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14
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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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.
Improved Moves for Truncated Convex Models
"... We consider the problem of obtaining the approximate maximum a posteriori estimate of a discrete random field characterized by pairwise potentials that form a truncated convex model. For this problem, we propose an improved stMINCUT based move making algorithm. Unlike previous move making approache ..."
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Cited by 21 (3 self)
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We consider the problem of obtaining the approximate maximum a posteriori estimate of a discrete random field characterized by pairwise potentials that form a truncated convex model. For this problem, we propose an improved stMINCUT based move making algorithm. Unlike previous move making approaches, which either provide a loose bound or no bound on the quality of the solution (in terms of the corresponding Gibbs energy), our algorithm achieves the same guarantees as the standard linear programming (LP) relaxation. Compared to previous approaches based on the LP relaxation, e.g. interiorpoint algorithms or treereweighted message passing (TRW), our method is faster as it uses only the efficient stMINCUT algorithm in its design. Furthermore, it directly provides us with a primal solution (unlike TRW and other related methods which solve the dual of the LP). We demonstrate the effectiveness of the proposed approach on both synthetic and standard real data problems. Our analysis also opens up an interesting question regarding the relationship between move making algorithms (such as αexpansion and the algorithms presented in this paper) and the randomized rounding schemes used with convex relaxations. We believe that further explorations in this direction would help design efficient algorithms for more complex relaxations.
MessagePassing for the Traveling Salesman Problem
"... This paper exploits the graphical model with the maxsum belief propagation to solve the traveling salesman problem which is commonly solved by heuristic algorithms. Based on the visitingship between each city and step, we represent the optimal tour search problem by a factor graph and utilize the m ..."
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This paper exploits the graphical model with the maxsum belief propagation to solve the traveling salesman problem which is commonly solved by heuristic algorithms. Based on the visitingship between each city and step, we represent the optimal tour search problem by a factor graph and utilize the maxsum belief propagation algorithm to achieve the neighborhood optimal solution. By applying some mathematical tricks to simplify the original messages, we obtain an efficient messagepassing algorithm. 1.
Generalized Fast Approximate Energy Minimization via Graph Cuts: αExpansion βShrink Moves
 CONFERENCE ON UNCERTAINTY IN ARTIFICIAL INTELLIGENCE
, 2011
"... We present αexpansion βshrink moves, a simple generalization of the widelyused αβswap and αexpansion algorithms for approximate energy minimization. We show that in a certain sense, these moves dominate both αβswap and αexpansion moves, but unlike previous generalizations the new moves require ..."
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We present αexpansion βshrink moves, a simple generalization of the widelyused αβswap and αexpansion algorithms for approximate energy minimization. We show that in a certain sense, these moves dominate both αβswap and αexpansion moves, but unlike previous generalizations the new moves require no additional assumptions and are still solvable in polynomialtime. We show promising experimental results with the new moves, which we believe could be used in any context where αexpansions are currently employed.
A Tiered Movemaking Algorithm for General Pairwise MRFs
"... A large number of problems in computer vision can be modeled as energy minimization problems in a markov random field (MRF) framework. Many methods have been developed over the years for efficient inference, especially in pairwise MRFs. In general there is a tradeoff between the complexity/efficien ..."
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A large number of problems in computer vision can be modeled as energy minimization problems in a markov random field (MRF) framework. Many methods have been developed over the years for efficient inference, especially in pairwise MRFs. In general there is a tradeoff between the complexity/efficiency of the algorithm and its convergence properties, with certain problems requiring more complex inference to handle general pairwise potentials. Graphcuts based αexpansion performs well on certain classes of energies, and sequential tree reweighted message passing (TRWS) and loopy belief propagation (LBP) can be used for nonsubmodular cases. These methods though suffer from poor convergence and often oscillate between solutions. In this paper, we propose a tiered move making algorithm which is an iterative method. Each move to the next configuration is based on the current labeling and an optimal tiered move, where each tiered move requires one application of the dynamic programming based tiered labeling method introduced in Felzenszwalb et. al. [2]. The algorithm converges to a local minimum for any general pairwise potential, and we give a theoretical analysis of the properties of the algorithm, characterizing the situations in which we can expect good performance. We evaluate the algorithm on many benchmark labeling problems such as stereo, image segmentation, image stitching and image denoising, as well as random energy minimization. Our method consistently gets better energy values than αexpansion, LBP, quadratic pseudoboolean optimization (QPBO), and is competitive with TRWS. 1.
FLARE: Fast Layout for Augmented Reality Applications
"... Figure 1: Designing an immersive augmented reality (AR) application such as a dynamic racing game is difficult. In our framework (a) declarative rules are used to define application elements and the rules governing them (b) in realtime we analyze an environment to extract scene geometry and horizon ..."
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Figure 1: Designing an immersive augmented reality (AR) application such as a dynamic racing game is difficult. In our framework (a) declarative rules are used to define application elements and the rules governing them (b) in realtime we analyze an environment to extract scene geometry and horizontal and vertical planes (c) our movemaking algorithm targets the application to the room (d) an additional result of our system in a different room with a longer track. Creating a layout for an augmented reality (AR) application which embeds virtual objects in a physical environment is difficult as it must adapt to any physical space. We propose a rulebased framework for generating object layouts for AR applications. Under our framework, the developer of an AR application specifies a set of rules (constraints) which enforce selfconsistency (rules regarding the interrelationships of application components) and sceneconsistency (application components are consistent with the physical environment they are placed in). When a user enters a new environment, we create, in realtime, a layout for the application, which is consistent with the defined constraints (as much as possible). We find the optimal configurations for each object by solving a constraintsatisfaction problem. Our stochastic move making algorithm is domainaware, and allows us to efficiently converge to a solution for most rulesets. In the paper we demonstrate several augmented reality applications that automatically adapt to different rooms and changing circumstances in each room.
