Gibbs random fields, cooccurrences, and texture modeling

Abstract

Gibbs random eld (GRF) models and co-occurrence statistics are typically considered as separate but useful tools for texture discrimination. In this paper we show an explicit relationship between co-occurrences and a large class of GRF's. This result comes from a new framework based on a set-theoretic concept called the \aura set" and on measures of this set, \aura measures". This framework is also shown to be useful for relating di erent texture analysis tools: We show how the aura set can be constructed with morphological dilation, how its measure yields co-occurrences, and how it can be applied to characterizing the behavior of the Gibbs model for texture. In particular, we show how the aura measure generalizes, to any number of gray levels and neighborhood order, some properties previously known for just the binary, nearest-neighbor GRF. Finally, we illustrate how these properties can guide one's intuition about the types of GRF patterns which are most likely to form.

Perceptually Motivated Image Features Using Contours

“…Since it is computationally expensive to calculate all pair-wise segment data within an image, we instead adapt the Grey Level Aura Matrix (GLAM) as defined in [22] and below, to represent segment-to-segment angle and position relationships.…”

“…Therefore the maximum sized neighbourhood considered was 23×23 pixels). Note also that we use the Aura Matrix defined in [22] instead of the Basic Aura Matrix [48] used in [18] and below, in order to reduce the SOAM dimensionality from & × ( − 1) to & .…”

“…In the first we compute an average segment distribution across contours (that is we compute pair-wise segment relationships within contours and then average across all contours in an image). In the second we use the aura matrix [22] to compute segment co-occurrence data with no regard as to which contour the segments belong and we restrict the pairs to those occurring within an $ local neighbourhood. In the third, we employ the basic aura matrix [48] to represent the spatial distributions of pixels (unit length segments) in a contour map.…”

“…Grey Level Aura Matrix (GLAM) [22] Given that { , 0 ≤ 6 ≤ 7 − 13 is a set of grey level sets of image 8(1), the GLAM of 8(1) over ) is computed as:…”

The Use of Boolean Model for Texture Analysis of Grey Images

“…The difficulty in dealing with texture manifests itself in the plethora of techniques proposed and the methods used [1]. Some of the most popular ones include co-occurrence matrices (e.g., [2]), parametric models (e.g., [3]) and filtering (e.g., [4]). We shall not attempt a comprehensive review here, as the list of relevant papers is enormous.…”