Medial Axis for the Cortical Representation of 3D Shape

Cortical representation of medial axis structure.

The identity of an object is not only specified by its parts but also by the relations among the parts. Rearranging parts can produce a completely different object, in the same manner as rearranging the phonemes in "fur" can yield "rough." How does the visual system represent the relative positions of parts? Between-part relations can be characterized by specifying the relations between the med...

Sampled medial loci for 3D shape representation

The medial axis transform is valuable for shape representation as it is complete and captures part structure. However, its exact computation for arbitrary 3D models is not feasible. We introduce a novel algorithm to approximate the medial axis of a polyhedron with a dense set of medial points, with a guarantee that each medial point is within a specified tolerance from the medial axis. Given th...

3D Surface Parameterization Using Manifold Learning for Medial Shape Representation

The choice of 3D shape representation for anatomical structures determines the effectiveness with which segmentation, visualization, deformation, and shape statistics are performed. Medial axis-based shape representations have attracted considerable attention due to their inherent ability to encode information about the natural geometry of parts of the anatomy. In this paper, we propose a novel...

Computing 3D Medial Axis for Chamfer Distances

Computing a compact spline representation of the medial axis transform of a 2D shape

We present a full pipeline for computing the medial axis transform of an arbitrary 2D shape. The instability of the medial axis transform is overcome by a pruning algorithm guided by a user-defined Hausdorff distance threshold. The stable medial axis transform is then approximated by spline curves in 3D to produce a smooth and compact representation. These spline curves are computed by minimizi...