Pentland observed (1982, 1984) that the human eye is sensitive to the change of intensities. On an image of a smooth surface, the change of intensities is maximal whenever the illuminant direction is perpendicular to the normal of the surface. This motivates us to introduce the concept of critical points, where the surface normal is perpendicular to some light source direction. Apparently, the illuminant direction has a simple geometric relationship with the corresponding critical points. In this paper, for simplicity reasons, we restrict our discussions to the shading of a Lambertian sphere of known size in a multiple distant light source environment. A novel global representation of the intensity function is derived. Based on this intensity characterization, the least-squares and iteration techniques are used to determine critical points and, thus, the light source directions and their intensities if certain conditions are satisfied. The performance of this new approach is evaluated using both synthetic images and real images. As an application, we use it as a tool to determine light sources in real image synthesis. The experimental results show that this technique can be used to superimpose synthetic objects with a real scene.

In this paper, a novel scheme of extracting multiple illuminant directions from an image of a Lambertian sphere of known size is proposed. The illuminant direction detection process is based on the concept of critical points introduced in the paper. We show that the illuminant directions have a close relationship to those critical points and that, by identifying those critical points as many as possible, illuminate direction may be recovered if certain conditions are satisfied. Our preliminary, experimental results show that illumination information can be obtained accurately.