Extracting the affine transformation from texture moments

Abstract

In this paper we propose a novel, efficient and geometrically intuitive method to compute the four components of an affine transformation from the change in simple statistics of images of texture. In particular we show how the changes in first, second and third moments of edge orientation and changes in density are directly related to the rotation (curl), scale (divergence) and deformation components of an affine transformation. A simple implementation is described which does not require point, edge or contour correspondences to be established. It is tested on a wide range of repetitive and non-repetitive visual textures which are neither isotropic nor homogeneous. As a demonstration of the power of this technique the estimated affine transforms are used as the first stage in shape from texture and structure from motion applications.