The Image Irradiance Equation: Its Solution and Application.

How much information about the shape of an object can be inferred from its image In particular, can the shape of an object be reconstructed by measuring the light it reflects from points on its surface These questions were raised by Horn H070 who formulated a set of conditions such that the image formation can be described in terms of a first order partial differential equation, the image irradiance equation. In general, an image irradiance equation has infinitely many solutions. Thus constraints necessary to find a unique solution need to be identified. First we study the continuous image irradiance equation. It is demonstrated when and how the knowledge of the position of edges on a surface can be used to reconstruct the surface. Furthermore we show how much about the shape of a surface can be deduced from so called singular points. At these points the surface orientation is uniquely determined by the measured brightness. Then we investigate images in which certain types of silhouettes, which we call b-silhouettes, can be detected. In particular we answer the following question in the affirmative Is there a set of constraints which assure that if an image irradiance equation has a solution, it is unique To this end we postulate three constraints upon the image irradiance equation and prove that they are sufficient to uniquely reconstruct the surface from its image.