A framework for the construction of reflectance maps for machine vision

Abstract A reflectance map is the transfer function from surface orientation and illumination geometry to the surface normal, and in machine vision it plays a fundamental role in the reconstruction of surface by shape-from-shading and photometric stereo algorithms. While reflectance maps for Lambertain and specular surfaces are well understood, maps for real-world diffusely reflecting surfaces are scant. In this paper, the fundamental mechanisms of reflection from such surfaces are reviewed. Based on this, it is proposed that for point light source illumination, the diffuse component of the reflectance map has three terms: a forescatter term, a normal term, and a backscatter term. The physical origin of the three terms is discussed in detail and useful mathematical expressions are obtained for them. The range of applicability of the proposed reflectance maps is established, and an example of their use in photometric stereo is provided. The mathematical form of the reflectance map obtained from physical theories is amenable to generalization and such a generalization is called the m-lobed reflectance map is proposed.