Results 1  10
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50
Entropy rate superpixel segmentation
, 2011
"... We propose a new objective function for superpixel segmentation. This objective function consists of two components: entropy rate of a random walk on a graph and a balancing term. The entropy rate favors formation of compact and homogeneous clusters, while the balancing function encourages clusters ..."
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Cited by 33 (1 self)
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We propose a new objective function for superpixel segmentation. This objective function consists of two components: entropy rate of a random walk on a graph and a balancing term. The entropy rate favors formation of compact and homogeneous clusters, while the balancing function encourages clusters with similar sizes. We present a novel graph construction for images and show that this construction induces a matroid — a combinatorial structure that generalizes the concept of linear independence in vector spaces. The segmentation is then given by the graph topology that maximizes the objective function under the matroid constraint. By exploiting submodular and monotonic properties of the objective function, we develop an efficient greedy algorithm. Furthermore, we prove an approximation bound of 1 2 for the optimality of the solution. Extensive experiments on the Berkeley segmentation benchmark show that the proposed algorithm outperforms the state of the art in all the standard evaluation metrics. 1.
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 32 (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.
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
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.
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
The Expressive Power of Binary Submodular Functions
, 2008
"... It has previously been an open problem whether all Boolean submodular functions can be decomposed into a sum of binary submodular functions over a possibly larger set of variables. This problem has been considered within several different contexts in computer science, including computer vision, arti ..."
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Cited by 15 (3 self)
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It has previously been an open problem whether all Boolean submodular functions can be decomposed into a sum of binary submodular functions over a possibly larger set of variables. This problem has been considered within several different contexts in computer science, including computer vision, artificial intelligence, and pseudoBoolean optimisation. Using a connection between the expressive power of valued constraints and certain algebraic properties of functions, we answer this question negatively. Our results have several corollaries. First, we characterise precisely which submodular functions of arity 4 can be expressed by binary submodular functions. Next, we identify a novel class of submodular functions of arbitrary arities which can be expressed by binary submodular functions, and therefore minimised efficiently using a socalled expressibility reduction to the MinCut problem. More importantly, our results imply limitations on this kind of reduction and establish for the first time that it cannot be used in general to minimise arbitrary submodular functions. Finally, we refute a conjecture of Promislow and Young on the structure of the extreme rays of the cone of Boolean submodular functions.
Markov Random Field Modeling, Inference & Learning in Computer Vision & Image Understanding: A Survey
, 2013
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Alphabet SOUP: A Framework for Approximate Energy Minimization
"... Many problems in computer vision can be modeled using conditional Markov random fields (CRF). Since finding the maximum a posteriori (MAP) solution in such models is NPhard, much attention in recent years has been placed on finding good approximate solutions. In particular, graphcut based algorith ..."
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Cited by 14 (1 self)
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Many problems in computer vision can be modeled using conditional Markov random fields (CRF). Since finding the maximum a posteriori (MAP) solution in such models is NPhard, much attention in recent years has been placed on finding good approximate solutions. In particular, graphcut based algorithms, such as αexpansion, are tremendously successful at solving problems with regular potentials. However, for arbitrary energy functions, message passing algorithms, such as maxproduct belief propagation, are still the only resort. In this paper we describe a general framework for finding approximate MAP solutions of arbitrary energy functions. Our algorithm (called Alphabet SOUP for Sequential Optimization for Unrestricted Potentials) performs a search over variable assignments by iteratively solving subproblems over a reduced statespace. We provide a theoretical guarantee on the quality of the solution when the inner loop of our algorithm is solved exactly. We show that this approach greatly improves the efficiency of inference and achieves lower energy solutions for a broad range of vision problems. 1.
Classes of submodular constraints expressible by graph cuts
 IN: PROCEEDINGS OF THE 14TH INTERNATIONAL CONFERENCE ON PRINCIPLES AND PRACTICE OF CONTRAINT PROGRAMMING (CP’08). VOLUME 5202 OF LNCS. (2008
, 2008
"... Submodular constraints play an important role both in theory and practice of valued constraint satisfaction problems (VCSPs). It has previously been shown, using results from the theory of combinatorial optimisation, that instances of VCSPs with submodular constraints can be minimised in polynomial ..."
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Cited by 13 (2 self)
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Submodular constraints play an important role both in theory and practice of valued constraint satisfaction problems (VCSPs). It has previously been shown, using results from the theory of combinatorial optimisation, that instances of VCSPs with submodular constraints can be minimised in polynomial time. However, the general algorithm is of order O(n 6) and hence rather impractical. In this paper, by using results from the theory of pseudoBoolean optimisation, we identify several broad classes of submodular constraints over a Boolean domain which are expressible using binary submodular constraints, and hence can be minimised in cubic time. Furthermore, we describe how our results translate to certain optimisation problems arising in computer vision.