Abstract

We present a new way of constraining the evolution of a region-based active contour with respect to a set of reference shapes. The approach is based on a description of shapes by the Legendre moments computed from their characteristic function. This provides a region-based representation that can handle arbitrary shape topologies. Moreover, ex- ploiting the properties of moments, it is possible to include intrinsic affine invariance in the descriptor, which solves the issue of shape alignment without increasing the number of d.o.f. of the initial problem and allows introducing geometric shape variabilities. Our new shape prior is based on a distance between the descriptors of the evolving curve and a ref- erence shape. The proposed model naturally extends to the case where multiple reference shapes are simultaneously considered. Minimizing the shape energy, leads to a geometric flow that does not rely on any par- ticular representation of the contour and can be implemented with any contour evolution algorithm. We introduce our prior into a two-class segmentation functional, showing its benefits on segmentation results in presence of severe occlusions and clutter. Examples illustrate the abil- ity of the model to deal with large affine deformation and to take into account a set of reference shapes of different topologies.