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First, symmetry invariant point sets can be detected robustly using critical points of the Average Geodesic Distance (AGD) function. Second, intrinsic symmetries are self\u2010isometries of surfaces and as such are contained in the low dimensional group of M\u00f6bius transformations. Based on these observations, we propose an algorithm that: 1) generates a set of symmetric points by detecting critical points of the AGD function, 2) enumerates small subsets of those feature points to generate candidate M\u00f6bius transformations, and 3) selects among those candidate M\u00f6bius transformations the one(s) that best map the surface onto itself. The main advantages of this algorithm stem from the stability of the AGD in predicting potential symmetric point features and the low dimensionality of the M\u00f6bius group for enumerating potential self\u2010mappings. During experiments with a benchmark set of meshes augmented with human\u2010specified symmetric correspondences, we find that the algorithm is able to find intrinsic symmetries for a wide variety of object types with moderate deviations from perfect symmetry.<\/jats:p>","DOI":"10.1111\/j.1467-8659.2010.01778.x","type":"journal-article","created":{"date-parts":[[2010,9,21]],"date-time":"2010-09-21T15:51:18Z","timestamp":1285084278000},"page":"1689-1700","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":58,"title":["M\u00f6bius Transformations For Global Intrinsic Symmetry Analysis"],"prefix":"10.1111","volume":"29","author":[{"given":"Vladimir G.","family":"Kim","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yaron","family":"Lipman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaobai","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Thomas","family":"Funkhouser","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2010,9,21]]},"reference":[{"key":"e_1_2_12_2_2","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073207"},{"key":"e_1_2_12_3_2","volume-title":"Numerical Geometry of Non\u2010Rigid Shapes","author":"Bronstein A. 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