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Joint 3d scene reconstruction and class segmentation
 In CVPR
, 2013
"... Both image segmentation and dense 3D modeling from images represent an intrinsically illposed problem. Strong regularizers are therefore required to constrain the solutions from being ’too noisy’. Unfortunately, these priors generally yield overly smooth reconstructions and/or segmentations in cert ..."
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Cited by 18 (4 self)
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Both image segmentation and dense 3D modeling from images represent an intrinsically illposed problem. Strong regularizers are therefore required to constrain the solutions from being ’too noisy’. Unfortunately, these priors generally yield overly smooth reconstructions and/or segmentations in certain regions whereas they fail in other areas to constrain the solution sufficiently. In this paper we argue that image segmentation and dense 3D reconstruction contribute valuable information to each other’s task. As a consequence, we propose a rigorous mathematical framework to formulate and solve a joint segmentation and dense reconstruction problem. Image segmentations provide geometric cues about which surface orientations are more likely to appear at a certain location in space whereas a dense 3D reconstruction yields a suitable regularization for the segmentation problem by lifting the labeling from 2D images to 3D space. We show how appearancebased cues and 3D surface orientation priors can be learned from training data and subsequently used for classspecific regularization. Experimental results on several real data sets highlight the advantages of our joint formulation. 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
A Survey and Comparison of Discrete and Continuous Multilabel Optimization Approaches for the Potts Model
 INT J COMPUT VIS
, 2013
"... We present a survey and a comparison of a variety of algorithms that have been proposed over the years to minimize multilabel optimization problems based on the Potts model. Discrete approaches based on Markov Random Fields as well as continuous optimization approaches based on partial differential ..."
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Cited by 12 (8 self)
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We present a survey and a comparison of a variety of algorithms that have been proposed over the years to minimize multilabel optimization problems based on the Potts model. Discrete approaches based on Markov Random Fields as well as continuous optimization approaches based on partial differential equations can be applied to the task. In contrast to the case of binary labeling, the multilabel problem is known to be NP hard and thus one can only expect nearoptimal solutions. In this paper, we carry out a theoretical comparison and an experimental analysis of existing approaches with respect to accuracy, optimality and runtime, aimed at bringing out the advantages and shortcomings of the respective algorithms. Systematic quantitative comparison is done on the Graz interactive image segmentation benchmark. This paper thereby generalizes a previous experimental comparison (Klodt et al. 2008) from the binary to the multilabel case.
What Is Optimized in Convex Relaxations for MultiLabel Problems: Connecting Discrete and ContinuouslyInspired MAP Inference
 SUBMITTED TO IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
"... In this work we present a unified view on Markov random fields and recently proposed continuous tight convex relaxations for multilabel assignment in the image plane. These relaxations are far less biased towards the grid geometry than Markov random fields (MRFs) on grids. It turns out that the con ..."
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Cited by 2 (2 self)
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In this work we present a unified view on Markov random fields and recently proposed continuous tight convex relaxations for multilabel assignment in the image plane. These relaxations are far less biased towards the grid geometry than Markov random fields (MRFs) on grids. It turns out that the continuous methods are nonlinear extensions of the wellestablished local polytope MRF relaxation. In view of this result a better understanding of these tight convex relaxations in the discrete setting is obtained. Further, a wider range of optimization methods is now applicable to find a minimizer of the tight formulation. We propose two methods to improve the efficiency of minimization. One uses a weaker, but more efficient continuously inspired approach as initialization and gradually refines the energy where it is necessary. The other one reformulates the dual energy enabling smooth approximations to be used for efficient optimization. We demonstrate the utility of our proposed minimization schemes in numerical experiments. Finally, we generalize the underlying energy formulation from isotropic metric smoothness costs to arbitrary nonmetric and orientation dependent smoothness terms.
Convex Relaxation of Vectorial Problems with Coupled Regularization
, 2014
"... We propose convex relaxations for nonconvex energies on vectorvalued functions which are both tractable yet as tight as possible. In contrast to existing relaxations, we can handle the combination of nonconvex data terms with coupled regularizers such as l2regularizers. The key idea is to consi ..."
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We propose convex relaxations for nonconvex energies on vectorvalued functions which are both tractable yet as tight as possible. In contrast to existing relaxations, we can handle the combination of nonconvex data terms with coupled regularizers such as l2regularizers. The key idea is to consider a collection of hypersurfaces with a relaxation that takes into account the entire functional rather than separately treating the data term and the regularizers. We provide a theoretical analysis, detail the implementations for different functionals, present run time and memory requirements, and experimentally demonstrate that the coupled l2regularizers give systematic improvements regarding denoising, inpainting and optical flow estimation.