Analysis of planar light fields from homogeneous convex curved surfaces under distant illumination

We consider the flatland or 2D properties of the light field generated when a homogeneous convex curved surface reflects a distant illumination field. Besides being of considerable theoretical interest, this problem has applications in computer vision and graphics - for instance, in determining lighting and bidirectional reflectance distribution functions (BRDFs), in rendering environment maps, and in image-based rendering. We demonstrate that the integral for the reflected light transforms to a simple product of coefficients in Fourier space. Thus, the operation of rendering can be viewed in simple signal processing terms as a filtering operation that convolves the incident illumination with the BRDF. This analysis leads to a number of interesting observations for computer graphics, computer vision, and visual perception.