We present a new class of deformable contours (snakes) and apply them to the segmentation of medical images. Our snakes are defined in terms of an affine cell image decomposition (ACID). The ‘snakes in ACID’ framework significantly extends conventional snakes, enabling topological flexibility among other features. The resulting topology adaptive snakes, or ‘T-snakes’, can be used to segment some of the most complex-shaped biological structures from medical images in an efficient and highly automated manner.