The Kuratowski convergence of medial axes and conflict sets

This paper consists of two parts. In the first one we study the behaviour of medial axes (skeletons) of closed sets in a connected complete Riemannian manifold \(\mathcal{M}\) under deformations. The second one is devoted to a similar study of conflict sets. We apply a new approach to the deformatio...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2022-10
Main Authors: Białożyt, Adam, Denkowska, Anna, Denkowski, Maciej P
Format: Article
Language:English
Subjects:
Axes (reference lines)
Convergence
Deformation
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Białożyt, Adam
Denkowska, Anna
Denkowski, Maciej P
description This paper consists of two parts. In the first one we study the behaviour of medial axes (skeletons) of closed sets in a connected complete Riemannian manifold \(\mathcal{M}\) under deformations. The second one is devoted to a similar study of conflict sets. We apply a new approach to the deformation process. Instead of seeing it as a `jump' from the initial to the final state, we perceive it as a continuous process, expressed using the Kuratowski convergence of sets (hence, unlike other authors, we do not require any regularity of the deformation). Our main `medial axis inner semi-continuity' result has already proved useful, as it was used to compute the tangent cone of the medial axis with application in singularity theory.
format article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2080822867</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2080822867</sourcerecordid><originalsourceid>FETCH-proquest_journals_20808228673</originalsourceid><addsrcrecordid>eNqNykEKwjAQQNEgCBbtHQZcF-LEtgGXoghuuy-hnWhrTTSTqsdXwQO4-ov3JyJBpVaZXiPORMrcSymxKDHPVSI21ZngOAYT_ZMvHTTePSicyDUE3sKV2s4MYF7EYFz7ZTt0TQSmyAsxtWZgSn-di-V-V20P2S34-0gc696PwX2oRqmlRtRFqf673v3tNzA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2080822867</pqid></control><display><type>article</type><title>The Kuratowski convergence of medial axes and conflict sets</title><source>Publicly Available Content Database</source><creator>Białożyt, Adam ; Denkowska, Anna ; Denkowski, Maciej P</creator><creatorcontrib>Białożyt, Adam ; Denkowska, Anna ; Denkowski, Maciej P</creatorcontrib><description>This paper consists of two parts. In the first one we study the behaviour of medial axes (skeletons) of closed sets in a connected complete Riemannian manifold \(\mathcal{M}\) under deformations. The second one is devoted to a similar study of conflict sets. We apply a new approach to the deformation process. Instead of seeing it as a `jump' from the initial to the final state, we perceive it as a continuous process, expressed using the Kuratowski convergence of sets (hence, unlike other authors, we do not require any regularity of the deformation). Our main `medial axis inner semi-continuity' result has already proved useful, as it was used to compute the tangent cone of the medial axis with application in singularity theory.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Axes (reference lines) ; Convergence ; Deformation</subject><ispartof>arXiv.org, 2022-10</ispartof><rights>2022. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.proquest.com/docview/2080822867?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>776,780,25731,36989,44566</link.rule.ids></links><search><creatorcontrib>Białożyt, Adam</creatorcontrib><creatorcontrib>Denkowska, Anna</creatorcontrib><creatorcontrib>Denkowski, Maciej P</creatorcontrib><title>The Kuratowski convergence of medial axes and conflict sets</title><title>arXiv.org</title><description>This paper consists of two parts. In the first one we study the behaviour of medial axes (skeletons) of closed sets in a connected complete Riemannian manifold \(\mathcal{M}\) under deformations. The second one is devoted to a similar study of conflict sets. We apply a new approach to the deformation process. Instead of seeing it as a `jump' from the initial to the final state, we perceive it as a continuous process, expressed using the Kuratowski convergence of sets (hence, unlike other authors, we do not require any regularity of the deformation). Our main `medial axis inner semi-continuity' result has already proved useful, as it was used to compute the tangent cone of the medial axis with application in singularity theory.</description><subject>Axes (reference lines)</subject><subject>Convergence</subject><subject>Deformation</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><recordid>eNqNykEKwjAQQNEgCBbtHQZcF-LEtgGXoghuuy-hnWhrTTSTqsdXwQO4-ov3JyJBpVaZXiPORMrcSymxKDHPVSI21ZngOAYT_ZMvHTTePSicyDUE3sKV2s4MYF7EYFz7ZTt0TQSmyAsxtWZgSn-di-V-V20P2S34-0gc696PwX2oRqmlRtRFqf673v3tNzA</recordid><startdate>20221023</startdate><enddate>20221023</enddate><creator>Białożyt, Adam</creator><creator>Denkowska, Anna</creator><creator>Denkowski, Maciej P</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PHGZM</scope><scope>PHGZT</scope><scope>PIMPY</scope><scope>PKEHL</scope><scope>PQEST</scope><scope>PQGLB</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20221023</creationdate><title>The Kuratowski convergence of medial axes and conflict sets</title><author>Białożyt, Adam ; Denkowska, Anna ; Denkowski, Maciej P</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_20808228673</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Axes (reference lines)</topic><topic>Convergence</topic><topic>Deformation</topic><toplevel>online_resources</toplevel><creatorcontrib>Białożyt, Adam</creatorcontrib><creatorcontrib>Denkowska, Anna</creatorcontrib><creatorcontrib>Denkowski, Maciej P</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>ProQuest Central (New)</collection><collection>ProQuest One Academic (New)</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Middle East (New)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Applied &amp; Life Sciences</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Białożyt, Adam</au><au>Denkowska, Anna</au><au>Denkowski, Maciej P</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>The Kuratowski convergence of medial axes and conflict sets</atitle><jtitle>arXiv.org</jtitle><date>2022-10-23</date><risdate>2022</risdate><eissn>2331-8422</eissn><abstract>This paper consists of two parts. In the first one we study the behaviour of medial axes (skeletons) of closed sets in a connected complete Riemannian manifold \(\mathcal{M}\) under deformations. The second one is devoted to a similar study of conflict sets. We apply a new approach to the deformation process. Instead of seeing it as a `jump' from the initial to the final state, we perceive it as a continuous process, expressed using the Kuratowski convergence of sets (hence, unlike other authors, we do not require any regularity of the deformation). Our main `medial axis inner semi-continuity' result has already proved useful, as it was used to compute the tangent cone of the medial axis with application in singularity theory.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2022-10
issn 2331-8422
language eng
recordid cdi_proquest_journals_2080822867
source Publicly Available Content Database
subjects Axes (reference lines)
Convergence
Deformation
title The Kuratowski convergence of medial axes and conflict sets
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-23T05%3A06%3A45IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=The%20Kuratowski%20convergence%20of%20medial%20axes%20and%20conflict%20sets&rft.jtitle=arXiv.org&rft.au=Bia%C5%82o%C5%BCyt,%20Adam&rft.date=2022-10-23&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2080822867%3C/proquest%3E%3Cgrp_id%3Ecdi_FETCH-proquest_journals_20808228673%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2080822867&rft_id=info:pmid/&rfr_iscdi=true