Gray-level Texture Characterization Based on a New Adaptive Nonlinear Auto-Regressive Filter

Abstract

In this paper, we propose a new nonlinear exponential adaptive two-dimensional (2-D) filter for texture
characterization. The filter adaptive coefficients are updated with the Least Mean Square (LMS) algorithm. The
proposed nonlinear model is used for texture characterization with a 2-D Auto-Regressive (AR) adaptive model. The
main advantage of the new nonlinear exponential adaptive 2-D filter is the reduced number of coefficients used to
characterize the nonlinear image regarding the 2-D second-order Volterra model. Whatever the degree of the nonlinearity,
the problem results in the same number of coefficients as in the linear case. The characterization efficiency of
the proposed exponential model is compared to the one provided by both 2-D linear and Volterra filters and the cooccurrence
matrix method. The comparison is based on two criteria usually used to evaluate the features discriminating
ability and the class quantification in characterization techniques. The first criterion is proposed to quantify the
classification accuracy based on a weighted Euclidean distance classifier. The second criterion is the characterization
degree based on the ratio of ";;;;;;;between-class";;;;;;; variances with respect to ";;;;;;;within-class";;;;;;; variances of the estimated
coefficients. Extensive experiments proved that the exponential model coefficients give better results in texture
discrimination than several other parametric characterization methods even in a noisy context.

Key words: Image Analysis, 2-D nonlinear filter, 2-D adaptive filter, texture characterization.