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11
Piecewise rigid scene flow
 IN: PROC. ICCV
, 2013
"... Estimating dense 3D scene flow from stereo sequences remains a challenging task, despite much progress in both classical disparity and 2D optical flow estimation. To overcome the limitations of existing techniques, we introduce a novel model that represents the dynamic 3D scene by a collection of p ..."
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Cited by 15 (1 self)
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Estimating dense 3D scene flow from stereo sequences remains a challenging task, despite much progress in both classical disparity and 2D optical flow estimation. To overcome the limitations of existing techniques, we introduce a novel model that represents the dynamic 3D scene by a collection of planar, rigidly moving, local segments. Scene flow estimation then amounts to jointly estimating the pixeltosegment assignment, and the 3D position, normal vector, and rigid motion parameters of a plane for each segment. The proposed energy combines an occlusionsensitive data term with appropriate shape, motion, and segmentation regularizers. Optimization proceeds in two stages: Starting from an initial superpixelization, we estimate the shape and motion parameters of all segments by assigning a proposal from a set of moving planes. Then the pixeltosegment assignment is updated, while holding the shape and motion parameters of the moving planes fixed. We demonstrate the benefits of our model on different realworld image sets, including the challenging KITTI benchmark. We achieve leading performance levels, exceeding competing 3D scene flow methods, and even yielding better 2D motion estimates than all tested dedicated optical flow techniques.
Markov Random Field Modeling, Inference & Learning in Computer Vision & Image Understanding: A Survey
, 2013
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Generalized roof duality and bisubmodular functions
, 2010
"... Consider a convex relaxation ˆ f of a pseudoboolean function f. We say that the relaxation is totally halfintegral if ˆ f(x) is a polyhedral function with halfintegral extreme points x, and this property is preserved after adding an arbitrary combination of constraints of the form xi = xj, xi = 1 ..."
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Cited by 12 (1 self)
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Consider a convex relaxation ˆ f of a pseudoboolean function f. We say that the relaxation is totally halfintegral if ˆ f(x) is a polyhedral function with halfintegral extreme points x, and this property is preserved after adding an arbitrary combination of constraints of the form xi = xj, xi = 1 − xj, and xi = γ where γ ∈ {0, 1, 1 2} is a constant. A wellknown example is the roof duality relaxation for quadratic pseudoboolean functions f. We argue that total halfintegrality is a natural requirement for generalizations of roof duality to arbitrary pseudoboolean functions. Our contributions are as follows. First, we provide a complete characterization of totally halfintegral relaxations ˆ f by establishing a onetoone correspondence with bisubmodular functions. Second, we give a new characterization of bisubmodular functions. Finally, we show some relationships between general totally halfintegral relaxations and relaxations based on the roof duality.
Minimizing Countbased High Order Terms in Markov Random Fields
"... Abstract. We present a technique to handle computer vision problems inducing models with very high order terms in fact terms of maximal order. Here we consider terms where the cost function depends only on the number of variables that are assigned a certain label, but where the dependence is arbitr ..."
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Cited by 2 (0 self)
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Abstract. We present a technique to handle computer vision problems inducing models with very high order terms in fact terms of maximal order. Here we consider terms where the cost function depends only on the number of variables that are assigned a certain label, but where the dependence is arbitrary. Applications include image segmentation with a histogrambased data term [28] and the recently introduced marginal probability fields [31]. The presented technique makes use of linear and integer linear programming. We include a set of customized cuts to strengthen the formulations. 1
A hybrid approach for MRF optimization problems: Combination of stochastic sampling and . . .
 COMPUTER VISION AND IMAGE UNDERSTANDING 115 (2011) 1623–1637
, 2011
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Markov Random Fields in Vision Perception: A Survey
, 2012
"... In this paper, we present a comprehensive survey of Markov Random Fields (MRFs) in computer vision, with respect to both the modeling and the inference. MRFs were introduced into the computer vision field about two decades ago, while they started to become a ubiquitous tool for solving visual perce ..."
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In this paper, we present a comprehensive survey of Markov Random Fields (MRFs) in computer vision, with respect to both the modeling and the inference. MRFs were introduced into the computer vision field about two decades ago, while they started to become a ubiquitous tool for solving visual perception problems at the turn of the millennium following the emergence of efficient inference methods. During the past decade, different MRF models as well as inference methods in particular those based on discrete optimization have been developed towards addressing numerous vision problems of low, mid and high level. While most of the literature concerns pairwise MRFs, during recent years, we have also witnessed significant progress on higherorder MRFs, which substantially enhances the expressiveness of graphbased models and enlarges the extent of solvable problems. We hope that this survey will provide a compact and informative summary of the main literature in this research topic.
Computer Vision and Image Understanding 117 (2013) 289–303 Contents lists available at SciVerse ScienceDirect Computer Vision and Image Understanding
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Stereo Reconstruction using High Order Likelihood
"... Under the popular Bayesian approach, a stereo problem can be formulated by defining likelihood and prior. Likelihoods are often associated with unary terms and priors are define by pairwise or higher cliques in Markov random field (MRF). In this paper, likelihood is proposed using higher order cliq ..."
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Under the popular Bayesian approach, a stereo problem can be formulated by defining likelihood and prior. Likelihoods are often associated with unary terms and priors are define by pairwise or higher cliques in Markov random field (MRF). In this paper, likelihood is proposed using higher order cliques. Numerous patch based matching methods such as normalized cross correlation, Laplacian of Gaussian, or census filters are under the naive assumption that a patch’s pixels all have same disparities. However, patchwise cost can be formulated as higher order clique for MRF so that the matching cost is a function of image patch’s disparities. A patch obtained from a projected image by disparity map should provide a better match without the blurring effect around disparity discontinuities. Among patchwise matching costs, census filter approach can be easily reduced to pairwise cliques. The experimental results on census filter high older likelihood demonstrate the advantages of high order likelihood over independent identically distributed unary model. 1.
HigherOrder Clique Reduction in Binary Graph Cut Hiroshi Ishikawa
"... We introduce a new technique that can reduce any higherorder Markov random field with binary labels into a firstorder one that has the same minima as the original. Moreover, we combine the reduction with the fusionmove and QPBO algorithms to optimize higherorder multilabel problems. While many ..."
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We introduce a new technique that can reduce any higherorder Markov random field with binary labels into a firstorder one that has the same minima as the original. Moreover, we combine the reduction with the fusionmove and QPBO algorithms to optimize higherorder multilabel problems. While many vision problems today are formulated as energy minimization problems, they have mostly been limited to using firstorder energies, which consist of unary and pairwise clique potentials, with a few exceptions that consider triples. This is because of the lack of efficient algorithms to optimize energies with higherorder interactions. Our algorithm challenges this restriction that limits the representational power of the models, so that higherorder energies can be used to capture the rich statistics of natural scenes. To demonstrate the algorithm, we minimize a thirdorder energy, which allows clique potentials with up to four pixels, in an image restoration problem. The problem uses the Fields of Experts model, a learned spatial prior of natural images that has been used to test two belief propagation algorithms capable of optimizing higherorder energies. The results show that the algorithm exceeds the BP algorithms in both optimization performance and speed. 1.