Symmetry is a powerful shape regularity that's been exploited by perceptual grouping researchers in both human and computer vision to recover part structure from an image without a priori knowledge of scene content. Drawing on the concept of a medial axis, defined as the locus of centers of maximal inscribed discs that sweep out a symmetric part, we model part recovery as the search for a sequence of deformable maximal inscribed disc hypotheses generated from a multiscale superpixel segmentation, a framework proposed by [Levinshtein et al., 2009]. However, we learn affinities between adjacent superpixels in a space that's invariant to bending and tapering along the symmetry axis, enabling us to capture a wider class of symmetric parts. Moreover, we introduce a global cost that perceptually integrates the hypothesis space by combining a pairwise and a higher-level smoothing term, which we minimize globally using dynamic programming. The new framework is demonstrated on two datasets, and is shown to significantly outperform the baseline [Levinshtein et al., 2009].