Abstract

What does it mean for a deforming ob ject to be “moving” (see Fig. 1)? How can we separate the overall motion (a finite-dimensional group action) from the more general deformation (a diffeomorphism)? In this paper we propose a deffnition of motion for a deforming ob ject and introduce a notion of “shape average” as the entity that separates the motion from the deformation. Our definition allows us to derive novel and efficient algorithms to register non-equivalent shapes using region-based methods, and to simultaneously approximate and register structures in grey-scale images. We also extend the notion of shape average to that of a “moving average” in order to track moving and deforming ob jects through time.