Inferring structure from motion: a homotopy algorithm

Theoretical investigations of the inference of three-dimensional structure from image motion often result in systems of coupled nonlinear equations which must be solved to infer the third dimension. If closed-form solutions cannot be obtained, then various search procedures, such as simulated annealing, are often used. Here, the authors discuss a relatively novel approach to solving coupled nonlinear systems of equations, an approach based on the so-called homotopy principle. This approach is discussed in the context of developing an algorithm for inferring structure from motion using an assumption of rigid fixed-axis motion. This approach is also discussed in the more general context of observer theory, a mathematical framework for the field of perception