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74
Beyond pairwise energies: Efficient optimization for higherorder MRFs
 in IEEE Conference on Computer Vision and Pattern Recognition : CVPR
, 2009
"... In this paper, we introduce a higherorder MRF optimization framework. On the one hand, it is very general; we thus use it to derive a generic optimizer that can be applied to almost any higherorder MRF and that provably optimizes a dual relaxation related to the input MRF problem. On the other han ..."
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Cited by 80 (11 self)
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In this paper, we introduce a higherorder MRF optimization framework. On the one hand, it is very general; we thus use it to derive a generic optimizer that can be applied to almost any higherorder MRF and that provably optimizes a dual relaxation related to the input MRF problem. On the other hand, it is also extremely flexible and thus can be easily adapted to yield far more powerful algorithms when dealing with subclasses of highorder MRFs. We thus introduce a new powerful class of highorder potentials, which are shown to offer enough expressive power and to be useful for many vision tasks. To address them, we derive, based on the same framework, a novel and extremely efficient messagepassing algorithm, which goes beyond the aforementioned generic optimizer and is able to deliver almost optimal solutions of very high quality. Experimental results on vision problems demonstrate the extreme effectiveness of our approach. For instance, we show that in some cases we are even able to compute the global optimum for NPhard higherorder MRFs in a very efficient manner. 1.
Surface Stereo with Soft Segmentation
"... This paper proposes a new stereo model which encodes the simple assumption that the scene is composed of a few, smooth surfaces. A key feature of our model is the surfacebased representation, where each pixel is assigned to a 3D surface (planes or Bsplines). This representation enables several impo ..."
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Cited by 30 (2 self)
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This paper proposes a new stereo model which encodes the simple assumption that the scene is composed of a few, smooth surfaces. A key feature of our model is the surfacebased representation, where each pixel is assigned to a 3D surface (planes or Bsplines). This representation enables several important contributions: Firstly, we formulate a higherorder prior which states that pixels of similar appearance are likely to belong to the same 3D surface. This enables to incorporate the very popular color segmentation constraint in a soft and principled way. Secondly, we use a global MDL prior to penalize the number of surfaces. Thirdly, we are able to incorporate, in a simple way, a prior which favors low curvature surfaces. Fourthly, we improve the asymmetric occlusion model by disallowing pixels of the same surface to occlude each other. Finally, we use the known fusion move approach which enables a powerful optimization of our model, despite the infinite number of possible labelings (surfaces). 1.
The shape Boltzmann machine: A strong model of object shape
 In CVPR
, 2012
"... A good model of object shape is essential in applications such as segmentation, object detection, inpainting and graphics. For example, when performing segmentation, local constraints on the shape can help where the object boundary is noisy or unclear, and global constraints can resolve ambiguities ..."
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Cited by 29 (2 self)
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A good model of object shape is essential in applications such as segmentation, object detection, inpainting and graphics. For example, when performing segmentation, local constraints on the shape can help where the object boundary is noisy or unclear, and global constraints can resolve ambiguities where background clutter looks similar to part of the object. In general, the stronger the model of shape, the more performance is improved. In this paper, we use a type of Deep Boltzmann Machine [22] that we call a Shape Boltzmann Machine (ShapeBM) for the task of modeling binary shape images. We show that the ShapeBM characterizes a strong model of shape, in that samples from the model look realistic and it can generalize to generate samples that differ from training examples. We find that the ShapeBM learns distributions that are qualitatively and quantitatively better than existing models for this task. 1.
Transformation of General Binary MRF Minimization to the First Order Case
 IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI
, 2011
"... Abstract—We introduce a transformation of general higherorder Markov random field with binary labels into a firstorder one that has the same minima as the original. Moreover, we formalize a framework for approximately minimizing higherorder multilabel MRF energies that combines the new reduction ..."
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Cited by 29 (3 self)
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Abstract—We introduce a transformation of general higherorder Markov random field with binary labels into a firstorder one that has the same minima as the original. Moreover, we formalize a framework for approximately minimizing higherorder multilabel MRF energies that combines the new reduction with the fusionmove and QPBO algorithms. While many computer 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. We also show that some minimization methods can be considered special cases of the present framework, as well as comparing the new method experimentally with other such techniques. Index Terms—Energy minimization, pseudoBoolean function, higher order MRFs, graph cuts. F 1
Energy Minimization for Linear Envelope MRFs
"... Markov random fields with higher order potentials have emerged as a powerful model for several problems in computer vision. In order to facilitate their use, we propose a new representation for higher order potentials as upper and lower envelopes of linear functions. Our representation concisely mod ..."
