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69
Object Segmentation in Video: A Hierarchical Variational Approach for Turning Point Trajectories into Dense Regions
"... Point trajectories have emerged as a powerful means to obtain high quality and fully unsupervised segmentation of objects in video shots. They can exploit the long term motion difference between objects, but they tend to be sparse due to computational reasons and the difficulty in estimating motion ..."
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Cited by 34 (5 self)
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Point trajectories have emerged as a powerful means to obtain high quality and fully unsupervised segmentation of objects in video shots. They can exploit the long term motion difference between objects, but they tend to be sparse due to computational reasons and the difficulty in estimating motion in homogeneous areas. In this paper we introduce a variational method to obtain dense segmentations from such sparse trajectory clusters. Information is propagated with a hierarchical, nonlinear diffusion process that runs in the continuous domain but takes superpixels into account. We show that this process raises the density from 3% to 100 % and even increases the average precision of labels. 1.
GLOBAL SOLUTIONS OF VARIATIONAL MODELS WITH CONVEX REGULARIZATION
"... Abstract. We propose an algorithmic framework to compute global solutions of variational models with convex regularity terms that permit quite arbitrary data terms. While the minimization of variational problems with convex data and regularity terms is straight forward (using for example gradient de ..."
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Cited by 32 (9 self)
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Abstract. We propose an algorithmic framework to compute global solutions of variational models with convex regularity terms that permit quite arbitrary data terms. While the minimization of variational problems with convex data and regularity terms is straight forward (using for example gradient descent), this is no longer trivial for functionals with nonconvex data terms. Using the theoretical framework of calibrations the original variational problem can be written as the maximum flux of a particular vector field going through the boundary of the subgraph of the unknown function. Upon relaxation this formulation turns the problem into a convex problem, however, in higher dimension. In order to solve this problem, we propose a fast primal dual algorithm which significantly outperforms existing algorithms. In experimental results we show the application of our method to outlier filtering of range images and disparity estimation in stereo images using a variety of convex regularity terms. Key words. Variational methods, calibrations, total variation, convex optimization. AMS subject classifications. 49M20, 49M29, 65K15, 68U10. 1. Introduction. Energy
Globally optimal segmentation of multiregion objects
 In ICCV
, 2009
"... colours are hard to separate. In the absence of user localization, above at center is the best result we can expect from such models. Now we can design multiregion models with geometric interactions to segment such objects more robustly in a single graph cut. Many objects contain spatially distinct ..."
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Cited by 32 (2 self)
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colours are hard to separate. In the absence of user localization, above at center is the best result we can expect from such models. Now we can design multiregion models with geometric interactions to segment such objects more robustly in a single graph cut. Many objects contain spatially distinct regions, each with a unique colour/texture model. Mixture models ignore the spatial distribution of colours within an object, and thus cannot distinguish between coherent parts versus randomly distributed colours. We show how to encode geometric interactions between distinct region+boundary models, such as regions being interior/exterior to each other along with preferred distances between their boundaries. With a single graph cut, our method extracts only those multiregion objects that satisfy such a combined model. We show applications in medical segmentation and scene layout estimation. Unlike Li et al. [17] we do not need “domain unwrapping” nor do we have topological limits on shapes. 1.
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.
A convex approach to minimal partitions
 J. IMAGING SCI
, 2012
"... We describe a convex relaxation for a family of problems of minimal perimeter partitions. The minimization of the relaxed problem can be tackled numerically, we describe an algorithm and show some results. In most cases, our relaxed problem finds a correct numerical approximation of the optimal solu ..."
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Cited by 24 (10 self)
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We describe a convex relaxation for a family of problems of minimal perimeter partitions. The minimization of the relaxed problem can be tackled numerically, we describe an algorithm and show some results. In most cases, our relaxed problem finds a correct numerical approximation of the optimal solution: we give some arguments to explain why it should be so, and also discuss some situation where it fails.
A STUDY ON CONTINUOUS MAXFLOW AND MINCUT APPROACHES
"... We propose and investigate novel maxflow models in the spatially continuous setting, with or without supervised constraints, under a comparative study of graph based maxflow / mincut. We show that the continuous maxflow models correspond to their respective continuous mincut models as primal a ..."
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Cited by 23 (6 self)
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We propose and investigate novel maxflow models in the spatially continuous setting, with or without supervised constraints, under a comparative study of graph based maxflow / mincut. We show that the continuous maxflow models correspond to their respective continuous mincut models as primal and dual problems, and the continuous mincut formulation without supervision constraints regards the wellknown ChanEsedogluNikolova model [15] as a special case. In this respect, basic conceptions and terminologies applied by discrete maxflow / mincut are revisited under a new variational perspective. We prove that the associated nonconvex partitioning problems, unsupervised or supervised, can be solved globally and exactly via the proposed convex continuous maxflow and mincut models. Moreover, we derive novel fast maxflow based algorithms whose convergence can be guaranteed by standard optimization theories. Experiments on image segmentation, both unsupervised and supervised, show that our continuous maxflow based algorithms outperform previous approaches in terms of efficiency and accuracy.
