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154
A duality based approach for realtime tvl1 optical flow
 In Ann. Symp. German Association Patt. Recogn
, 2007
"... Abstract. Variational methods are among the most successful approaches to calculate the optical flow between two image frames. A particularly appealing formulation is based on total variation (TV) regularization and the robust L 1 norm in the data fidelity term. This formulation can preserve discont ..."
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Cited by 197 (15 self)
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Abstract. Variational methods are among the most successful approaches to calculate the optical flow between two image frames. A particularly appealing formulation is based on total variation (TV) regularization and the robust L 1 norm in the data fidelity term. This formulation can preserve discontinuities in the flow field and offers an increased robustness against illumination changes, occlusions and noise. In this work we present a novel approach to solve the TVL 1 formulation. Our method results in a very efficient numerical scheme, which is based on a dual formulation of the TV energy and employs an efficient pointwise thresholding step. Additionally, our approach can be accelerated by modern graphics processing units. We demonstrate the realtime performance (30 fps) of our approach for video inputs at a resolution of 320 × 240 pixels. 1
A convex formulation of continuous multilabel problems
 In ECCV, pages III: 792–805
, 2008
"... Abstract. We propose a spatially continuous formulation of Ishikawa’s discrete multilabel problem. We show that the resulting nonconvex variational problem can be reformulated as a convex variational problem via embedding in a higher dimensional space. This variational problem can be interpreted a ..."
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Cited by 65 (13 self)
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Abstract. We propose a spatially continuous formulation of Ishikawa’s discrete multilabel problem. We show that the resulting nonconvex variational problem can be reformulated as a convex variational problem via embedding in a higher dimensional space. This variational problem can be interpreted as a minimal surface problem in an anisotropic Riemannian space. In several stereo experiments we show that the proposed continuous formulation is superior to its discrete counterpart in terms of computing time, memory efficiency and metrication errors. 1
Geometric Applications of the Split Bregman Method: Segmentation and Surface Reconstruction
, 2009
"... Variational models for image segmentation have many applications, but can be slow to compute. Recently, globally convex segmentation models have been introduced which are very reliable, but contain TVregularizers, making them difficult to compute. The previously introduced Split Bregman method is a ..."
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Cited by 58 (7 self)
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Variational models for image segmentation have many applications, but can be slow to compute. Recently, globally convex segmentation models have been introduced which are very reliable, but contain TVregularizers, making them difficult to compute. The previously introduced Split Bregman method is a technique for fast minimization of L1 regularized functionals, and has been applied to denoising and compressed sensing problems. By applying the Split Bregman concept to image segmentation problems, we build fast solvers which can outperform more conventional schemes, such as duality based methods and graphcuts. We also consider the related problem of surface reconstruction from unorganized data points, which is used for constructing level set representations in 3 dimensions.
An improved algorithm for TVL1 optical flow
 In: Visual Motion Analysis Workshop, LNCS 5604
, 2009
"... Fig. 1. Optical flow for the backyard and mini cooper scene of the Middlebury optical flow benchmark. Optical flow captures the dynamics of a scene by estimating the motion of every pixel between two frames of an image sequence. The displacement of every pixel is shown as displacement vectors on top ..."
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Cited by 52 (5 self)
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Fig. 1. Optical flow for the backyard and mini cooper scene of the Middlebury optical flow benchmark. Optical flow captures the dynamics of a scene by estimating the motion of every pixel between two frames of an image sequence. The displacement of every pixel is shown as displacement vectors on top of the commonly used flow color scheme (see Figure 5). Abstract. A look at the Middlebury optical flow benchmark [5] reveals that nowadays variational methods yield the most accurate optical flow fields between two image frames. In this work we propose an improvement variant of the original duality based TVL 1 optical flow algorithm in [31] and provide implementation details. This formulation can preserve discontinuities in the flow field by employing total variation (TV) regularization. Furthermore, it offers robustness against outliers by applying the robust L 1 norm in the data fidelity term. Our contributions are as follows. First, we propose to perform a structuretexture decomposition of the input images to get rid of violations in the optical flow constraint due to illumination changes. Second, we propose to integrate a median filter into the numerical scheme to further increase the robustness to sampling artefacts in the image data. We experimentally show that very precise and robust estimation of optical flow can be achieved with a variational approach in realtime. The numerical scheme and the implementation are described in a detailed way, which enables reimplementation of this highend method. 2 A. Wedel, T. Pock, C. Zach, H. Bischof, and D. Cremers 1
An algorithm for minimizing the mumfordshah functional
 in Proc. International Conference on Computer Vision, 2009
"... In this work we revisit the MumfordShah functional, one of the most studied variational approaches to image segmentation. The contribution of this paper is to propose an algorithm which allows to minimize a convex relaxation of the MumfordShah functional obtained by functional lifting. The algorit ..."
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Cited by 49 (14 self)
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In this work we revisit the MumfordShah functional, one of the most studied variational approaches to image segmentation. The contribution of this paper is to propose an algorithm which allows to minimize a convex relaxation of the MumfordShah functional obtained by functional lifting. The algorithm is an efficient primaldual projection algorithm for which we prove convergence. In contrast to existing algorithms for minimizing the full MumfordShah this is the first one which is based on a convex relaxation. As a consequence the computed solutions are independent of the initialization. Experimental results confirm that the proposed algorithm determines smooth approximations while preserving discontinuities of the underlying signal. 1.
Fast Global Labeling for RealTime Stereo Using Multiple Plane Sweeps
, 2008
"... This work presents a realtime, dataparallel approach for global label assignment on regular grids. The labels are selected according to a Markov random field energy with a Potts prior term for binary interactions. We apply the proposed method to accelerate the cleanup step of a realtime dense ste ..."
