{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T09:50:22Z","timestamp":1777715422230,"version":"3.51.4"},"reference-count":19,"publisher":"SAGE Publications","issue":"5","license":[{"start":{"date-parts":[[1995,10,1]],"date-time":"1995-10-01T00:00:00Z","timestamp":812505600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[1995,10]]},"abstract":"<jats:p>This article discusses the detection and use of symmetry in planar shapes. The methods are especially useful for indus trial workpieces, where symmetry is omnipresent. \"Symmetry\" is interpreted in a broad sense as repeated, coplanar shape fragments. In particular, fragments that are \"similar\" in the mathematical sense are considered symmetric. As a general tool for the extraction and analysis of symmetries, \"Arc Length Space\" is proposed. In this space symmetries take on a very simple form: they correspond to straight-line segments, as suming an appropriate choice is made for the shapes' contour parameterizations. Reasoning about the possible coexistence of symmetries also becomes easier in this space. Only a restricted number of symmetry patterns can be formed. By making ap propriate choices for the contour parameters, the essential properties of Arc Length Space can be inherited for general viewpoints. Invariance to affine transformations is a key is sue. Specific results include the (informal) deduction of the five possible symmetry patterns within single connected con tour segments, the importance of rotational rather than mirror symmetries for deprojection purposes, and relations between simultaneous symmetries and critical contour points.<\/jats:p>","DOI":"10.1177\/027836499501400502","type":"journal-article","created":{"date-parts":[[2007,3,17]],"date-time":"2007-03-17T21:44:02Z","timestamp":1174167842000},"page":"407-424","source":"Crossref","is-referenced-by-count":22,"title":["Symmetry From Shape and Shape From Symmetry"],"prefix":"10.1177","volume":"14","author":[{"given":"L.","family":"Van Gool","sequence":"first","affiliation":[{"name":"Katholieke Universiteit Leuven Kardinaal Mercierlaan 94 B-3001 Leuven, Belgium"}]},{"given":"T.","family":"Moons","sequence":"additional","affiliation":[{"name":"Katholieke Universiteit Leuven Kardinaal Mercierlaan 94 B-3001 Leuven, Belgium"}]},{"given":"D.","family":"Ungureanu","sequence":"additional","affiliation":[{"name":"Katholieke Universiteit Leuven Kardinaal Mercierlaan 94 B-3001 Leuven, Belgium"}]},{"given":"E.","family":"Pauwels","sequence":"additional","affiliation":[{"name":"Katholieke Universiteit Leuven Kardinaal Mercierlaan 94 B-3001 Leuven, Belgium"}]}],"member":"179","published-online":{"date-parts":[[1995,10,1]]},"reference":[{"key":"atypb1","first-page":"724","author":"Blake, A.","year":"1993","journal-title":"Computer Vision"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/0031-3203(78)90025-0"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1177\/027836498400300302"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.1984.4767521"},{"key":"atypb5","volume-title":"Estimation of surface orientation using the hypothesis of object symmetry. Tech. Rep. TR-1324. Centre for Automation Research","author":"Hakalahti, H.","year":"1983"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1016\/0004-3702(81)90031-X"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/0734-189X(87)90117-4"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/0004-3702(88)90039-2"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1007\/BF00128526"},{"key":"atypb10","volume-title":"Transformation Geometry, an Introduction to Symmetry","author":"Martin, G.","year":"1982"},{"key":"atypb11","volume-title":"Shape from symmetry\u2014detecting and exploiting symmetry in affine images","author":"Mukherjee, D.","year":"1993"},{"issue":"1","key":"atypb12","first-page":"88","volume":"53","author":"Ulupinar, F.","year":"1991","journal-title":"Comp. Vision Graph. Image Proc.: Image Understanding"},{"key":"atypb13","volume-title":"Proc. British Machine Vision Conf","author":"Van Diest, M."},{"key":"atypb14","volume-title":"Similarity detection in computer vision","author":"Van Gool, L.","year":"1991"},{"key":"atypb15","unstructured":"Van Gool, L., Moons, T., Pauwels, E., and Oosterlinck, A. 1992. Semi-differential invariants. In Mundy, J., and Zisserman, A. (eds.): Applications of Invariance in Vision. Boston : MIT Press, pp. 157-192."},{"key":"atypb16","volume-title":"Symmetry and shape","author":"Van Gool, L.","year":"1993"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1117\/12.961648"},{"key":"atypb18","first-page":"138","volume":"1095","author":"Van Gool, L.","year":"1989","journal-title":"Proc. SPIE Applications of Artificial Intelligence"},{"key":"atypb19","volume-title":"IEEE Int. Conf. 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