{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T06:03:32Z","timestamp":1781762612640,"version":"3.54.5"},"reference-count":302,"publisher":"Emerald","issue":"3-4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2010,12,8]]},"abstract":"<jats:p>This monograph reviews both the theory and practice of the numerical computation of geodesic distances on Riemannian manifolds . The notion of Riemannian manifold allows one to define a local metric (a symmetric positive tensor field) that encodes the information about the problem one wishes to solve. This takes into account a local isotropic cost (whether some point should be avoided or not) and a local anisotropy (which direction should be preferred). Using this local tensor field, the geodesic distance is used to solve many problems of practical interest such as segmentation using geodesic balls and Voronoi regions, sampling points at regular geodesic distance or meshing a domain with geodesic Delaunay triangles. The shortest paths for this Riemannian distance, the so-called geodesics, are also important because they follow salient curvilinear structures in the domain. We show several applications of the numerical computation of geodesic distances and shortest paths to problems in surface and shape processing, in particular segmentation, sampling, meshing and comparison of shapes. All the figures from this review paper can be reproduced by following the Numerical Tours of Signal Processing.<\/jats:p>\n                  <jats:p>http:\/\/www.ceremade.dauphine.fr\/\u223cpeyre\/numerical-tour\/<\/jats:p>\n                  <jats:p>Several textbooks exist that include description of several manifold methods for image processing, shape and surface representation and computer graphics. In particular, the reader should refer to [42, 147, 208, 209, 213, 255] for fascinating applications of these methods to many important problems in vision and graphics. This review paper is intended to give an updated tour of both foundations and trends in the area of geodesic methods in vision and graphics.<\/jats:p>","DOI":"10.1561\/0600000029","type":"journal-article","created":{"date-parts":[[2010,12,21]],"date-time":"2010-12-21T06:24:44Z","timestamp":1292912684000},"page":"197-397","source":"Crossref","is-referenced-by-count":84,"title":["Geodesic Methods in Computer Vision and Graphics"],"prefix":"10.1108","volume":"5","author":[{"given":"Gabriel","family":"Peyr\u00e9","sequence":"first","affiliation":[{"name":"Ceremade, UMR CNRS 7534, Universit\u00e9 Paris-Dauphine , Place de Lattre de Tassigny, Paris Cedex 16, 75775,","place":["France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mickael","family":"P\u00e9chaud","sequence":"additional","affiliation":[{"name":"DI \u00c9cole Normale Sup\u00e9rieure , 45 rue d\u2019Ulm, Paris, 75005, 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matching","volume-title":"INRIA Report,","author":"Wang","year":"2010"},{"issue":"2","key":"2026032614265763000_ref286","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1680\/ipeds.1952.11259","article-title":"Some theoretical aspects of road traffic research","volume":"2","author":"Wardrop","year":"1952","journal-title":"Proceedings\u2014Institution of Civil Engineers"},{"issue":"4","key":"2026032614265763000_ref287","doi-asserted-by":"crossref","DOI":"10.1145\/1409625.1409626","article-title":"Parallel algorithms for approximation of distance maps on parametric surfaces","volume":"27","author":"Weber","year":"2008","journal-title":"ACM Transactions on Graphics"},{"key":"2026032614265763000_ref288","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1145\/512274.3734138","article-title":"Algorithm 232: Heapsort","volume":"7","author":"Williams","year":"1964","journal-title":"Communications of the ACM"},{"issue":"4","key":"2026032614265763000_ref289","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1162\/neco.1997.9.4.837","article-title":"Stochastic completion fields: A neural model of illusory contour shape and salience","volume":"9","author":"Williams","year":"1997","journal-title":"Neural Computation"},{"issue":"9","key":"2026032614265763000_ref290","doi-asserted-by":"crossref","first-page":"1001","DOI":"10.1109\/34.35505","article-title":"Computing minimal distances on polyhedral surfaces","volume":"11","author":"Wolfson","year":"1989","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"issue":"3","key":"2026032614265763000_ref291","doi-asserted-by":"crossref","first-page":"769","DOI":"10.1016\/S1053-8119(03)00019-3","article-title":"Characterizing volume and surface deformations in an atlas framework: Theory, applications, and implementation","volume":"18","author":"Woods","year":"2003","journal-title":"NeuroImage"},{"key":"2026032614265763000_ref292","first-page":"263","article-title":"High quality anisotropic tetrahedral mesh generation via ellipsoidal bubble packing","volume-title":"9th International Meshing Roundtable","author":"Yamakawa","year":"2000"},{"issue":"2","key":"2026032614265763000_ref293","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1016\/j.jcp.2005.08.005","article-title":"O(n) implementation of the fast marching algorithm","volume":"212","author":"Yatziv","year":"2006","journal-title":"Journal of Computational Physics"},{"key":"2026032614265763000_ref294","article-title":"Guaranteed-quality anisotropic mesh generation for domains with curves","volume-title":"Proceedings of EWCG\u201906","author":"Yokosuka","year":"2006"},{"issue":"3","key":"2026032614265763000_ref295","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1109\/TC.1972.5008949","article-title":"Fourier 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