We present a single-shot system to recover surface geometry of objects with spatially-varying albedos, from images captured under a calibrated RGB photometric stereo setup---with three light directions multiplexed across different color channels in the observed RGB image. Since the problem is ill-posed point-wise, we assume that the albedo map can be modeled as piece-wise constant with a restricted number of distinct albedo values. We show that under ideal conditions, the shape of a non-degenerate local constant albedo surface patch can theoretically be recovered exactly. Moreover, we present a practical and efficient algorithm that uses this model to robustly recover shape from real images. Our method first reasons about shape locally in a dense set of patches in the observed image, producing shape distributions for every patch. These local distributions are then combined to produce a single consistent surface normal map. We demonstrate the efficacy of the approach through experiments on both synthetic renderings as well as real captured images.
An exception is the work of Fyffe al @cite_8 , who like us, rely on the statistics of natural albedos. They assume that surface albedo, as a function of spectral wavelength, is low-dimensional. Since this assumption doesn't provide an informative constraint for albedos in just three color channels, their setup involves multi-spectral capture under six spectrally distinct color sources. However, this requires a more complex imaging system and also suffers from lower light efficiency---since the visible spectrum now is split into six, instead of three, non-overlapping bands for both illumination and sensing. In contrast, we rely on the spatial, instead of spectral, statistics of albedos, and are able to employ regular three-channel RGB cameras.
@cite_8
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Spectral multiplexing allows multiple channels of information to be captured simultaneously, using readily available color cameras. Information may be multiplexed across the color channels of a camera by use of colored lights (e.g. [Woodham 1980; Hernandez and Vogiatzis 2010]) or colored filters (e.g. [ 2008]). We propose a novel method for single-shot photometric stereo by spectral multiplexing. The output of our method is a simultaneous per-pixel estimate of the surface normal and full-color reflectance. Our method is well suited to materials with varying color and texture, requires no time-varying illumination, and no high-speed cameras. Being a single-shot method, it may be applied to dynamic scenes without any need for optical flow. Our key contributions are a generalization of three-color photometric stereo to multiple (more than three) color channels, and the design of a practical six-color-channel system using off-the-shelf parts only.