{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,2]],"date-time":"2024-06-02T18:40:23Z","timestamp":1717353623841},"reference-count":57,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2014,9,20]],"date-time":"2014-09-20T00:00:00Z","timestamp":1411171200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int J Comput Vis"],"published-print":{"date-parts":[[2015,5]]},"DOI":"10.1007\/s11263-014-0762-0","type":"journal-article","created":{"date-parts":[[2014,9,19]],"date-time":"2014-09-19T09:58:07Z","timestamp":1411120687000},"page":"285-306","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Distances and Means of Direct Similarities"],"prefix":"10.1007","volume":"112","author":[{"given":"Minh-Tri","family":"Pham","sequence":"first","affiliation":[]},{"given":"Oliver J.","family":"Woodford","sequence":"additional","affiliation":[]},{"given":"Frank","family":"Perbet","sequence":"additional","affiliation":[]},{"given":"Atsuto","family":"Maki","sequence":"additional","affiliation":[]},{"given":"Riccardo","family":"Gherardi","sequence":"additional","affiliation":[]},{"given":"Bj\u00f6rn","family":"Stenger","sequence":"additional","affiliation":[]},{"given":"Roberto","family":"Cipolla","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,9,20]]},"reference":[{"key":"762_CR1","doi-asserted-by":"crossref","unstructured":"Agrawal, M. (2006). A Lie algebraic approach for consistent pose registration for general euclidean motion. In: Proceedings of the international conference on intelligent Robot and systems (pp. 1891\u20131897).","DOI":"10.1109\/IROS.2006.282313"},{"key":"762_CR2","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1051\/ps\/2013033","volume":"18","author":"M Arnaudon","year":"2014","unstructured":"Arnaudon, M., & Miclo, L. (2014). Means in complete manifolds: Uniqueness and approximation. ESAIM: Probability and Statistics, 18, 185\u2013206.","journal-title":"ESAIM: Probability and Statistics"},{"key":"762_CR3","doi-asserted-by":"crossref","unstructured":"Arnold, V., Vogtmann, K., & Weinstein, A. (1989). Mathematical methods of classical mechanics. Graduate Texts in Mathematics. Springer.","DOI":"10.1007\/978-1-4757-2063-1"},{"key":"762_CR4","doi-asserted-by":"crossref","unstructured":"Arsigny, V., Commowick, O., Pennec, X., & Ayache, N. (2006a). A Log-Euclidean polyaffine framework for locally rigid or affine registration. In: Biomedical image registration (Vol. 4057, pp 120\u2013127).","DOI":"10.1007\/11784012_15"},{"key":"762_CR5","unstructured":"Arsigny, V., Pennec, X., & Ayache, N. (2006b). Bi-invariant means in lie groups. Applications to left-invariant polyaffine transformations. Tech. rep., INRIA Technical Report No. 5885."},{"key":"762_CR6","doi-asserted-by":"crossref","unstructured":"Begelfor, E., & Werman, M. (2006). Affine invariance revisited. In: Proceedings of the IEEE conference on computer vision and pattern recognition (Vol. 2, pp. 2087\u20132094), Washington, DC, USA: IEEE Computer Society.","DOI":"10.1109\/CVPR.2006.50"},{"key":"762_CR7","doi-asserted-by":"crossref","unstructured":"Beltrami, E. (1868). Teoria fondamentale degli spazi di curvatura constante. Annali di Mat, II(2), 232\u2013255.","DOI":"10.1007\/BF02419615"},{"issue":"1","key":"762_CR8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1214\/aos\/1046294456","volume":"31","author":"R Bhattacharya","year":"2003","unstructured":"Bhattacharya, R., & Patrangenaru, V. (2003). Large sample theory of intrinsic and extrinsic sample means on manifolds. The Annals of Statistics, 31(1), 1\u201329.","journal-title":"The Annals of Statistics"},{"key":"762_CR9","unstructured":"Bossa, M. N., & Olmos, S. (2006). Statistical model of similarity transformations: Building a multi-object pose model of brain structures. In: Workshop on mathematical methods in biomedical image analysis."