Modeling Bidirectional Texture Functions with Multivariate Spherical Radial Basis Functions


Raw image

Tensor approximation

Fixed parameterization

Optimized parameterization




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 materials. 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.




·        Yu-Ting Tsai, Kuei-Li Fang, Wen-Chieh Lin, and Zen-Chung Shih, “Modeling Bidirectional Texture Functions with Multivariate Spherical Radial Basis Functions,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 33, No. 7, 2011. pp. 1356-1369.


Real-time rendering results


Cloth with Wool BTF

Bunny with Hole BTF