We present a new method for detecting deformable shapes in images. The main difficulty with deformable template models is the very large (or infinite) number of possible non-rigid transformations of the templates. This makes the problem of finding an optimal match of a deformable template to an image incredibly hard. Using a new representation for deformable shapes we show how to efficiently find a global optimal solution to the non-rigid matching problem. Our matching algorithm can minimize a large class of energy functions, making it applicable to a wide range of problems. We present experimental results of detecting shapes in medical and natural images. Because we don?t rely on local search techniques, our method is very robust, yielding good matches even in images with high clutter.