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Beyond Lambert Reconstructing Surfaces with Arbitrary BRDFs Sebastian Magda David J Kriegman Todd Zickler Peter N Belhumeur Beckman Institute Computer Science University of Illinois Urbana Champaign Urbana IL 61801 Center for Comp Vision Control EE and CS Yale University New Haven C T 06520 8267 Abstract W e address a n open and hitherto neglected problem i n computer vision how to reconstruct the geometry of objects with arbitrary and possibly anisotropic bidirectional reflectance distribution functions B R D F s Present reconstruction techniques whether stereo vision structure f r o m motion laser range finding etc make explicit or implicit assumptions about the B R D F Here we introduce two methods that were developed by re examining the underlying image formation process the methods make n o assumptions about the object s shape the presence or absence of shadowing o r the nature of the B R D F which m a y vary over the surface The first method takes advantage of Helmholtz reciprocity while the second method exploits the fact that the radiance along a ray of light is constant I n particular the first method uses stereo pairs of images in which point light sources are co located at the centers of projection of the stereo cameras The second method is based on double covering a scene s incident light field the depths of surface points are estimated using a large collection of images in which the viewpoint remains fixed and a point light source illuminates the object Results f r o m our implementations lend empirical support to both techniques 1 Introduction We address an open problem in computer vision how t o reconstruct the shape geometry of an object with an arbitrary unknown bidirectional reflectance distribution function BRDF 8 Our solutions stand in contrast t o existing methods which assume either implicitly or explicitly that the BRDF of points on the object s surface are Lambertian approximately Lambertian or of some known parametric form A BRDF at a point

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