Last update: July 23, 2002

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References for Computational Geometry & Skeletons by Hyeong In Choi, Sung Woo Choi, Hwan Pyo Moon, et al.:

BibTeX references

Linear One-sided Stability of MAT for Weakly Injective 3D Domain

Sung Woo Choi and H.-P. Seidel

7th ACM Symposium on Solid Modeling and Applications,
Saarbruecken, Germany, June 17-21, 2002.

Two-dimensional Offsets via Medial Axis Transform I:
Mathematical Theory

H.I. Choi, C.Y. Han, Sung Woo Choi, H.P. Moon, K.H. Roh, N.-S. Wee

2001+

Two-dimensional Offsets via Medial Axis Transform II:
Algorithm

H.I. Choi, C.Y. Han, Sung Woo Choi, H.P. Moon, K.H. Roh, N.-S. Wee

2001+

Stability Analysis of Medial Axis Transform under Relative Hausdorff Distance

Sung Woo Choi and S.-W. Lee

Proceedings of 15th International Conference on Pattern Recognition,
Barcelona, Spain, vol. 3, pp. 139-142, September 3-8, 2000.

New Algorithm for Medial Axis Transform of Plane Domain

Hyeong In Choi, Sung Woo Choi and Hwan Pyo Moon

Graphical Models and Image Processing, Vol. 59, No. 6, pp. 463-483, November 1997.

Mathematical Theory of Medial Axis Transform

Hyeong In Choi, Sung Woo Choi and Hwan Pyo Moon

Pacific Journal of Mathematics, Vol. 181, No. 1, pp. 57-88, November 1997.

Abstract

The medial axis of a plane domain is defined to be the set of the centers of the maximal inscribed disks. It is essentially the cut loci of the inward unit normal bundle of the boundary. We prove that if a plane domain has finite number of boundary curves each of which consists of finite number of real analytic pieces, then the medial axis is a connected geometric graph in R^2 with finitely many vertices and edges. And each edge is a real analytic curve which can be extended in the C^1 manner at the end vertices. We clarify the relation between the vertex degree and the local geometry of the domain. We also analyze various continuity and regularity results in detail, and show that the medial axis is a strong deformation retract of the domain which means in the practical sense that it retains all the topological informations of the domain. We also obtain parallel results for the medial axis transform.

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