The mid-sphere cousin of the medial axis transform
Edelsbrunner H, Stephenson ER, Thoresen MH. 2025. The mid-sphere cousin of the medial axis transform. 4th International Joint Conference on Discrete Geometry and Mathematical Morphology. DGMM: Discrete Geometry and Mathematical Morphology, LNCS, vol. 16296, 133–147.
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LNCS
Abstract
The medial axis of a smoothly embedded surface in R^3 consists of all points for which the Euclidean distance function on the surface has at least two global minima. We generalize this notion to the mid-sphere axis, which consists of all points for which the Euclidean distance function has two interchanging saddles that swap their partners in the pairing by persistent homology. It offers a discrete-algebraic multi-scale approach to computing ridge-like structures on the surface. As a proof of concept, an algorithm that computes stair-case approximations of the mid-sphere axis is provided.
Publishing Year
Date Published
2025-11-01
Proceedings Title
4th International Joint Conference on Discrete Geometry and Mathematical Morphology
Publisher
Springer Nature
Volume
16296
Page
133-147
Conference
DGMM: Discrete Geometry and Mathematical Morphology
Conference Location
Groningen, The Netherlands
Conference Date
2025-11-03 – 2025-11-06
ISBN
ISSN
eISSN
IST-REx-ID
Cite this
Edelsbrunner H, Stephenson ER, Thoresen MH. The mid-sphere cousin of the medial axis transform. In: 4th International Joint Conference on Discrete Geometry and Mathematical Morphology. Vol 16296. Springer Nature; 2025:133-147. doi:10.1007/978-3-032-09544-2_10
Edelsbrunner, H., Stephenson, E. R., & Thoresen, M. H. (2025). The mid-sphere cousin of the medial axis transform. In 4th International Joint Conference on Discrete Geometry and Mathematical Morphology (Vol. 16296, pp. 133–147). Groningen, The Netherlands: Springer Nature. https://doi.org/10.1007/978-3-032-09544-2_10
Edelsbrunner, Herbert, Elizabeth R Stephenson, and Martin H Thoresen. “The Mid-Sphere Cousin of the Medial Axis Transform.” In 4th International Joint Conference on Discrete Geometry and Mathematical Morphology, 16296:133–47. Springer Nature, 2025. https://doi.org/10.1007/978-3-032-09544-2_10.
H. Edelsbrunner, E. R. Stephenson, and M. H. Thoresen, “The mid-sphere cousin of the medial axis transform,” in 4th International Joint Conference on Discrete Geometry and Mathematical Morphology, Groningen, The Netherlands, 2025, vol. 16296, pp. 133–147.
Edelsbrunner H, Stephenson ER, Thoresen MH. 2025. The mid-sphere cousin of the medial axis transform. 4th International Joint Conference on Discrete Geometry and Mathematical Morphology. DGMM: Discrete Geometry and Mathematical Morphology, LNCS, vol. 16296, 133–147.
Edelsbrunner, Herbert, et al. “The Mid-Sphere Cousin of the Medial Axis Transform.” 4th International Joint Conference on Discrete Geometry and Mathematical Morphology, vol. 16296, Springer Nature, 2025, pp. 133–47, doi:10.1007/978-3-032-09544-2_10.
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