We introduce a framework for analyzing symmetry of 3D
anatomical structures using elastic deformations of their
boundaries (surfaces). The basic idea is to define a space
of parameterized surfaces and to compute geodesic paths
between the objects and their arbitrary reflections using
a Riemannian structure. Elastic matching, based on opti-
mal (non-linear) re-parameterizations (grid deformations)
of surfaces, provides a better registration of points across
shapes, as compared to the commonly-used linear regis-
trations. A crucial step of orientation alignment, akin to
finding planes of symmetry, is performed as a search for
shortest geodesic paths. This framework is fully automatic
and provides a measure of symmetry, the nearest symmet-
ric shape and the optimal deformation to make an object
symmetric. We demonstrate this framework through multi-
ple toy examples on simple and complicated surfaces. We
also explore the use of symmetry analysis in differentiating
between healthy and subjects with Attention Deficit Hyper-
activity Disorder.