NOISE REDUCTION IN PHOTOMETRIC STEREO WITH NON-DISTANT LIGHT SOURCES

Abstract

In classical photometric stereo, a Lambertian surface is illuminated from multiple distant point light-sources. In the present paper we consider nearby light-sources instead, so that the unknown surface, is illuminated by non-parallel beams of light. In continuous noiseless cases, the recovery of a Lambertian surface from non-distant illuminations, reduces to solving a system of non-linear partial differential equations for a bivariate function u, whose graph is the visible part of the surface. This system is more difficult to analyse than its counterpart, where light-sources are at infinity. We consider here a similar task, but with slightly more realistic assumptions: the photographic images are discrete and contaminated by Gaussian noise. This leads to a non-quadratic optimization problem involving a large number of independent variables. The latter imposes a heavy computational burden (due to the large matrices involved) for standard optimization schemes. We test here a feasible alternative: an iterative scheme called 2-dimensional Leap-Frog Algorithm (14). For this we describe an implementation for three light-sources in sufficient detail to permit code to be written. Then we give examples verifying experimentally the performance of Leap-Frog.