Image segmentation with elastic shape priors via global geodesics in product spaces

We propose an efficient polynomial time algorithm to match an elastically deforming shape to an image. It is based on finding a globally optimal geodesic in the product space spanned by the image and the prior contour. To this end a branch-and-bound scheme is combined with shortest path techniques. We compare this algorithm with a recently proposed ratio minimization approach. While we show that generally the ratio is the better model, for many instances the two perform similarly. We identify a class of problems where the proposed method is likely to be faster.