{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:48:16Z","timestamp":1787323696062,"version":"build-2736575974"},"reference-count":9,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Imaging Sci."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>The area distance to a convex plane curve is an important concept in computer vision. In this paper we describe a strong link between area distances and improper affine spheres. Based on this link, we propose an extremely fast algorithm to compute the inner area distance. Moreover, the concepts of the theory of affine spheres lead to a new definition of an area distance on the outer part of a convex plane curve. On the other hand, area distances provide a good geometrical understanding of improper affine spheres.<\/jats:p>","DOI":"10.1137\/080714610","type":"journal-article","created":{"date-parts":[[2008,10,29]],"date-time":"2008-10-29T13:45:01Z","timestamp":1225287901000},"page":"209-227","source":"Crossref","is-referenced-by-count":14,"title":["Area Distances of Convex Plane Curves and Improper Affine Spheres"],"prefix":"10.1137","volume":"1","author":[{"given":"Marcos","family":"Craizer","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Moacyr","family":"Alvim","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ralph","family":"Teixeira","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,7,30]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1080\/10586458.1999.10504404"},{"key":"R2","unstructured":"A. I. Bobenko and Y. B. Suris,\n                      Discrete Differential Geometry: Consistency as Integrability\n                      , preprint, 2005; available online from http:\/\/www.arxiv.org\/abs\/math\/0504358."},{"key":"R3","unstructured":"S. Buchin,\n                      Affine Differential Geometry\n                      , Science Press, Beijing, China, Gordon and Breach, Science Publishers, New York, 1983."},{"key":"R4","unstructured":"A.M. Li, U. Simon, and G. S. Zhao,\n                      Global Affine Differential Geometry of Hypersurfaces\n                      , De Gruyter Exp. Math. 11, Walter de Gruyter, Berlin, 1993."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/S0393-0440(02)00134-1"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1109\/83.661191"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1023\/B:VISI.0000036835.28674.d0"},{"key":"R8","unstructured":"M. A. Silva,\n                      Esqueletos Afins e Equa\u00e7\u00f5es de Propaga\u00e7\u00e3o\n                      , Ph.D. thesis, Instituto de Matem\u00e1tica Pura e Aplicada (IMPA), 2005 (in Portuguese); available online from http:\/\/www.preprint.impa.br."},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1007\/s10851-007-0038-1"}],"container-title":["SIAM Journal on Imaging Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/080714610","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:12:18Z","timestamp":1787321538000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/080714610"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1]]},"references-count":9,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["10.1137\/080714610"],"URL":"https:\/\/doi.org\/10.1137\/080714610","relation":{},"ISSN":["1936-4954"],"issn-type":[{"value":"1936-4954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1]]}}}