Shape Statistics for Image Segmentation with Prior

We propose a new approach to compute non-linear, intrinsic shape statistics and to incorporate them into a shape prior for an image segmentation task. Given a sample set of contours, we first define their mean shape as the one which is simultaneously closest to all samples up to rigid motions, and compute it in a gradient descent framework. We consider here a differentiable approximation of the Hausdorff distance between shapes. Statistics on the instantaneous deformation fields that the mean shape should undergo to move towards each sample lead to sensible characteristic modes of deformation that convey the shape variability. Contour statistics are turned into a shape prior which is rigid-motion invariant. Image segmentation results show the improvement gained by the shape prior.