Fast Bidirectional Texture Function Modeling based on 2D Causal Auto-Regressive model

The bidirectional texture function (BTF) describes rough texture appearance variations due to varying illumination and viewing conditions. Such a function consists of thousands of measurements (images) per sample. Resulted BTF size excludes its direct rendering in graphical applications and some compression of these huge BTF data spaces is obviously inevitable. In this paper we present a novel fast probabilistic model-based algorithm for realistic BTF modelling allowing such an efficient compression with possibility of direct implementation inside the graphics card. The analytical step of the algorithm starts with the BTF space segmentation and range map estimation of the BTF surface followed by the spectral and spatial factorisation of selected sub-space multispectral texture images. Single monospectral band-limited factors are independently modelled by their dedicated causal autoregressive models (CAR). During rendering the corresponding sub-space images of arbitrary size are synthesised and both multispectral and range information is combined in a bump mapping filter of the rendering hardware according to view and illumination positions. The presented model offers huge BTF compression ratio unattainable by any alternative sampling-based BTF synthesis method. Simultaneously this model can be used to reconstruct missing parts of the BTF measurement space.
Original BTF size for one material 1.2GB.

Overal schema of proposed BTF model

Detail scheme of 2D Causal Auto-Regressive smooth texture model from previous scheme

Results of 2D CAR BTF model without bump mapping (20 sub-space images). Materials wood01, wood02. Approx. size of models is 80KB.

Results of 2D CAR BTF model with bump+mapping (15-20 sub-space images) in comparison with original BTF measurements (slightly different view & illumination conditions). Materials fabric01, fabric02, foil01, foil02. Approx size of models is 200KB.

Original BTF measurements Proposed BTF model

All BTF data by courtesy of R. Klein, Bonn University.
Mercedes Class-C 3D model by courtesy of DaimlerChrysler.

This work was partially supported by the European Community within the scope of the RealReflect project (IST-2001-34744) ``Realtime visualization of complex reflectance behavior in virtual prototyping''.

Haindl, M., and J. Filip, "A fast probabilistic Bidirectional Texture Function model", Image Analysis and Recognition, Heidelberg, Springer, pp. 298-305, September, 2004.