. In this paper we introduce the truncated primal-infeasible dual-feasible interior point algorithm for linear programming and describe an implementation of this algorithm for solving the minimum cost network flow problem. In each iteration, the linear system that determines the search direction is computed inexactly, and the norm of the resulting residual vector is used in the stopping criteria of the iterative solver employed for the solution of the system. In the implementation, a preconditioned conjugate gradient method is used as the iterative solver. The details of the implementation are described and the code, pdnet, is tested on a large set of standard minimum cost network flow test problems. Computational results indicate that the implementation is competitive with state-of-the-art network flow codes. Key Words. Interior point method, linear programming, network flows, primal-infeasible dualfeasible, truncated Newton method, conjugate gradient, maximum flow, experimental test...

The cost scaling push-relabel method has been shown to be efficient for solving minimum-cost flow problems. In this paper we apply the method to the assignment problem and investigate implementations of the method that take advantage of assignment's special structure. The results show that the method is very promising for practical use.

An important and difficult problem in computer vision is to determine 2D image feature correspondences over a set of images. In this paper, two new affinity measures for image points and lines from different images are presented, and are used to construct unweighted and weighted bipartite graphs. It is shown that the image feature matching problem can be reduced to an unweighted matching problem in the bipartite graphs. It is further shown that the problem can be formulated as the general maximum-weight bipartite matching problem, thus generalizing the above unweighted bipartite matching technique. Keywords: image feature matching, bipartite matching, image sequence analysis, computer vision 1 INTRODUCTION A fundamental and important problem in computer vision is to acquire 3D models of objects and scenes from a set of images. The basic principles involved in 3D model acquisition are feature matching and triangulation, with the two commonly used types of image features being points an...

We study and compare preconditioners available for network interior point methods. We derive upper bounds for the condition number of the preconditioned matrices used in the solution of systems of linear equations defining the algorithm search directions. The preconditioners...

. Computational algorithms for the solution of network flow problems are of great practical significance. In the last decade, a new class of computationally efficient algorithms, based on the interior point method, has been proposed and applied to solve large scale network flow problems. In this chapter, we review interior point approaches for network flows, with emphasis on computational issues. Key words. Network flow problems, interior point methods, computational testing, computer implementation. AMS(MOS) subject classifications. 90B10, 90C05, 90C06, 90C35, 65-05, 65F10, 65F50 1. Introduction. A large number of problems in transportation, communications, and manufacturing can be modeled as network flow problems. In these problems one seeks to find the most efficient, or optimal, way to move flow (e.g. materials, information, buses, electrical currents) on a network (e.g. postal network, computer network, transportation grid, power grid). Among these optimization problems, many a...

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Three-dimensional reconstruction from a set of images is an important and difficult problem in computer vision. In this paper, we address the problem of determining image feature correspondences while simultaneously reconstructing the corresponding 3D features, given the camera poses of disparate monocular views. First, two new affinity measures are presented that capture the degree to which candidate features from different images consistently represent the projection of the same 3D point or 3D line. An affinity measure for point features in two different views is defined with respect to their distance from a hypothetical projected 3D pseudo-intersection point. Similarly, an affinity measure for 2D image line segments across three views is defined with respect to a 3D pseudo-intersection line. These affinity measures provide a foundation for determining unknown correspondences using weighted bipartited graphs representing candidate point and line matches across different images. As a result of this graph representation, a standard graph-theoretic algorithm can provide an optimal, simultaneous matching and triangulation of points across two views, and lines across three views. Experimental results on synthetic and real data demonstrate the effectiveness of the approach.

Abstract—A protein molecule consists one or more chains of amino acid sequences that fold into a complex threedimensional structure. A protein’s functions are often determined by its 3D structure, and so comparing the similarity of 3D structures between proteins is an important problem. To accomplish such comparison, one must align two proteins properly with rotation and translation in 3D space. Finding the correspondences between structural elements in the two proteins is the key step in many protein structure alignment algorithms. In this paper, we introduce a new graph theoretic framework based on bipartite graph matching for finding sufficiently good correspondences. It is capable of providing both sequence-dependent and sequence-independent correspondences. It is a general framework for pair-wise matching of atoms, amino acids residues or secondary structure elements.