The max-sum labeling problem, defined as maximizing a sum of functions of pairs of discrete variables, is a general optimization problem with numerous applications, e.g., computing MAP assignments of a Markov random field. We review a not widely known approach to the problem based on linear programming relaxation, developed by . We also show how this old approach contributes to more recent results, most importantly by Wainwright et al. In particular, we review Schlesinger's upper bound on the max-sum criterion, its minimization by equivalent transformations, its relation to constraint satisfaction problem, how it can be understood as a linear programming relaxation, and three kinds of consistency necessary for optimality of the upper bound. As special cases, we revisit problems with two labels and supermodular problems. We describe two algorithms for decreasing the upper bound. We present an example application to structural image analysis.

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A RANSAC-based algorithm for robust estimation of epipolar geometry from point correspondences in the possible presence of a dominant scene plane is presented. The algorithm handles scenes with (i) all points in a single plane, (ii) majority of points in a single plane and the rest off the plane, (iii) no dominant plane. It is not required to know a priori which of the cases (i) -(iii) occurs.The algorithm exploits a theorem we proved, that if five or more of seven correspondences are related by a homography then there is an epipolar geometry consistent with the seven-tuple as well as with all correspondences related by the homography. This means that a seven point sample consisting of two outliers and five inliers lying in a dominant plane produces an epipolar geometry which is wrong and yet consistent with a high number of correspondences. The theorem explains why RANSAC often fails to estimate epipolar geometry in the presence of a dominant plane.Rather surprisingly, the theorem also implies that RANSAC-based homography estimation is faster when drawing non-minimal samples of seven correspondences than minimal samples of four correspondences.

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Abstract-We present a number of contributions to the LP relaxation approach to weighted constraint satisfaction (= Gibbs energy minimization). We link this approach to many works from constraint programming, which relation has so far been ignored in machine vision and learning. While the approach has been mostly considered only for binary constraints, we generalize it to n-ary constraints in a simple and natural way. This includes a simple algorithm to minimize the LP-based upper bound, n-ary max-sum diffusionhowever, we consider using other bound-optimizing algorithms as well. The diffusion iteration is tractable for a certain class of higharity constraints represented as a black-box, which is analogical to propagators for global constraints CSP. Diffusion exactly solves permuted n-ary supermodular problems. A hierarchy of gradually tighter LP relaxations is obtained simply by adding various zero constraints and coupling them in various ways to existing constraints. Zero constraints can be added incrementally, which leads to a cutting plane algorithm. The separation problem is formulated as finding an unsatisfiable subproblem of a CSP.

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This paper presents a new approach to rendering arbitrary views of real-world 3-D objects of complex shapes. We propose to represent an object by a sparse set of corresponding .2-D views, and to construct any other view as a combination of these reference views. We show that this combination can be linear, assuming proximity of the views, and we suggest how the visibility of constructed points can be determined. Our approach makes it possible to avoid difficult 3-D reconstruction, assuming only rendering is required. Moreover, almost no calibration of views is needed. We present preliminary results on real objects, indicating that the approach is feasible.

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