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Imaging Sci."],"published-print":{"date-parts":[[2024,12,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>Density-equalizing maps are a class of mapping methods in which the shape deformation is driven by prescribed density information. In recent years, they have been widely used for data visualization on planar domains and planar parameterization of open surfaces.\u00a0However, the theory and computation of density-equalizing maps for closed surfaces are much less explored. In this work, we develop a novel method for computing spherical density-equalizing maps for genus-0 closed surfaces. Specifically, we first compute a conformal parameterization of the given genus-0 closed surface onto the unit sphere. Then we perform density equalization on the spherical domain based on the given density information to achieve a spherical density-equalizing map. The bijectivity of the mapping is guaranteed by introducing an overlap correction scheme based on quasi-conformal theory throughout the density-equalizing iterative process.\u00a0We further propose a method for incorporating the harmonic energy and landmark constraints into our formulation to achieve landmark-aligned spherical density-equalizing maps balancing different distortion measures. Using the proposed methods, a large variety of spherical parameterizations can be achieved. Applications to surface registration, remeshing, and data visualization are presented to demonstrate the effectiveness of our methods.<\/jats:p>","DOI":"10.1137\/24m1633911","type":"journal-article","created":{"date-parts":[[2024,10,18]],"date-time":"2024-10-18T07:03:26Z","timestamp":1729235006000},"page":"2110-2141","source":"Crossref","is-referenced-by-count":12,"title":["Spherical Density-Equalizing Map for Genus-0 Closed Surfaces"],"prefix":"10.1137","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-8655-8716","authenticated-orcid":true,"given":"Zhiyuan","family":"Lyu","sequence":"first","affiliation":[{"name":"Department of Mathematics, The Chinese University of Hong Kong, Hong Kong."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9152-0743","authenticated-orcid":true,"given":"Lok Ming","family":"Lui","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The Chinese University of Hong Kong, Hong Kong."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5407-9111","authenticated-orcid":true,"given":"Gary P. T.","family":"Choi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The Chinese University of Hong Kong, Hong Kong."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2024,10,18]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1090\/ulect\/038"},{"key":"ref2","doi-asserted-by":"crossref","unstructured":"S. Angenent, S. Haker, A. Tannenbaum, and R. 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