This paper presents a universal statistical model for texture images based on the joint statistics of complex wavelet coefficients. The model is parameterized by a set of statistics computed on pairs of coefficients corresponding to basis functions at adjacent spatial locations, orientations, and scales. An efficient algorithm is developed for synthesizing random images subject to these constraints, by iteratively projecting onto the set of images satisfying each constraint. The model is tested for perceptual validity by demonstrating the necessity of subgroups of the parameter set through examples of texture synthesis that fail when those parameters are removed. The model is also shown to be powerful by successfully synthesizing examples from a diverse collection of artificial and natural textures. The paper re-examines the Julesz conjecture in the context of this model by comparing the appearance of original texture images with synthesized images that are considered equivalent under the model. The model is based on a fixed overcomplete multi-scale complex wavelet representation, and the Markov statistical descriptors are based on pairs of wavelet coefficients at adjacent spatial locations, orientations, and scales. The model includes statistics such as the expected product of raw coefficient pairs (i.e., correlation), the expected product of their magnitudes, and the expected product of the fine scale coefficient with the phase-doubled coarse scale coefficient. It also includes marginal statistics of the image pixels and lowpass coefficients at different scales. The paper discusses the importance of human perception in texture modeling and presents a framework for statistical texture modeling. It also discusses the implications of the Julesz conjecture for texture modeling, and the need for a set of statistical measurements that can capture perceptual equivalence. The paper concludes that the ultimate goal of texture modeling is to achieve a representation that captures independent textural features and is based on visually meaningful parameters.This paper presents a universal statistical model for texture images based on the joint statistics of complex wavelet coefficients. The model is parameterized by a set of statistics computed on pairs of coefficients corresponding to basis functions at adjacent spatial locations, orientations, and scales. An efficient algorithm is developed for synthesizing random images subject to these constraints, by iteratively projecting onto the set of images satisfying each constraint. The model is tested for perceptual validity by demonstrating the necessity of subgroups of the parameter set through examples of texture synthesis that fail when those parameters are removed. The model is also shown to be powerful by successfully synthesizing examples from a diverse collection of artificial and natural textures. The paper re-examines the Julesz conjecture in the context of this model by comparing the appearance of original texture images with synthesized images that are considered equivalent under the model. The model is based on a fixed overcomplete multi-scale complex wavelet representation, and the Markov statistical descriptors are based on pairs of wavelet coefficients at adjacent spatial locations, orientations, and scales. The model includes statistics such as the expected product of raw coefficient pairs (i.e., correlation), the expected product of their magnitudes, and the expected product of the fine scale coefficient with the phase-doubled coarse scale coefficient. It also includes marginal statistics of the image pixels and lowpass coefficients at different scales. The paper discusses the importance of human perception in texture modeling and presents a framework for statistical texture modeling. It also discusses the implications of the Julesz conjecture for texture modeling, and the need for a set of statistical measurements that can capture perceptual equivalence. The paper concludes that the ultimate goal of texture modeling is to achieve a representation that captures independent textural features and is based on visually meaningful parameters.