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80
Dense Nonrigid Surface Registration Using HighOrder Graph Matching
"... In this paper, we propose a highorder graph matching formulation to address nonrigid surface matching. The singleton terms capture the geometric and appearance similarities (e.g., curvature and texture) while the highorder terms model the intrinsic embedding energy. The novelty of this paper incl ..."
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Cited by 48 (11 self)
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In this paper, we propose a highorder graph matching formulation to address nonrigid surface matching. The singleton terms capture the geometric and appearance similarities (e.g., curvature and texture) while the highorder terms model the intrinsic embedding energy. The novelty of this paper includes: 1) casting 3D surface registration into a graph matching problem that combines both geometric and appearance similarities and intrinsic embedding information, 2) the first implementation of highorder graph matching algorithm that solves a nonconvex optimization problem, and 3) an efficient twostage optimization approach to constrain the search space for dense surface registration. Our method is validated through a series of experiments demonstrating its accuracy and efficiency, notably in challenging cases of large and/or nonisometric deformations, or meshes that are partially occluded. 1.
An Augmented Lagrangian Approach to Constrained MAP Inference
"... We propose a new algorithm for approximate MAP inference on factor graphs, by combining augmented Lagrangian optimization with the dual decomposition method. Each slave subproblem is given a quadratic penalty, which pushes toward faster consensus than in previous subgradient approaches. Our algorith ..."
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Cited by 37 (3 self)
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We propose a new algorithm for approximate MAP inference on factor graphs, by combining augmented Lagrangian optimization with the dual decomposition method. Each slave subproblem is given a quadratic penalty, which pushes toward faster consensus than in previous subgradient approaches. Our algorithm is provably convergent, parallelizable, and suitable for fine decompositions of the graph. We show how it can efficiently handle problems with (possibly global) structural constraints via simple sort operations. Experiments on synthetic and realworld data show that our approach compares favorably with the stateoftheart. 1.
Accelerated dual decomposition for MAP inference
 In ICML
, 2010
"... Approximate MAP inference in graphical models is an important and challenging problem for many domains including computer vision, computational biology and natural language understanding. Current stateoftheart approaches employ convex relaxations of these problems as surrogate objectives, but ..."
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Cited by 37 (1 self)
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Approximate MAP inference in graphical models is an important and challenging problem for many domains including computer vision, computational biology and natural language understanding. Current stateoftheart approaches employ convex relaxations of these problems as surrogate objectives, but only provide weak running time guarantees. In this paper, we develop an approximate inference algorithm that is both efficient and has strong theoretical guarantees. Specifically, our algorithm is guaranteed to converge to an accurate solution of the convex relaxation in O
Submodularity beyond submodular energies: coupling edges in graph cuts
 IN CVPR
, 2011
"... We propose a new family of nonsubmodular global energy functions that still use submodularity internally to couple edges in a graph cut. We show it is possible to develop an efficient approximation algorithm that, thanks to the internal submodularity, can use standard graph cuts as a subroutine. We ..."
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Cited by 32 (17 self)
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We propose a new family of nonsubmodular global energy functions that still use submodularity internally to couple edges in a graph cut. We show it is possible to develop an efficient approximation algorithm that, thanks to the internal submodularity, can use standard graph cuts as a subroutine. We demonstrate the advantages of edge coupling in a natural setting, namely image segmentation. In particular, for finestructured objects and objects with shading variation, our structured edge coupling leads to significant improvements over standard approaches.
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.
ModelBased 3D Hand Pose Estimation from Monocular Video
"... A novel modelbased approach to 3D hand tracking from monocular video is presented. The 3D hand pose, the hand texture and the illuminant are dynamically estimated through minimization of an objective function. Derived from an inverse problem formulation, the objective function enables explicit use ..."
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Cited by 25 (2 self)
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A novel modelbased approach to 3D hand tracking from monocular video is presented. The 3D hand pose, the hand texture and the illuminant are dynamically estimated through minimization of an objective function. Derived from an inverse problem formulation, the objective function enables explicit use of temporal texture continuity and shading information, while handling important selfocclusions and timevarying illumination. The minimization is done efficiently using a quasiNewton method, for which we provide a rigorous derivation of the objective function gradient. Particular attention is given to terms related to the change of visibility near selfocclusion boundaries that are neglected in existing formulations. To this end we introduce new occlusion forces and show that using all gradient terms greatly improves the performance of the method. Qualitative and quantitative experimental results demonstrate the potential of the approach.
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
Beyond Trees: MRF Inference via OuterPlanar Decomposition
, 2010
"... Maximum a posteriori (MAP) inference in Markov Random Fields (MRFs) is an NPhard problem, and thus research has focussed on either finding efficiently solvable subclasses (e.g. trees), or approximate algorithms (e.g. Loopy Belief Propagation (BP) and Treereweighted (TRW) methods). This paper prese ..."
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Cited by 17 (1 self)
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Maximum a posteriori (MAP) inference in Markov Random Fields (MRFs) is an NPhard problem, and thus research has focussed on either finding efficiently solvable subclasses (e.g. trees), or approximate algorithms (e.g. Loopy Belief Propagation (BP) and Treereweighted (TRW) methods). This paper presents a unifying perspective of these approximate techniques called “Decomposition Methods”. These are methods that decompose the given problem over a graph into tractable subproblems over subgraphs and then employ message passing over these subgraphs to merge the solutions of the subproblems into a global solution. This provides a new way of thinking about BP and TRW as successive steps in a hierarchy of decomposition methods. Using this framework, we take a principled first step towards extending this hierarchy beyond trees. We leverage a new class of graphs amenable to exact inference, called outerplanar graphs, and propose an approximate inference algorithm called OuterPlanar Decomposition (OPD). OPD is a strict generalization of BP and TRW, and contains both of them as special cases. Our experiments show that this extension beyond trees is indeed very powerful – OPD outperforms current stateofart inference methods on hard nonsubmodular synthetic problems and is competitive on real computer vision applications.