},{"issue":"5","key":"762_CR10","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1109\/TPAMI.2007.1057","volume":"29","author":"M Carreira Perpinan","year":"2007","unstructured":"Carreira Perpinan, M. (2007). Gaussian mean-shift is an EM algorithm. IEEE Transactions on Pattern Analysis and Machine Intelligence, 29(5), 767\u2013776.","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"762_CR11","doi-asserted-by":"crossref","unstructured":"Cetingul, H., & Vidal, R. (2009). Intrinsic mean shift for clustering on Stiefel and Grassmann manifolds. In: Proceedings of IEEE conference on computer vision and pattern recognition (pp. 1896\u20131902).","DOI":"10.1109\/CVPR.2009.5206806"},{"key":"762_CR12","doi-asserted-by":"crossref","first-page":"1112","DOI":"10.1137\/S0895479899364015","volume":"22","author":"SH Cheng","year":"2000","unstructured":"Cheng, S. H., Higham, N. J., Kenney, C. S., & Laub, A. J. (2000). Approximating the logarithm of a matrix to specified accuracy. SIAM Journal on Matrix Analysis and Applications, 22, 1112\u20131125.","journal-title":"SIAM Journal on Matrix Analysis and Applications"},{"key":"762_CR13","doi-asserted-by":"crossref","first-page":"790","DOI":"10.1109\/34.400568","volume":"17","author":"Y Cheng","year":"1995","unstructured":"Cheng, Y. (1995). Mean shift, mode seeking, and clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17, 790\u2013799.","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"762_CR14","volume-title":"Introduction to geometry","author":"HSM Coxeter","year":"1961","unstructured":"Coxeter, H. S. M. (1961). Introduction to geometry. New York: Wiley."},{"key":"762_CR15","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1093\/biomet\/59.3.665","volume":"59","author":"T Downs","year":"1972","unstructured":"Downs, T. (1972). Orientation statistics. Biometrika, 59, 665\u2013676.","journal-title":"Biometrika"},{"key":"762_CR16","doi-asserted-by":"crossref","unstructured":"Drost, B., Ulrich, M., Navab, N., & Ilic, S. (2010). Model globally, match locally: Efficient and robust 3D object recognition. In: Proceedings of IEEE conference on computer vision and pattern recognition (pp. 998\u20131005).","DOI":"10.1109\/CVPR.2010.5540108"},{"key":"762_CR17","doi-asserted-by":"crossref","unstructured":"Dubbelman, G., Dorst, L., & Pijls, H. (2012). Manifold statistics for essential matrices. In: Proceedings of European conference on computer vision (pp. 531\u2013544). Lecture Notes in Computer Science. Berlin: Springer.","DOI":"10.1007\/978-3-642-33709-3_38"},{"key":"762_CR18","unstructured":"Eade, E. (2011). Lie groups for 2d and 3d transformations, http:\/\/ethaneade.com\/lie.pdf , revised Dec. 2013."},{"key":"762_CR19","first-page":"215","volume":"10","author":"M Fr\u00e9chet","year":"1948","unstructured":"Fr\u00e9chet, M. (1948). Les lments alatoires de nature quelconque dans un espace distanci. Annales de l\u2019Institut Henri Poincare, 10, 215\u2013310.","journal-title":"Annales de l\u2019Institut Henri Poincare"},{"issue":"4","key":"762_CR20","first-page":"10","volume":"17","author":"J Gallier","year":"2002","unstructured":"Gallier, J., & Xu, D. (2002). Computing exponentials of Skew-Symmetric matrices and logarithms of orthogonal matrices. International Journal of Robotics and Automation, 17(4), 10\u201320.","journal-title":"International Journal of Robotics and Automation"},{"key":"762_CR21","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-21554-9","volume-title":"Lie groups, lie algebras, and representations: An elementary introduction","author":"BC Hall","year":"2003","unstructured":"Hall, B. C. (2003). Lie groups, lie algebras, and representations: An elementary introduction. Berlin: Springer."