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.