One-shot integral invariant shape priors for variational segmentation

We match shapes, even under severe deformations, via a smooth reparametrization of their integral invariant signatures. These robust signatures and correspondences are the foundation of a shape energy functional for variational image segmentation. Integral invariant shape templates do not require registration and allow for significant deformations of the contour, such as the articulation of the object's parts. This enables generalization to multiple instances of a shape from a single template, instead of requiring several templates for searching or training. This paper motivates and presents the energy functional, derives the gradient descent direction to optimize the functional, and demonstrates the method, coupled with a data term, on real image data where the object's parts are articulated.