This paper presents a novel parametric representation for bidirectional texture functions. Our method mainly relies on two original techniques, namely, multivariate spherical radial basis functions (SRBFs) and optimized parameterization. First, since the surface appearance of a real-world object is frequently a mixed effect of different physical factors, the proposed sum-of-products model based on multivariate SRBFs especially provides an intrinsic and efficient representation for heterogenous

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... aterials. Second, optimized parameterization particularly aims at overcoming the major disadvantage of traditional fixed parameterization. By using a parametric model to account for variable transformations, the parameterization process can be tightly integrated with multivariate SRBFs into a unified framework. Finally, a hierarchical fitting algorithm for bidirectional texture functions is developed to exploit spatial coherence and reduce computational cost. Our experimental results further reveal that the proposed representation can easily achieve high-quality approximation and real-time rendering performance. Index Terms-Reflectance and shading models, bidirectional texture functions, parameterization, spherical radial basis functions.