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Cited by 48 (2 self)
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This work presents a realtime, dataparallel approach for global label assignment on regular grids. The labels are selected according to a Markov random field energy with a Potts prior term for binary interactions. We apply the proposed method to accelerate the cleanup step of a realtime dense stereo method based on plane sweeping with multiple sweeping directions, where the label set directly corresponds to the employed directions. In this setting the Potts smoothness model is suitable, since the set of labels does not possess an intrinsic metric or total order. The observed runtimes are approximately 30 times faster than the ones obtained by graph cut approaches. 1
Fast Global Optimization of Curvature
"... Two challenges in computer vision are to accommodate noisy data and missing data. Many problems in computer vision, such as segmentation, filtering, stereo, reconstruction, inpainting and optical flow seek solutions that match the data while satisfying an additional regularization, such as total var ..."
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Cited by 28 (3 self)
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Two challenges in computer vision are to accommodate noisy data and missing data. Many problems in computer vision, such as segmentation, filtering, stereo, reconstruction, inpainting and optical flow seek solutions that match the data while satisfying an additional regularization, such as total variation or boundary length. A regularization which has received less attention is to minimize the curvature of the solution. One reason why this regularization has received less attention is due to the difficulty in finding an optimal solution to this image model, since many existing methods are complicated, slow and/or provide a suboptimal solution. Following the recent progress of Schoenemann et al. [28], we provide a simple formulation of curvature regularization which admits a fast optimization which gives globally optimal solutions in practice. We demonstrate the effectiveness of this method by applying this curvature regularization to image segmentation. 1.
Local Histogram based Segmentation using the Wasserstein Distance
, 2008
"... We propose and analyze a nonparametric regionbased active contour model for segmenting cluttered scenes. The proposed model is unsupervised and assumes that pixel intensity is independently identically distributed. The proposed energy functional consists of a geometric regularization term that pena ..."
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Cited by 26 (0 self)
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We propose and analyze a nonparametric regionbased active contour model for segmenting cluttered scenes. The proposed model is unsupervised and assumes that pixel intensity is independently identically distributed. The proposed energy functional consists of a geometric regularization term that penalizes the length of region boundaries, and a regionbased image term that uses the probability density function (or histogram) of pixel intensity to distinguish different regions. More specifically, the region data encourages partitioning the image domain so that the local histograms within each region are approximately homogeneous. The solutions of the proposed model do not need to differentiate histograms. The similarity between normalized histograms is measured by the Wasserstein distance with exponent 1, which is able to fairly compare two histograms, both continuous and discontinuous. We employ a fast global minimization method based on [11, 6] to solve the proposed model. The advantages of this method include less computational time compared with the minimization method by gradient descent of the associated EulerLagrange equation [12] and the abil
Saliency Driven Total Variation Segmentation
"... This paper introduces an unsupervised color segmentation method. The underlying idea is to segment the input image several times, each time focussing on a different salient part of the image and to subsequently merge all obtained results into one composite segmentation. We identify salient parts of ..."
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Cited by 24 (1 self)
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This paper introduces an unsupervised color segmentation method. The underlying idea is to segment the input image several times, each time focussing on a different salient part of the image and to subsequently merge all obtained results into one composite segmentation. We identify salient parts of the image by applying affinity propagation clustering to efficiently calculated local color and texture models. Each salient region then serves as an independent initialization for a figure/ground segmentation. Segmentation is done by minimizing a convex energy functional based on weighted total variation leading to a global optimal solution. Each salient region provides an accurate figure/ground segmentation highlighting different parts of the image. These highly redundant results are combined into one composite segmentation by analyzing local segmentation certainty. Our formulation is quite general, and other salient region detection algorithms in combination with any semisupervised figure/ground segmentation approach can be used. We demonstrate the high quality of our method on the wellknown Berkeley segmentation database. Furthermore we show that our method can be used to provide good spatial support for recognition frameworks. 1.
The Piecewise Smooth MumfordShah Functional on an Arbitrary Graph
"... Abstract—The MumfordShah functional has had a major impact on a variety of image analysis problems including image segmentation and filtering and, despite being introduced over two decades ago, it is still in widespread use. Present day optimization of the MumfordShah functional is predominated by ..."
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Cited by 20 (8 self)
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Abstract—The MumfordShah functional has had a major impact on a variety of image analysis problems including image segmentation and filtering and, despite being introduced over two decades ago, it is still in widespread use. Present day optimization of the MumfordShah functional is predominated by active contour methods. Until recently, these formulations necessitated optimization of the contour by evolving via gradient descent, which is known for its overdependence on initialization and the tendency to produce undesirable local minima. In order to reduce these problems, we reformulate the corresponding MumfordShah functional on an arbitrary graph and apply the techniques of combinatorial optimization to produce a fast, lowenergy solution. In contrast to traditional optimization methods, use of these combinatorial techniques necessitates consideration of the reconstructed image outside of its usual boundary, requiring additionally the inclusion of regularization for generating these values. The energy of the solution provided by this graph formulation is compared with the energy of the solution computed via traditional gradient descentbased narrowband level set methods. This comparison demonstrates that our graph formulation and optimization produces lower energy solutions than the traditional gradient descent based contour evolution methods in significantly less time. Finally, we demonstrate the usefulness of the graph formulation to apply the MumfordShah functional to new applications such as point clustering and filtering of nonuniformly sampled images. Index Terms—Level sets, active contours, piecewise smooth MumfordShah, combinatorial optimization, graph reformulation I.