Texture Representation and Synthesis Using Correlation of Complex Wavelet Coefficient Magnitudes

Javier Portilla and Eero Simoncelli

We present a statistical characterization of texture images in the context of an overcomplete complex wavelet transform. The characterization is based on empirical observations of statistical regularities in such images, and parameterized by (1) the local auto-correlation of the coefficients in each subband; (2) both the local auto-correlation and cross-correlation of coefficient magnitudes at other orientations and spatial scales; and (3) the first few moments of the image pixel histogram. We develop an efficient algorithm for synthesizing random images subject to these constraints using alternated projections, and demonstrate its effectiveness on a wide range of synthetic and natural textures. We also show the flexibility of the representation, by applying to a variety of tasks which can be viewed as constrained image synthesis problems, such as spatial and spectral extrapolation. Our results show how an important set of the structural elements in textures, e.g. edges, repeated patterns or alternated patches of simpler textures, can be captured through the joint second order statistics of the outputs (in magnitude), of a fixed set of quadrature-pair, band-pass filters. These characteristic non-linear dependencies among the filter responses, which have a low spectral overlapping, reveal the strong non-Gaussian behavior of most real-life textures.

gzipped postscript file