A continuous maxflow approach to Potts model
 In European Conference on Computer Vision (ECCV), Iraklion
, 2010
"... Abstract. We address the continuous problem of assigning multiple (unordered) labels with the minimum perimeter. The corresponding discrete Potts model is typically addressed with aexpansion which can generate metrication artifacts. Existing convex continuous formulations of the Potts model use TV ..."
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Cited by 18 (3 self)
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Abstract. We address the continuous problem of assigning multiple (unordered) labels with the minimum perimeter. The corresponding discrete Potts model is typically addressed with aexpansion which can generate metrication artifacts. Existing convex continuous formulations of the Potts model use TVbased functionals directly encoding perimeter costs. Such formulations are analogous to ’mincut ’ problems on graphs. We propose a novel convex formulation with a continous ’maxflow ’ functional. This approach is dual to the standard TVbased formulations of the Potts model. Our continous maxflow approach has significant numerical advantages; it avoids extra computational load in enforcing the simplex constraints and naturally allows parallel computations over different labels. Numerical experiments show competitive performance in terms of quality and significantly reduced number of iterations compared to the previous state of the art convex methods for the continuous Potts model. 1
TIGHT CONVEX RELAXATIONS FOR VECTORVALUED LABELING
"... Abstract. Multilabel problems are of fundamental importance in computer vision and image analysis. Yet, finding global minima of the associated energies is typically a hard computational challenge. Recently, progress has been made by reverting to spatially continuous formulations of respective prob ..."
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Cited by 15 (7 self)
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Abstract. Multilabel problems are of fundamental importance in computer vision and image analysis. Yet, finding global minima of the associated energies is typically a hard computational challenge. Recently, progress has been made by reverting to spatially continuous formulations of respective problems and solving the arising convex relaxation globally. In practice this leads to solutions which are either optimal or within an a posteriori bound of the optimum. Unfortunately, in previous methods, both run time and memory requirements scale linearly in the total number of labels, making them very inefficient and often not applicable to problems with higher dimensional label spaces. In this paper, we propose a reduction technique for the case that the label space is a continuous product space and the regularizer is separable, i.e. a sum of regularizers for each dimension of the label space. On typical realworld labeling problems, the resulting convex relaxation requires orders of magnitude less memory and computation time than previous methods. This enables us to apply it to largescale problems like optic flow, stereo with occlusion detection, segmentation into a very large number of regions, and joint denoising and local noise estimation. Experiments show that despite the drastic gain in performance, we do not arrive at less accurate solutions than the original
Interactive Texture Segmentation using Random Forests and Total Variation
, 2009
"... Common methods for interactive texture segmentation rely on probability maps based on low dimensional features such as e.g. intensity or color, that are usually modeled using basic learning algorithms such as histograms or Gaussian Mixture Models. The use of low level features allows for fast genera ..."
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Cited by 14 (2 self)
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Common methods for interactive texture segmentation rely on probability maps based on low dimensional features such as e.g. intensity or color, that are usually modeled using basic learning algorithms such as histograms or Gaussian Mixture Models. The use of low level features allows for fast generation of these hypotheses but limits applicability to a small class of images. We address this problem by learning complex descriptors with Random Forests and exploiting their inherent parallelism in a GPU implementation. The segmentation itself is based on a convex energy functional that uses weighted Total Variation regularization and a pointwise data term allowing for continuous foreground/background membership hypotheses. Its globally optimal solution is obtained by a fast primaldual algorithm providing a reasonable convergence criterion. As a result, we present a versatile interactive texture segmentation framework. We show experiments with natural, artificial and medical data and demonstrate superior results compared to two recent approaches.
Minimization and parameter estimation for seminorm regularization models with Idivergence constraints
, 2012
"... In this papers we analyze the minimization of seminorms ‖L · ‖ on R n under the constraint of a bounded Idivergence D(b,H·) for rather general linear operators H and L. The Idivergence is also known as KullbackLeibler divergence and appears in many models in imaging science, in particular when d ..."
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Cited by 13 (2 self)
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In this papers we analyze the minimization of seminorms ‖L · ‖ on R n under the constraint of a bounded Idivergence D(b,H·) for rather general linear operators H and L. The Idivergence is also known as KullbackLeibler divergence and appears in many models in imaging science, in particular when dealing with Poisson data. Often H represents, e.g., a linear blur operator and L is some discrete derivative or frame analysis operator. We prove relations between the the parameters of Idivergence constrained and penalized problems without assuming the uniqueness of their minimizers. To solve the Idivergence constrained problem we apply firstorder primaldual algorithms which reduce the problem to the solution of certain proximal minimization problems in each iteration step. One of these proximation problems is an Idivergence constrained least squares problem which can be solved based on Morosov’s discrepancy principle by a Newton method. Interestingly, the algorithm produces not only a sequence of vectors which converges to a minimizer of the constrained problem but also a sequence of parameters which convergences to a regularization parameter so that the corresponding penalized problem has the same solution as our constrained one. We demonstrate the performance of various algorithms for different image restoration tasks both for images corrupted by Poisson noise and multiplicative Gamma noise. 1