Photometric stereo using LCD displays

Abstract

This paper considers the problem of shape-from-shading using nearby extended light sources. The paper reviews a number of methods that employ nearby illuminants, and describes a new technique that assumes a rectangular planar nearby distributed uniform isotropic illuminant. It is shown that such a light source illuminating a small Lambertian surface patch is equivalent to a single isotropic point light source at infinity, in the absence of shadowing. A closed-form solution is given for the equivalent point light source direction in terms of the illuminant corner locations. Equivalent point light sources can be obtained for distinct illuminant patterns allowing standard photometric stereo algorithms to be used. An extension is given to the case of a rectangular planar illuminant with arbitrary radiance distribution. Experimental results are shown demonstrating the application of the theory to photometric stereo using illumination from a LCD computer monitor. Details on the photometric calibration of the illumination source and image acquisition device are provided.

Introduction

Methods for the extraction of surface shape information from images of the surface have been the focus of much research since the foundational work of Horn [7]. Much of this research has concentrated on situations involving point light sources at large distances from the surfaces in question (i.e. the point-light-source-at-infinity model). There are two significant paths by which the classical point-source-at-infinity methods can be extended. The first is to bring the light source close to the object being illuminated, while the other is to distribute the light source across an extended area of space.

Using nearby light sources provides a number of advantages, but gives rise to serious difficulties as well. The primary advantages of using nearby light sources are the possibility of obtaining absolute depth information and the increased flexibility of illuminant positioning. The use of nearby light sources permits the imaging setups to be relatively compact, an important issue in many applications. Clark [2], Iwahori et al. [10], [11], [12] and Kim and Burger [13] point out that the shading induced by nearby illuminants is dependent on the distance between the illuminant and the surface. While this dependence is usually non-linear and complicates the shading equations, it also provides the possibility of extracting absolute depth information from the shading. The inherent difficulties with nearby illuminants are many, however. They include increased shadowing effects (since the range of incident angles is typically larger than for sources at infinity), increased dynamic range (due to the intensity variation induced by depth variations and the $1/r^2$ falloff with distance), and the non-linearity of the resulting shading equations.

The use of distributed light sources has a number of inherent advantages, and attendent difficulties, over point illuminants. Primary among the positive aspects of distributed illuminants is that they require less intense light sources with reduced power density. This lowers illuminant temperature and simplifies construction. As noted by Schechner et al. [15], a problem with practical shape-from-shading systems using point light sources is that the illuminant might not be bright enough to provide adequate signal-to-noise ratios in the cameras, except perhaps at specularities. Schechner et al. suggest using controllable distributed light sources, and integrating multiple images acquired under differing patterns of illumination. As shown by Clark and Pekau [3], distributed light sources can be used to alleviate the noise-sensitivity of some shape-from-shading algorithms by transforming gradient-based algorithms into integral-based algorithms. On the down side, distributed light sources have issues with lack of uniformity and isotropy. Recent advances in LCD projection technology have alleviated this concern somewhat.