Three-Dimensional Textured Image Blocks Model Based on Wold Decomposition

In this paper, we present a new parametric modeling of three-dimensional homogeneous volumes of textured images (3D texture) based on 3D Wold decomposition for discrete processes. This decomposition additively separates any 3D discrete homogeneous process into three mutually orthogonal components: a purely indeterministic, a "remote past" - type deterministic and an evanescent component. The evanescent component can be further decomposed into two orthogonal components called type 1 evanescent and type 2 evanescent. Assuming that the 3D image volume is a finite realization of a discrete homogeneous stochastic process, the 3D texture field can be uniquely represented as a sum of four mutually orthogonal components with different spectral properties. The aim of this paper is to present new parametric models able to describe both the spectral support and spatial characteristics of each component. A spectral decomposition algorithm to separate a 3D texture into structured and unstructured parts is also proposed.