This paper presents estimates of the convergence rate and complexity of an algebraic multilevel preconditioner based on piecewise constant coarse vector spaces applied to the graph Laplacian. A bound is derived on the energy norm of the projection operator onto any piecewise constant vector space, which results in an estimate of the two-level convergence rate where the coarse level graph is obt...

Conformal geometry has deep roots in pure mathematics. It is the intersection of complex analysis, Riemann surface theory, algebraic geometry, differential geometry and algebraic topology. Computational conformal geometry plays an important role in digital geometry processing. Recently, theory of discrete conformal geometry and algorithms of computational conformal geometry have been developed....

In this paper we present approximate algorithms for matching two polygonal curves with respect to the Fréchet distance. We define a discrete version of the Fréchet distance as a distance measure between polygonal curves and show that this discrete version is bounded by the continuous version of the Fréchet distance. For the task of matching with respect to the discrete Fréchet distance, we deve...

This thesis concerns exact and inexact graph matching algorithms based on algebraic representsations of graphs, i.e., matrices or vectors. We focus on approximate graph matching with the use of descriptors, understood as pattern vectors associated to graphs. Several graph descriptors are presented, including ones known in literature and new ones created on the basis of various vertex-gathered i...

We present fast and simple algebraic algorithms for the linear matroid parity problem and its applications. For the linear matroid parity problem, we obtain a simple randomized algorithm with running time O(mrω−1) where m and r are the number of columns and the number of rows and ω ≈ 2.3727 is the matrix multiplication exponent. This improves the O(mrω)-time algorithm by Gabow and Stallmann, an...

Basic path-matchings, introduced by Cunningham and Geelen (FOCS 1996), are a common generalization of matroid intersection and non-bipartite matching. The main results of this paper are a new algebraic characterization of basic path-matching problems and an algorithm for constructing basic path-matchings in Õ(nω) time, where n is the number of vertices and ω is the exponent for matrix multiplic...

Basic path-matchings, introduced by Cunningham and Geelen (FOCS 1996), are a common generalization of matroid intersection and non-bipartite matching. The main results of this paper are a new algebraic characterization of basic path-matching problems and an algorithm for constructing basic path-matchings in Õ(nω) time, where n is the number of vertices and ω is the exponent for matrix multiplic...

Given a set of n 2 uncalibrated views, for any corresponding point across n views, there exist three types of matching constraints: bilinear constraints (for n 2), trilinear constraints (for n 3, [12]) and quadrilinear constraints (for n 4, [6, 14, 3]). The exact algebraic relations among these multi-linear constraints have not been elucidated by previous authors. This paper examines the relati...

Given a set of n 2 2 uncalibrated views, for any corresponding point across n views, there exist three types of matching constraints: bilinear constraints (for n 2 2), trilinear constraints (for n 2 3, [12]) and quadrilinear constraints (for n 2 4, 16, 14, 31). The exact algebraic relations among these multi-1inea.r constraints have not been elu~ida~ted by previous authors. This paper examines ...

Imagery integration has a variety of open questions in image registration, conflation, and search. A new promising approach is based on the algebraic paradigm that differs from the more traditional geometric and topological approaches. In previous research, algebraic methods have been based on algebraic structural analysis of features represented as open polylines called linear features. In thi...