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Abstract : |
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 autocorrelation of the coecients in each subband; (2) both the local auto-correlation and cross-correlation of coecient magnitudes at other orientations and spatial scales; and (3) the rst few moments of the image pixel histogram. We develop an ecient algorithm for synthesizing random images subject to these constraints using alternated projections, and demonstrate its eectiveness 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 coecient magnitudes. We also show the exibility 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. 1, |
