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10
Fast approximate energy minimization with label costs
, 2010
"... The αexpansion algorithm [7] has had a significant impact in computer vision due to its generality, effectiveness, and speed. Thus far it can only minimize energies that involve unary, pairwise, and specialized higherorder terms. Our main contribution is to extend αexpansion so that it can simult ..."
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Cited by 44 (6 self)
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The αexpansion algorithm [7] has had a significant impact in computer vision due to its generality, effectiveness, and speed. Thus far it can only minimize energies that involve unary, pairwise, and specialized higherorder terms. Our main contribution is to extend αexpansion so that it can simultaneously optimize “label costs ” as well. An energy with label costs can penalize a solution based on the set of labels that appear in it. The simplest special case is to penalize the number of labels in the solution. Our energy is quite general, and we prove optimality bounds for our algorithm. A natural application of label costs is multimodel fitting, and we demonstrate several such applications in vision: homography detection, motion segmentation, and unsupervised image segmentation. Our C++/MATLAB implementation is publicly available.
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 16 (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.
Segmentation with nonlinear regional constraints via linesearch cuts
"... Abstract. This paper is concerned with energybased image segmentation problems. We introduce a general class of regional functionals defined as an arbitrary nonlinear combination of regional unary terms. Such (highorder) functionals are very useful in vision and medical applications and some spec ..."
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Cited by 5 (2 self)
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Abstract. This paper is concerned with energybased image segmentation problems. We introduce a general class of regional functionals defined as an arbitrary nonlinear combination of regional unary terms. Such (highorder) functionals are very useful in vision and medical applications and some special cases appear in prior art. For example, our general class of functionals includes but is not restricted to soft constraints on segment volume, its appearance histogram, or shape. Our overall segmentation energy combines regional functionals with standard lengthbased regularizers and/or other submodular terms. In general, regional functionals make the corresponding energy minimization NPhard. We propose a new greedy algorithm based on iterative line search. A parametric maxflow technique efficiently explores all solutions along the direction (line) of the steepest descent of the energy. We compute the best “step size”, i.e. the globally optimal solution along the line. This algorithm can make large moves escaping weak local minima, as demonstrated on many real images. 1
Minimizing Energies with Hierarchical Costs
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 2012
"... Computer vision is full of problems elegantly expressed in terms of energy minimization. We characterize a class of energies with hierarchical costs and propose a novel hierarchical fusion algorithm. Hierarchical costs are natural for modeling an array of difficult problems. For example, in semantic ..."
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Cited by 3 (0 self)
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Computer vision is full of problems elegantly expressed in terms of energy minimization. We characterize a class of energies with hierarchical costs and propose a novel hierarchical fusion algorithm. Hierarchical costs are natural for modeling an array of difficult problems. For example, in semantic segmentation one could rule out unlikely object combinations via hierarchical context. In geometric model estimation, one could penalize the number of unique model families in a solution, not just the number of models—a kind of hierarchical MDL criterion. Hierarchical fusion uses the wellknown αexpansion algorithm as a subroutine, and offers a much better approximation bound in important cases.
Interactive Segmentation with SuperLabels
 In Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR
, 2011
"... *authors contributed equally ..."
Fast fusion moves for multimodel estimation
 IN: PROCEEDINGS OF THE EUROPEAN CONFERENCE ON COMPUTER VISION
, 2012
"... We develop a fast, effective algorithm for minimizing a wellknown objective function for robust multimodel estimation. Our work introduces a combinatorial step belonging to a family of powerful movemaking methods like αexpansion and fusion. We also show that our subproblem can be quickly transf ..."
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Cited by 3 (2 self)
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We develop a fast, effective algorithm for minimizing a wellknown objective function for robust multimodel estimation. Our work introduces a combinatorial step belonging to a family of powerful movemaking methods like αexpansion and fusion. We also show that our subproblem can be quickly transformed into a comparatively small instance of minimumweighted vertexcover. In practice, these vertexcover subproblems are almost always bipartite and can be solved exactly by specialized network flow algorithms. Experiments indicate that our approach achieves the robustness of methods like affinity propagation, whilst providing the speed of fast greedy heuristics.
