Regularizing 3D Medial Axis Using Medial Scaffold Transforms

Ming-Ching Chang and Benjamin B. Kimia
CVPR, 2008

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We present a 3D medial-axis (MA) regularization framework for symmetry-based shape representation and modeling. The MA is regularized by applying a set of transforms toward simplification of the MA while maintaining a consistent underlying shape. The proposed transforms are based on the previous works of (i) the hierarchical organization of the 3D MA into a hypergraph form—the medial scaffold (MS), and (ii) the classification of the MA instabilities (transitions, sudden topological changes under perturbation) and simplify the MS by moving unstable configurations toward close-by transition points, thus simplifying its hypergraph topology and geometry. We identify the transforms necessary to handle all 7 possible MA transitions and organize them into 3 categories (11 in total): (i) 2 splice transforms, (ii) 5 contract transforms, and (iii) 4 merge transforms. These are augmented with additional gap and loop transforms to regularize the MA well in practice. The approach is iterative: we first compute the MS hypergraph from unorganized points, organize it into a dual-scale (coarse and fine) representation, and then transform it iteratively in a greedy scheme. We have extensively tested this approach and show that the results indicate the simplified MA’s potential use in various applications including shape analysis, manipulation, and matching.

Regularizing 3D Medial Axis Using Medial Scaffold Transforms

Ming-Ching Chang and Benjamin B. Kimia, “Regularizing 3D Medial Axis Using Medial Scaffold Transforms”, accepted to IEEE Computer Vision and Pattern Recognition (CVPR), Anchorage, Alaska, USA, June 2008.
Paper (PDF), Poster (PPT), BibTex.