| Kelemen, C., Szirmay-Kalos, L. A microfacet based coupled specular-matte BRDF model with importance sampling [pdf] |
| This paper presents a BRDF model based on the analysis of the photon collisions with the microfacets of the surface. The new model is not only physically plausible, i.e. symmetric and energy conserving, but provides other important features of real materials, including the off-specular peak and the mirroring limit case. Using theoretical considerations the reflected light is broken down to a specular component representing single reflections and a matte component accounting for multiple reflections and re-emissions of previously absorbed photons. Unlike most of the previous models, the proportion of the matte and specular components is not constant but varies with the viewing angle. In order to keep the resulting formulae simple, several approximations are made, which are quite accurate but allow for tabulation, fast calculation and even for accurate importance sampling. |
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| Koenderink, J.J., van Doorn, A.J., Kristin, D.J., Nayar, S. Bidirectional reflection distribution function of thoroughly pitted surfaces International Journal of Computer Vision 1999 (31)2/3:129-144 [pdf] |
| We derive the BRDF (Bidirectional Reflection Distribution Function) at the mega scale of opaque surfaces that are rough on the macro and micro scale. The roughness at the micro scale is modeled as a uniform, isotropically scattering, Lambertian surface. At the macro scale the roughness is modeled by way of a distribution of spherical concavities. These pits influence the BRDF via vignetting, cast shadow, interreflection and interposition, causing it to differ markedly from Lambertian. Pitted surfaces show strong backward scattering (so called opposition effect ). When we assume that the macro scale can be resolved, the radiance histogram and the spatial structure of the textons of the textured surface (at the mega scale) can be calculated. This is the main advantage of the model over previous ones: One can do exact (numerical) calculations for a surface geometry that is physically realizable. |
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| Schreiber, T. Measuring Information Transfer Physical review letters 2000 (85)2 [html] |
| An information theoretic measure is derived that quantifies the statistical coherence between systems evolving in time. The standard time delayed mutual information fails to distinguish information that is actually exchanged from shared information due to common history and input signals. In our new approach, these influences are excluded by appropriate conditioning of transition probabilities. The resulting transfer entropy is able to distinguish effectively driving and responding elements and to detect asymmetry in the interaction of subsystems. |
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| Penrose, R. Techniques of Differential Topology in Relativity 1972 |
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