Texton finding and lattice creation for near-regular texture

Abstract

A regular texture is formed from a regular congruent tiling of perceptually meaningful texture elements, also known as textons. If the tiling statistically deviates from regularity, either by texton structure, colour, or size, the texture is called near-regular. If we continue to perturb the tiling, the texture becomes stochastic. The set of possible textures that lie between regular and stochastic make up the texture spectrum: regular, near-regular, regular, near-stochastic, and stochastic. In this thesis we provide a solution to the problem of creating, from a near-regular texture, a lattice which defines the placement of textons. We divide the problem into two distinct sub-areas: finding textons within an image, and lattice creation using both an ad-hoc method and a graph-theoretic method. The problem of finding textons within an image is addressed using correlation. A texton selected by the user is correlated with the image and points of high correlation are extracted using non-maximal suppression. To extend this framework to irregular textures, we present early results on the use of feature space during correlation. We also present a method of correcting for a specific type of error in the texton finding result using frequency-space analysis. Given texton locations, we provide two methods of creating a lattice. The ad-hoc method is able to create a lattice in spite of inconsistencies in the texton locating data. However, as texture becomes irregular the ad-hoc lattice construction method fails to correctly connect textons. To overcome this failure we adapt methods of creating proximity graphs, which join two textons whose neighbourhoods satisfy certain criteria, to our problem. The proximity graphs are parameterized for selection of the most appropriate graph choice for a given texture, solving the general lattice construction problem given correct texton locations. In the output of the algorithm, centres of textons will be connected by edges in the lattice following the structure of texton placement within the input image. More precisely, for a texture T, we create a graph G = (V,E) dependent on T, where V is a set of texton centres, and E ={(v_i, v_j)} is a set of edges, where v_i, v_j are in V. Each edge e in E connects texton centre v in V to its most perceptually sensible neighbours.