Minimizing Sparse HighOrder Energies by Submodular Vertexcover
, 2012
"... Inference in highorder graphical models has become important in recent years. Several approaches are based, for example, on generalized messagepassing, or on transformation to a pairwise model with extra ‘auxiliary ’ variables. We focus on a special case where a much more efficient transformation ..."
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Cited by 3 (1 self)
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Inference in highorder graphical models has become important in recent years. Several approaches are based, for example, on generalized messagepassing, or on transformation to a pairwise model with extra ‘auxiliary ’ variables. We focus on a special case where a much more efficient transformation is possible. Instead of adding variables, we transform the original problem into a comparatively small instance of submodular vertexcover. These vertexcover instances can then be attacked by existing algorithms (e.g. belief propagation, QPBO), where they often run 4–15 times faster and find better solutions than when applied to the original problem. We evaluate our approach on synthetic data, then we show applications within a fast hierarchical clustering and modelfitting framework.
BoykovJolly Ours
"... user scribbles label 1 appearance models superlabel 1 sublabeling appearance models Fig. 1. Given user scribbles, typical MRF segmentation (BoykovJolly) uses a GMM to model the appearance of each object label. This makes the strong assumption that pixels inside each object are i.i.d. In contrast, ..."
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user scribbles label 1 appearance models superlabel 1 sublabeling appearance models Fig. 1. Given user scribbles, typical MRF segmentation (BoykovJolly) uses a GMM to model the appearance of each object label. This makes the strong assumption that pixels inside each object are i.i.d. In contrast, we define a twolevel MRF to encourage interobject coherence among superlabels and intraobject coherence among sublabels. Abstract. In interactive segmentation, the most common way to model object appearance is by GMM or histogram, while MRFs are used to encourage spatial coherence among the object labels. This makes the strong assumption that pixels within each object are i.i.d. when in fact most objects have multiple distinct appearances and exhibit strong spatial correlation among their pixels. At the very least, this calls for an MRFbased appearance model within each object itself and yet, to the best of our knowledge, such a “twolevel MRF ” has never been proposed. We propose a novel segmentation energy that can model complex appearance. We represent the appearance of each object by a set of distinct spatially coherent models. This results in a twolevel MRF with “superlabels” at the top level that are partitioned into “sublabels ” at the bottom. We introduce the hierarchical Potts (hPotts) prior to govern spatial coherence within each level. Finally, we introduce a novel algorithm with EMstyle alternation of proposal, αexpansion and reestimation steps. Our experiments demonstrate the conceptual and qualitative improvement that a twolevel MRF can provide. We show applications in binary segmentation, multiclass segmentation, and interactive cosegmentation. Finally, our energy and algorithm have interesting interpretations in terms of semisupervised learning. 1
Minimizing Sparse HighOrder Energies by
"... Inference in highorder graphical models has become important in recent years. Several approaches are based, for example, on generalized messagepassing, or on transformation to a pairwise model with extra ‘auxiliary ’ variables. We focus on a special case where a much more efficient transformation ..."
Abstract
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Inference in highorder graphical models has become important in recent years. Several approaches are based, for example, on generalized messagepassing, or on transformation to a pairwise model with extra ‘auxiliary ’ variables. We focus on a special case where a much more efficient transformation is possible. Instead of adding variables, we transform the original problem into a comparatively small instance of submodular vertexcover. These vertexcover instances can then be attacked by existing algorithms (e.g. belief propagation, QPBO), where they often run 4–15 times faster and find better solutions than when applied to the original problem. We evaluate our approach on synthetic data, then we show applications within a fast hierarchical clustering and modelfitting framework. 1