Abstract

The Least Median of Squares robust regression provides an automatic method for outlier detection in linear regression. Here we apply the method to the problem of recovering surface normals from a single color image of a uniformly colored object, illuminated by colored light that varies spectrally with orientation from the surface. This physical model generalizes the photometric stereo problem in Computer Vision. A spectrally varying illumination environment is provided in nature by mutual illumination and other effects. Outlier detection is important in this problem because not all points on the surface see all lights. For non-outliers, i.e. pixels corresponding to points that do see the complete lighting environment, the Lambertian model states that the observed color is related by a linear transformation to the normal vector. Outliers arise because of shadowing, self-shadowing, color variations, or specularities on the surface. Using a synthetic image, we show that the robust regress...

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