{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T06:41:08Z","timestamp":1698043268660},"reference-count":15,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2007,3,21]],"date-time":"2007-03-21T00:00:00Z","timestamp":1174435200000},"content-version":"vor","delay-in-days":6959,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems & Computers in Japan"],"published-print":{"date-parts":[[1988,3]]},"abstract":"Abstract<\/jats:title>In order to determine the shape and the motion of the object from its projection, it suffices to derive and solve the equation relating the parameters specifying the shape and the motion of the object with the features measured on the image. The equation is usually nonlinear, and is difficult to solve in the analytic way. This paper notes that there is no inherent coordinate system on the image, and any two coordinate systems are equivalent. By combining the features of the image, coordinate\u2010rotation\u2010invariant parameters (invariances) are derived. By this scheme, the geometrical meaning of the image characteristics is made clear, and the analytic solution is obtained in a natural way. The idea is demonstrated for the cases of the optical flow analysis and the surface recovery by texture, as examples.<\/jats:p>","DOI":"10.1002\/scj.4690190310","type":"journal-article","created":{"date-parts":[[2007,7,7]],"date-time":"2007-07-07T15:16:57Z","timestamp":1183821417000},"page":"87-97","source":"Crossref","is-referenced-by-count":2,"title":["Coordinate rotation invariance of image characteristics for 3d shape and motion recovery"],"prefix":"10.1002","volume":"19","author":[{"given":"Ken\u2010Ichi","family":"Kanatani","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2007,3,21]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1119\/1.1941790"},{"key":"e_1_2_1_3_2","article-title":"Transformation rule and invariant decomposition of optical flow","volume":"85","author":"Kanatani K.","year":"1985","journal-title":"Tech. Rep. I.E.C.E., Japan"},{"issue":"3","key":"e_1_2_1_4_2","first-page":"373","article-title":"Theory of object motion recognition without using correspondence pointm","volume":"27","author":"Kanatani K.","year":"1986","journal-title":"Trans. Inf. Proc. Soc. Jap."},{"issue":"5","key":"e_1_2_1_5_2","first-page":"1035","article-title":"3D Euclid space or 2D non\u2010Euclid space?\u2014Methodology for image recognition","volume":"70","author":"Kanatani K.","year":"1987","journal-title":"Trans. (D), I.E.C.E., Japan"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0734-189X(86)90026-5"},{"key":"e_1_2_1_7_2","article-title":"Structure and motion from optical flow under perspective projection","volume":"37","author":"Kanatani K.","year":"1987","journal-title":"Comput. Vision Graphics Image Process"},{"key":"e_1_2_1_8_2","article-title":"Camera rotation invariance of image characteristicsm","volume":"38","author":"Kanatani K.","year":"1987","journal-title":"Comput. Vision Graphics Image Process"},{"key":"e_1_2_1_9_2","volume-title":"Group Theoretical Methods on Image Understanding","author":"Kanatani K.","year":"1987"},{"key":"e_1_2_1_10_2","unstructured":"K.KantaniandT. \u2010C.Chou. Shape from texture: General principle Proc. 17th Image Eng. 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