Similarity-based shape priors for 2D spline snakes

We present a new formulation of a shape space containing all continuously defined 2D spline curves up to a similarity transform of a reference shape. We are able to measure a distance between an arbitrary curve and the shape space itself. Our contribution is an explicit formula for this distance measure in the continuous domain. This allows us to define efficient snake energies based on shape-dependent prior knowledge to facilitate segmentation in bioimaging. The spline-based algorithm that we propose allows us to implement continuous-domain solutions with no additional computational cost compared to the case where curves are described by a discrete set of landmarks. The proposed implementation is freely available in the public domain.