| Oren, M., Nayar, S.K. A theory of specular surface geometry International Journal of Computer Vision 1996 (24):105-124 [pdf] |
| Atheoretical framework is introduced for the perception of specular surface geometry.Whenan observer moves in three-dimensional space, real scene features such as surface markings remain stationary with respect to the surfaces they belong to. In contrast, a virtual feature which is the specular reflection of a real feature, travels on the surface. Based on the notion of caustics, a feature classification algorithm is developed that distinguishes real and virtual features from their image trajectories that result from observer motion. Next, using support functions of curves, a closed-form relation is derived between the image trajectory of a virtual feature and the geometry of the specular surface it travels on. It is shown that, in the 2D case, where camera motion and the surface profile are coplanar, the profile is uniquely recovered by tracking just two unknown virtual features. Finally, these results are generalized to the case of arbitrary 3D surface profiles that are traveled by virtual features when camera motion is not confined to a plane. This generalization includes a number of mathematical results that substantially enhance the present understanding of specular surface geometry. An algorithm is developed that uniquely recovers 3D surface profiles using a single virtual feature tracked from the occluding boundary of the object. All theoretical derivations and proposed algorithms are substantiated by experiments. |
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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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| Nayar, S.K., Xi-Sheng, F., Boult, T. Separation of reflection components using color and polarization International Journal of Computer Vision 1997 (21)3:163-186 [pdf] |
| Specular reflections and interreflections produce strong highlights in brightness images. These highlights can cause vision algorithms for segmentation, shape from shading, binocular stereo, and motion estimation to produce erroneous results. A technique is developed for separating the specular and diffuse components of reflection from images. The approach is to use color and polarization information, simultaneously, to obtain constraints on the reflection components at each image point. Polarization yields local and independent estimates of the color of specular reflection. The result is a linear subspace in color space in which the local diffuse component must lie. This subspace constraint is applied to neighboring image points to determine the diffuse component. In contrast to previous separation algorithms, the proposed method can handle highlights on surfaces with substantial texture, smoothly varying diffuse reflectance, and varying material properties. The separation algorithm is applied to several complex scenes with textured objects and strong interreflections. The separation results are then used to solve three problems pertinent to visual perception; determining illumination color, estimating illumination direction, and shape recovery. |
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