(Left) The reflectance function at x1 determines the percentage of light reflected from light source L towards each of cameras C1 and C2. (Right) The spatial position of all components is the same, but the light distribution has been altered. Although the incident intensity at x1 has changed, the percentage of light reflected remains constant

Abstract

Nearly all existing methods for stereo reconstruction assume that scene reflectance is Lambertian and make use of brightness constancy as a matching invariant. We introduce a new invariant for stereo reconstruction called Light Transport Constancy, which allows completely arbitrary scene reflectance (BRDFs). This invariant can be used to formulate a rank constraint on multiview stereo matching when the scene is observed by several lighting configurations, in which only the lighting intensity varies. In addition, we show that this multiview constraint can be used with as few as two cameras and two lighting configurations. Unlike previous methods for BRDF invariant stereo, Light Transport Constancy does not require precisely configured or calibrated light sources, or calibration objects in the scene. Importantly, the new constraint can be used to provide BRDF invariance to any existing stereo method, whenever appropriate lighting variation is available.

Keywords: Stereo,  BRDF,  Rank Constraint, Light Transport Constancy, Non-Lambertian

(Left) Tree with non-Lambertian reflectance properties and many depth discontinuities. (Right) Disparity map computed from thirty lighting variations.

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