Deformations

The authors propose using an implicit shape representation for the source and the target shapes. The Euclidean signed distance transform is used to model the shape of interest as the zero level set of a distance function. Let $\Phi: \Omega \to R^+$ denote the distance transform of a shape $S$. The shape defines a partition of the image domain $\Omega$ - the region enclosed by $S$ is denoted by $[R_S]$ and the background region is denoted by $[\Omega - R_S]$. Using signed Euclidean distance transform, we have ...