explicitely encodes all those properties. This variational problem is then solved using the gradient flowdefined by theEulerLw7458) equations associated to the energy. In order to reduce the risk to be trapped within some irrelevant minimum, a focusing strategy based on a multiresolution technique is used to converge toward the solution. Promising experimental results on both synthetic and real images are presented to illustrate the capabilities of this symmetrical variational approach to recover accurate optical flow. 1
A multigrid platform for realtime motion computation with discontinuitypreserving variational methods
 International Journal of Computer Vision
, 2006
"... Abstract. Variational methods are among the most accurate techniques for estimating the optic flow. They yield dense flow fields and can be designed such that they preserve discontinuities, estimate large displacements correctly and perform well under noise and varying illumination. However, such ad ..."
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Cited by 40 (12 self)
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Abstract. Variational methods are among the most accurate techniques for estimating the optic flow. They yield dense flow fields and can be designed such that they preserve discontinuities, estimate large displacements correctly and perform well under noise and varying illumination. However, such adaptations render the minimisation of the underlying energy functional very expensive in terms of computational costs: Typically one or more large linear or nonlinear equation systems have to be solved in order to obtain the desired solution. Consequently, variational methods are considered to be too slow for realtime performance. In our paper we address this problem in two ways: (i) We present a numerical framework based on bidirectional multigrid methods for accelerating a broad class of variational optic flow methods with different constancy and smoothness assumptions. Thereby, our work focuses particularly on regularisation strategies that preserve discontinuities. (ii) We show by the examples of five classical and two recent variational techniques that realtime performance is possible in all cases—even for very complex optic flow models that offer high accuracy. Experiments show that frame rates up to 63 dense flow fields per second for image sequences of size 160 × 120 can be achieved on a standard PC. Compared to classical iterative methods this constitutes a speedup of two to four orders of magnitude.
Diffusion and Regularization of Vector and MatrixValued Images
, 2002
"... The goal of this paper is to present a unified description of diffusion and regularization techniques for vectorvalued as well as matrixvalued data fields. In the vectorvalued setting, we first review a number of existing methods and classify them into linear and nonlinear as well as isotropic an ..."
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Cited by 38 (9 self)
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The goal of this paper is to present a unified description of diffusion and regularization techniques for vectorvalued as well as matrixvalued data fields. In the vectorvalued setting, we first review a number of existing methods and classify them into linear and nonlinear as well as isotropic and anisotropic methods. For these approaches we present corresponding regularization methods. This taxonomy is applied to the design of regularization methods for variational motion analysis in image sequences. Our vectorvalued framework is then extended to the smoothing of positive semidefinite matrix fields. In this context a novel class of anisotropic di usion and regularization methods is derived and it is shown that suitable algorithmic realizations preserve the positive semidefiniteness of the matrix field without any additional constraints. As an application, we present an anisotropic nonlinear structure tensor and illustrate its advantages over the linear structure tensor.
Orthonormal Vector Sets Regularization with PDE's and Applications
, 2001
"... We are interested in regularizing fields of orthonormal vector sets, using constraintpreserving anisotropic diffusion PDE's. Each point of such a field is defined by multiple orthogonal and unitary vectors and can indeed represent a lot of interesting orientation features such as direction vectors ..."
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Cited by 35 (3 self)
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We are interested in regularizing fields of orthonormal vector sets, using constraintpreserving anisotropic diffusion PDE's. Each point of such a field is defined by multiple orthogonal and unitary vectors and can indeed represent a lot of interesting orientation features such as direction vectors or orthogonal matrices (among other examples). We first develop a general variational framework that solves this regularization problem, thanks to a constrained minimization of phifunctionals. This leads to a set of coupled vectorvalued PDE's preserving the orthonormal constraints. Then, we focus on particular applications of this general framework, including the restoration of noisy direction fields, noisy chromaticity color images, estimated camera motions and DTMRI (Diffusion Tensor MRI) datasets.
Variational SpaceTime Motion Segmentation
, 2003
"... We propose a variational method for segmenting image sequences into spatiotemporal domains of homogeneous motion. To this end, we formulate the problem of motion estimation in the framework of Bayesian inference, using a prior which favors domain boundaries of minimal surface area. We derive a cost ..."
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Cited by 26 (5 self)
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We propose a variational method for segmenting image sequences into spatiotemporal domains of homogeneous motion. To this end, we formulate the problem of motion estimation in the framework of Bayesian inference, using a prior which favors domain boundaries of minimal surface area. We derive a cost functional which depends on a surface in spacetime separating a set of motion regions, as well as a set of vectors modeling the motion in each region. We propose a multiphase level set formulation of this functional, in which the surface and the motion regions are represented implicitly by a vectorvalued level set function. Joint minimization of the proposed functional results in an eigenvalue problem for the motion model of each region and in a gradient descent evolution for the separating interface. Numerical results on realworld sequences demonstrate that minimization of a single cost functional generates a segmentation of spacetime into multiple motion regions.