Minimizing sparse higher order functions of discrete variables
 in CVPR
, 2009
"... Higher order energy functions have the ability to encode high level structural dependencies between pixels, which have been shown to be extremely powerful for image labeling problems. Their use, however, is severely hampered in practice by the intractable complexity of representing and minimizi ..."
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Higher order energy functions have the ability to encode high level structural dependencies between pixels, which have been shown to be extremely powerful for image labeling problems. Their use, however, is severely hampered in practice by the intractable complexity of representing and minimizing such functions. We observed that higher order functions encountered in computer vision are very often “sparse”, i.e. many labelings of a higher order clique are equally unlikely and hence have the same high cost. In this paper, we address the problem of minimizing such sparse higher order energy functions. Our method works by transforming the problem into an equivalent quadratic function minimization problem. The resulting quadratic function can be minimized using popular message passing or graph cut based algorithms for MAP inference. Although this is primarily a theoretical paper, we also show how labeling problems such as texture denoising and inpainting can be formulated using sparse higher order energy functions. We demonstrate experimentally that for some challenging tasks our formulation is able to outperform various stateofthe art techniques, especially the wellknown patchbased approach of Freeman et al. [11]. Given the broad use of patchbased models in computer vision, we believe that our contributions will be applicable in many problem domains. 1
Dynamic Programming for Approximate Expansion Algorithm
"... Abstract. Expansion algorithm is a popular optimization method for labeling problems. For many common energies, each expansion step can be optimally solved with a mincut/max flow algorithm. While the observed performance of maxflow for the expansion algorithm is fast, its theoretical time complexi ..."
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Abstract. Expansion algorithm is a popular optimization method for labeling problems. For many common energies, each expansion step can be optimally solved with a mincut/max flow algorithm. While the observed performance of maxflow for the expansion algorithm is fast, its theoretical time complexity is worse than linear in the number of pixels. Recently, Dynamic Programming (DP) was shown to be useful for 2D labeling problems via a “tiered labeling ” algorithm, although the structure of allowed (tiered) is quite restrictive. We show another use of DP in a 2D labeling case. Namely, we use DP for an approximate expansion step. Our expansionlike moves are more limited in the structure than the maxflow expansion moves. In fact, our moves are more restrictive than the tiered labeling structure, but their complexity is linear in the number of pixels, making them extremely efficient in practice. We illustrate the performance of our DPexpansion on the Potts energy, but our algorithm can be used for any pairwise energies. We achieve better efficiency with almost the same energy compared to the maxflow expansion moves. 1
Analysis of the Intact Surface Layer of Caulobacter crescentus by
, 2010
"... The surface layers (S layers) of those bacteria and archaea that elaborate these crystalline structures have been studied for 40 years. However, most structural analysis has been based on electron microscopy of negatively stained Slayer fragments separated from cells, which can introduce staining a ..."
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The surface layers (S layers) of those bacteria and archaea that elaborate these crystalline structures have been studied for 40 years. However, most structural analysis has been based on electron microscopy of negatively stained Slayer fragments separated from cells, which can introduce staining artifacts and allow rearrangement of structures prone to selfassemble. We present a quantitative analysis of the structure and organization of the S layer on intact growing cells of the Gramnegative bacterium Caulobacter crescentus using cryoelectron tomography (CET) and statistical image processing. Instead of the expected longrange order, we observed different regions with hexagonally organized subunits exhibiting shortrange order and a broad distribution of periodicities. Also, areas of stacked double layers were found, and these increased in extent when the Slayer protein (RsaA) expression level was elevated by addition of multiple rsaA copies. Finally, we combined highresolution amino acid residuespecific Nanogold labeling and subtomogram averaging of CET volumes to improve our understanding of the correlation between the linear protein sequence and the structure at the 2nm level of resolution that is presently available. The results support the view that the Ushaped RsaA monomer predicted from negativestain tomography proceeds from the N terminus at one vertex, corresponding to the axis of 3fold symmetry, to the C terminus at the opposite vertex, which forms the prominent 6fold symmetry axis. Such information will help future efforts to analyze subunit interactions and guide selection of
Exhaustive Family of Energies Minimizable Exactly by a Graph Cut
"... Graph cuts are widely used in many fields of computer vision in order to minimize in small polynomial time complexity certain classes of energies. These specific classes depend on the way chosen to build the graphs representing the problems to solve. We study here all possible ways of building graph ..."
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Graph cuts are widely used in many fields of computer vision in order to minimize in small polynomial time complexity certain classes of energies. These specific classes depend on the way chosen to build the graphs representing the problems to solve. We study here all possible ways of building graphs and the associated energies minimized, leading to the exhaustive family of energies minimizable exactly by a graph cut. To do this, we consider the issue of coding pixel labels as states of the graph, i.e. the choice of state interpretations. The family obtained comprises many new classes, in particular energies that do not satisfy the submodularity condition, including energies that are even not permutedsubmodular. A generating subfamily is studied in details, in particular we propose a canonical form to represent Markov random fields, which proves useful to recognize energies in this subfamily in linear complexity almost surely, and then to build the associated graph in quasilinear time. A few experiments are performed, to illustrate the new possibilities offered.