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Cited by 26 (8 self)
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Markov random fields with higher order potentials have emerged as a powerful model for several problems in computer vision. In order to facilitate their use, we propose a new representation for higher order potentials as upper and lower envelopes of linear functions. Our representation concisely models several commonly used higher order potentials, thereby providing a unified framework for minimizing the corresponding Gibbs energy functions. We exploit this framework by converting lower envelope potentials to standard pairwise functions with the addition of a small number of auxiliary variables. This allows us to minimize energy functions with lower envelope potentials using conventional algorithms such as BP, TRW and αexpansion. Furthermore, we show how the minimization of energy functions with upper envelope potentials leads to a difficult minmax problem. We address this difficulty by proposing a new message passing algorithm that solves a linear programming relaxation of the problem. Although this is primarily a theoretical paper, we demonstrate the efficacy of our approach on the binary (fg/bg) segmentation problem. 1.
A graph cut algorithm for higherorder markov random fields
 IN: INT. CONF. COMPUTER VISION
, 2011
"... Higherorder Markov Random Fields, which can capture important properties of natural images, have become increasingly important in computer vision. While graph cuts work well for firstorder MRF’s, until recently they have rarely been effective for higherorder MRF’s. Ishikawa’s graph cut technique ..."
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Cited by 20 (5 self)
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Higherorder Markov Random Fields, which can capture important properties of natural images, have become increasingly important in computer vision. While graph cuts work well for firstorder MRF’s, until recently they have rarely been effective for higherorder MRF’s. Ishikawa’s graph cut technique [8, 9] shows great promise for many higherorder MRF’s. His method transforms an arbitrary higherorder MRF with binary labels into a firstorder one with the same minima. If all the terms are submodular the exact solution can be easily found; otherwise, pseudoboolean optimization techniques can produce an optimal labeling for a subset of the variables. We present a new transformation with better performance than [8, 9], both theoretically and experimentally. While [8, 9] transforms each higherorder term independently, we transform a group of terms at once. For n binary variables, each of which appears in terms with k other variables, at worst we produce n nonsubmodular terms, while [8, 9] produces O(nk). We identify a local completeness property that makes our method perform even better, and show that under certain assumptions several important vision problems (including common variants of fusion moves) have this property. Running on the same field of experts dataset used in [8, 9] we optimally label significantly more variables (96 % versus 80%) and converge more rapidly to a lower energy. Preliminary experiments suggest that some other higherorder MRF’s used in stereo [20] and segmentation [1] are also locally complete and would thus benefit from our work.
Filterbased meanfield inference for random fields with higher order terms and product labelspaces
 In ECCV
, 2012
"... Abstract. Recently, a number of cross bilateral filtering methods have been proposed for solving multilabel problems in computer vision, such as stereo, optical flow and object class segmentation that show an order of magnitude improvement in speed over previous methods. These methods have achieved ..."
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Cited by 17 (5 self)
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Abstract. Recently, a number of cross bilateral filtering methods have been proposed for solving multilabel problems in computer vision, such as stereo, optical flow and object class segmentation that show an order of magnitude improvement in speed over previous methods. These methods have achieved good results despite using models with only unary and/or pairwise terms. However, previous work has shown the value of using models with higherorder terms e.g. to represent label consistency over large regions, or global cooccurrence relations. We show how these higherorder terms can be formulated such that filterbased inference remains possible. We demonstrate our techniques on joint stereo and object labeling problems, as well as object class segmentation, showing in addition for joint objectstereo labeling how our method provides an efficient approach to inference in product labelspaces. We show that we are able to speed up inference in these models around 1030 times with respect to competing graphcut/movemaking methods, as well as maintaining or improving accuracy in all cases. We show results on PascalVOC10 for object class segmentation, and Leuven for joint objectstereo labeling. 1
Structured Output Learning with High Order Loss Functions
"... Often when modeling structured domains, it is desirable to leverage information that is not naturally expressed as simply a label. Examples include knowledge about the evaluation measure that will be used at test time, and partial (weak) label information. When the additional information has structu ..."
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Cited by 16 (4 self)
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Often when modeling structured domains, it is desirable to leverage information that is not naturally expressed as simply a label. Examples include knowledge about the evaluation measure that will be used at test time, and partial (weak) label information. When the additional information has structure that factorizes according to small subsets of variables (i.e., is low order, or decomposable), several approaches can be used to incorporate it into a learning procedure. Our focus in this work is the more challenging case, where the additional information does not factorize according to low order graphical model structure; we call this the high order case. We propose to formalize various forms of this additional information as high order loss functions, which may have complex interactions over large subsets of variables. We then address the computational challenges inherent in learning according to such loss functions, particularly focusing on the lossaugmented inference problem that arises in large margin learning; we show that learning with high order loss functions is often practical, giving strong empirical results, with one popular and several novel highorder loss functions, in several settings. 1