Shape from interreflections - Computer Vision, 1990. Proceedings, Third International Conference on

All shape-from-intensity methods assume that points in a scene are only illuminated by sources of light. Most scenes consist of concave surfaces and/orconcavities that result from multipleobjects in the scene. In such cases, points in the scene reflect light between themselves. In the presence of these interreflections, shape-from-intensity methods produce erroneous (pseudo) estimates of shape and reflectance. The pseudo shape and reflectance estimates, however, are shown to cany information about the actual shape and reflectance of the surface. An iterative algorithm is presented that simultaneously recovers the actual shape and the actual reflectance from the pseudo estimates. The recovery algorithm works on Lambertian surfaces of arbitrary shape with possibly varying andunknown reflectance. The general behavior ofthe algorithm and its convergence properties are discussed. Both simulation as well as experimental results are included to demonstrate the accuracy and stability of the algorithm. 1 The Interreflection Problem We address a challenging vision problem ''iat has remained unsolved for the past two decades. Surface elements in a scene, when illuminated, reflect light not only in the direction of the sensor but also between themselves. This is always the case except when the scene consists of only a single convex surface. These interreflections, also referred to as mutual illuminations, can appreciably alter the appearance of the scene. None of the existing vision algorithms reason about, or even take into account, the effects of interreflections. Consequently, interreflections often confuse vision algorithms and cause them to produce erroneous results. A class of vision algorithms that are particularly affected by interreflections are shape-from-intensify algorithms, such as, shape-fromshading [SI, photometric s t e m [12], and photometric sampling [9]. All these methods, are based on the assumption that points in the scene are illuminated only by the sources of light and not other points in the scene; interreflections are assumed not to exist. As a result, existing shape-from-intensity methods produce erroneous results when applied to concave surfaces and concavities that result from multiple objects in the scene. As an example, Figure l a shows a concave Lambertian surface of constant reflectance (albedo = 0.75). and Figure l b shows its shape extracted using photometric stereo. The inability to deal with interreflections has in the past limited the utility of shape-from-intensity methods.