Texture Modeling and Synthesis using Joint Statistics of
Complex Wavelet Coefficients
Published as:
IEEE Workshop on Statistical and Computational Theories of Vision
Fort Collins, CO, 22 June 1999.
Subsequent full-length journal publication:
Int'l Journal of Computer Vision, 2000
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. In
particular, we show that many important structural elements in
textures (e.g., edges, repeated patterns or alternated patches of
simpler texture), can be captured through joint second order
statistics of the coefficient magnitudes. 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.
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