[{"author":[{"last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"id":"2D04F932-F248-11E8-B48F-1D18A9856A87","first_name":"Elizabeth R","last_name":"Stephenson","full_name":"Stephenson, Elizabeth R","orcid":"0000-0002-6862-208X"},{"id":"47CB1472-F248-11E8-B48F-1D18A9856A87","first_name":"Martin H","last_name":"Thoresen","full_name":"Thoresen, Martin H"}],"date_updated":"2025-11-24T10:05:11Z","date_created":"2025-11-23T23:01:37Z","year":"2025","citation":{"apa":"Edelsbrunner, H., Stephenson, E. R., &#38; Thoresen, M. H. (2025). The mid-sphere cousin of the medial axis transform. In <i>4th International Joint Conference on Discrete Geometry and Mathematical Morphology</i> (Vol. 16296, pp. 133–147). Groningen, The Netherlands: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-032-09544-2_10\">https://doi.org/10.1007/978-3-032-09544-2_10</a>","ama":"Edelsbrunner H, Stephenson ER, Thoresen MH. The mid-sphere cousin of the medial axis transform. In: <i>4th International Joint Conference on Discrete Geometry and Mathematical Morphology</i>. Vol 16296. Springer Nature; 2025:133-147. doi:<a href=\"https://doi.org/10.1007/978-3-032-09544-2_10\">10.1007/978-3-032-09544-2_10</a>","ista":"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.","mla":"Edelsbrunner, Herbert, et al. “The Mid-Sphere Cousin of the Medial Axis Transform.” <i>4th International Joint Conference on Discrete Geometry and Mathematical Morphology</i>, vol. 16296, Springer Nature, 2025, pp. 133–47, doi:<a href=\"https://doi.org/10.1007/978-3-032-09544-2_10\">10.1007/978-3-032-09544-2_10</a>.","short":"H. Edelsbrunner, E.R. Stephenson, M.H. Thoresen, in:, 4th International Joint Conference on Discrete Geometry and Mathematical Morphology, Springer Nature, 2025, pp. 133–147.","ieee":"H. Edelsbrunner, E. R. Stephenson, and M. H. Thoresen, “The mid-sphere cousin of the medial axis transform,” in <i>4th International Joint Conference on Discrete Geometry and Mathematical Morphology</i>, Groningen, The Netherlands, 2025, vol. 16296, pp. 133–147.","chicago":"Edelsbrunner, Herbert, Elizabeth R Stephenson, and Martin H Thoresen. “The Mid-Sphere Cousin of the Medial Axis Transform.” In <i>4th International Joint Conference on Discrete Geometry and Mathematical Morphology</i>, 16296:133–47. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/978-3-032-09544-2_10\">https://doi.org/10.1007/978-3-032-09544-2_10</a>."},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2504.14743"}],"publication":"4th International Joint Conference on Discrete Geometry and Mathematical Morphology","scopus_import":"1","abstract":[{"text":"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.","lang":"eng"}],"doi":"10.1007/978-3-032-09544-2_10","day":"01","date_published":"2025-11-01T00:00:00Z","month":"11","oa_version":"Preprint","publisher":"Springer Nature","conference":{"location":"Groningen, The Netherlands","start_date":"2025-11-03","name":"DGMM: Discrete Geometry and Mathematical Morphology","end_date":"2025-11-06"},"external_id":{"arxiv":["2504.14743"]},"_id":"20658","alternative_title":["LNCS"],"department":[{"_id":"HeEd"}],"quality_controlled":"1","intvolume":"     16296","volume":16296,"publication_identifier":{"issn":["0302-9743"],"isbn":["9783032095435"],"eissn":["1611-3349"]},"status":"public","OA_type":"green","type":"conference","title":"The mid-sphere cousin of the medial axis transform","publication_status":"published","fulldoi":"https://doi.org/10.1007/978-3-032-09544-2_10","arxiv":1,"oa":1,"article_processing_charge":"No","page":"133-147","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"OA_place":"repository"}]