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Extended Bidirectional Texture Function Moving Average Model

   Michal Havlíček
Abstract: 
The bidirectional texture function (BTF) is the recent most advanced representation of visual properties of material surface. It specifies its appearance due to varying spatial, illumination, and viewing conditions. Corresponding enormous BTF measurements require compact mathematical representation for visual fidelity preserving compression. We present a novel BTF model based on a set of underlying three dimensional moving average random field (3D MA RF) models. 3D MA assumes the texture considered as a product of a convolution of an uncorrelated three dimensional random field with a three dimensional filter which completely characterizes the texture. The BTF model combines several spatial factors, subsequently factorized into a set of 3D MA representations, and range map to produce the required BTF texture. This enables high BTF space compression ratio, unrestricted texture enlargement, and reconstruction of unmeasured parts of the BTF space. We also compare proposed model with its simpler two dimensional variant in terms of colour distribution fidelity.
Keywords: 
bidirectional texture function,  texture analysis,  texture synthesis,  data compression,  virtual reality,  moving average random field model

Results
We tested the model on BTF textures from the University of Bonn BTF database which consists of several materials such as aluminium foil, corduroy, graved granite stone, leather, upholstery, wood. Each BTF material sample included in the database was measured in 81 illumination and 81 viewing angles and the resulting images have a resolution 800x800 pixels. Several achieved results can be observed here showing BTF texture of lacquered wood applied on nontrivial geometrical body. The presented scene was rendered with several different light conditions to demonstrate the effect and meaning of BTF texture use. We used used BTF texture plug in for Blender (a free and open source 3D animation suite). Comparison of the presented model with existing alternatives is hardly feasible as there is still a need for a reliable criterion for such validation. Many already developed approaches are limited to monospectral images that is clearly major disadvantage as colour is arguably the most significant visual feature. Currently, psychophysical experiments, i.e. quality assessments performed by humans, represent the only reliable option. Methods of this type require time demanding experiment setup design, strictly controlled laboratory conditions and representative set of human testing subjects. So that such experiments are extremely impractical, expensive, generally demanding. We simply render several common three dimensional textures modelled both by 3D MA model and its simpler two dimensional variant (2D MA). Several examples, which can be seen here as well, clearly shows the information loss and therefore visual quality of the result caused by spectral decorrelation and thus definite advantage of the extended model.

Comparison of original common three dimensional texture (the first image in each triplet) with 3D MA synthesis (the second image in each triplet) and with 2D MA synthesis (the third image in each triplet).

Reference: 
Havlíček, M., "Extended Bidirectional Texture Function Moving Average Model", Doktorandské dny 2015, Praha, České vysoké učení technické v Praze, pp. 37-43, 2015.