While global methods for matching shapes to images have recently been proposed, so far research has focused on small deformations of a fixed template. In this paper we present the first global method able to pixel-accurately match non-rigidly deformable shapes across images at amenable run-times. By finding cycles of optimal ratio in a four-dimensional graph ? spanned by the image, the prior shape and a set of rotation angles ? we simultaneously compute a segmentation of the image plane, a matching of points on the template to points on the segmenting boundary, and a decomposition of the template into a set of deformable parts. In particular, the interpretation of the shape template as a collection of an a priori unknown number of deformable parts ? an important aspect of higher-level shape representations ? emerges as a byproduct of our matching algorithm. On real-world data of running people and walking animals, we demonstrate that the proposed method can match strongly deformed sha...