[{"data":1,"prerenderedAt":58},["ShallowReactive",2],{"method-horn1987absolute":3},{"method":4,"reference":38,"equipment":56,"figures":57,"results":35},{"id":5,"label":6,"shortName":7,"title":8,"year":9,"era":10,"cluster":11,"scope":12,"keyIdeaZh":13,"keyIdeaEn":14,"fulltextStatus":15,"publicationStatus":16,"recommendation":17,"constructionRelevance":18,"validationEnvironment":19,"strengths":20,"limitations":24,"sensors":30,"platform":31,"estimator":32,"association":33,"timeModel":34,"deskew":34,"loopClosure":34,"globalOptimization":34,"mapRepresentation":34,"prior":34,"outputGeometry":34,"compute":34,"codeUrl":35,"codeLicense":36,"relatedVersions":37},"horn1987absolute","Horn, 1987","Horn absolute orientation","Closed-form solution of absolute orientation using unit quaternions",1987,"classic","C10","evaluation_method_or_metric","給定兩座標系中三個以上不共線的對應點，作者提出最小平方意義下的閉式解：平移為一組點的形心與另一組點經旋轉、縮放後之形心的差；若採作者建議的對稱誤差式，尺度為兩組點相對形心的均方根偏差之比，且不需先求旋轉；旋轉以單位四元數表示，為一個 4×4 對稱矩陣最大正特徵值對應的特徵向量。作者也指出，若某一組座標的精度遠高於另一組，採非對稱的尺度式可能較合適；附錄說明可加入權重以反映不同點的量測可信度。","Closed-form least-squares rotation, translation and scale between corresponding point sets using unit quaternions.","full_text_reviewed","peer_reviewed_published","background","not_reported（通用座標轉換方法）",[],[21,22,23],"Exact closed-form result preferred to approximate methods (abstract)","Symmetric treatment of scale (scale section)","Weights can be incorporated (Appendix A2)",[25,26,27,28,29],"Assumes known point correspondences and equal measurement quality unless weights are introduced (Appendix A2)","Requires at least three non-collinear points; two points do not provide enough constraint (Sec. 1.B, 2.A)","The optimal scale depends on the chosen error term: two asymmetric forms and one symmetric form give different scales; the symmetric form is preferred unless one coordinate set is known much more precisely (Sec. 2.D, 2.E, Appendix A1)","The rotation is unique only if the most positive eigenvalue of the 4x4 matrix is distinct (Appendix A3)","(inference, corrected) The reflection failure described in Umeyama (1991) does not apply to this unit-quaternion solution: Horn shows that the composite product preserves cross products, so the result is a rotation, not a reflection (Sec. 3.E, proof in Appendix A6). Umeyama's abstract criticises 'Horn et al.', and Umeyama's reference list contains both this paper and Horn, Hilden & Negahdaripour (1988, orthonormal-matrix method, 10.1364\u002FJOSAA.5.001127); the criticism most plausibly targets the latter and the SVD method of Arun et al.",[],[],"closed-form least squares (unit quaternion eigenvector)","known point correspondences","not_applicable",null,"not_verified",[],{"id":5,"kind":39,"shortName":7,"title":8,"authors":40,"year":9,"venue":42,"venueType":43,"publisher":44,"volumeIssuePages":45,"doi":46,"arxivId":35,"url":47,"firstPublicDate":48,"publicationStatus":16,"metadataStatus":49,"fulltextStatus":15,"era":10,"classicReason":50,"codeUrl":35,"cluster":11,"topics":51,"mdpi":52,"verification":53,"label":6,"fulltextRoute":54,"versionRead":55,"addedByCensus":52},"component",[41],"Berthold K. P. Horn","Journal of the Optical Society of America A","journal","Optica Publishing Group (formerly OSA)","4(4):629-642","10.1364\u002Fjosaa.4.000629","https:\u002F\u002Fpeople.csail.mit.edu\u002Fbkph\u002Fpapers\u002FAbsolute_Orientation.pdf","1987-04-01","metadata_verified","evaluation-calibration method: the closed-form least-squares alignment used before computing ATE (cited by the TUM RGB-D benchmark).",[11],false,"corrected","author copy","Version of record page images (J. Opt. Soc. Am. A 4(4):629-642, April 1987) with OCR text, hosted on the author's MIT page",[],[],1790510665049]