A linear algorithm for computing the phase portraits of oriented textures

Abstract

Phase portraits are a powerful mathematical model for describing oriented textures. An isotangent-based approach is presented which is a linear formulation to the problem, to locate the critical points and compute the parameter sets of this model for the nonsingular two-dimensional first-order phase portraits. The authors classify flow patterns by Jordan canonical forms of the characteristic matrix made up of the estimated parameters. For these systems, they prove that all the isotangent curves are straight lines which intersect at a critical point. They also apply least median of squares (LMS) estimators to find the isotangent lines and locate the critical point. A linear regression technique is used to estimate the parameters of the two-dimensional first-order phase portrait of a given flow pattern. Results of applying the algorithm to synthetic and real images are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>