There are two topics on shape analysis. One is on 2D shape analysis and the other is on the recovery of 3D shape from shading information. A very exciting new approach in applying the principles of physics has been developed to locate corners and to compute the medial axis of a 2D outline. The approach that we propose is the electrostatic field-based approach to detector corners and to perform skeletonization, the latter of which is a technique to compute the medial axis. The rationale of the electrostatic field-based approach comes from a very simple observation, namely, the field is high at corners of an electrostatically charged object. Our proposed approach is also the first one to unify two seemingly different areas of research in computer vision, namely, corner detection and skeletonization.
With respect to recovering shape from shading, we have developed the first heuristic-based approach to recover the three-dimensional shape of an object based solely on its shading information. Although the approach is heuristically based, the experimental results show that it has much better performance than an existing mathematical-based approach. Recently, we have extended this approach to include recovering the shade of objects with non-Lambertian surfaces. The experimental results are impressive.