},{"key":"762_CR22","doi-asserted-by":"crossref","unstructured":"Hartley, R., Trumpf, J., Dai, Y., & Li, H. (2013). Rotation averaging. International Journal of Computer Vision, 103(3), 267\u2013305.","DOI":"10.1007\/s11263-012-0601-0"},{"key":"762_CR23","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511811685","volume-title":"Multiple view geometry in computer vision","author":"RI Hartley","year":"2004","unstructured":"Hartley, R. I., & Zisserman, A. (2004). Multiple view geometry in computer vision (2nd ed.). Cambridge: Cambridge University Press.","edition":"2"},{"key":"762_CR24","doi-asserted-by":"crossref","first-page":"1771","DOI":"10.1162\/089976602760128018","volume":"14","author":"GE Hinton","year":"2002","unstructured":"Hinton, G. E. (2002). Training products of experts by minimizing contrastive divergence. Neural Computation, 14, 1771\u20131800.","journal-title":"Neural Computation"},{"issue":"5","key":"762_CR25","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1002\/cpa.3160300502","volume":"30","author":"H Karcher","year":"1977","unstructured":"Karcher, H. (1977). Riemannian center of mass and mollifier smoothing. Communications on Pure and Applied Mathematics, 30(5), 509\u2013541.","journal-title":"Communications on Pure and Applied Mathematics"},{"key":"762_CR26","unstructured":"Khoshelham, K. (2007). Extending generalized Hough transform to detect 3D objects in laser range data. Workshop on Laser Scanning, XXXVI, 206\u2013210."},{"key":"762_CR27","doi-asserted-by":"crossref","unstructured":"Knopp, J., Prasad, M., Willems, G., Timofte, R., & Van Gool, L. (2010). Hough transform and 3D SURF for robust three dimensional classification. In: Proceedings of European conference on computer vision (pp. 589\u2013602).","DOI":"10.1007\/978-3-642-15567-3_43"},{"key":"762_CR28","doi-asserted-by":"crossref","unstructured":"Lee, J. (1997). Riemannian manifolds: An introduction to curvature. Graduate Texts in Mathematics. Springer.","DOI":"10.1007\/b98852"},{"issue":"1\u20133","key":"762_CR29","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1007\/s11263-007-0095-3","volume":"77","author":"B Leibe","year":"2008","unstructured":"Leibe, B., Leonardis, A., & Schiele, B. (2008). Robust object detection with interleaved categorization and segmentation. International Journal of Computer Vision, 77(1\u20133), 259\u2013289.","journal-title":"International Journal of Computer Vision"},{"key":"762_CR30","first-page":"1989","volume":"45","author":"DC Liu","year":"1989","unstructured":"Liu, D. C., & Nocedal, J. (1989). On the limited memory BFGS method for large scale optimization. Mathematical Programming, 45, 1989.","journal-title":"Mathematical Programming"},{"key":"762_CR31","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/S0895479801383877","volume":"24","author":"M Moakher","year":"2002","unstructured":"Moakher, M. (2002). Means and averaging in the group of rotations. SIAM Journal on Matrix Analysis and Applications, 24, 1\u201316.","journal-title":"SIAM Journal on Matrix Analysis and Applications"},{"key":"762_CR32","unstructured":"O\u2019Neill, B. (1983). Semi-Riemannian geometry: With applications to relativity. No. v. 103 in pure and applied mathematics. Academic Press."},{"key":"762_CR33","doi-asserted-by":"crossref","unstructured":"Opelt, A., Pinz, A., & Zisserman, A. (2008). Learning an alphabet of shape and appearance for multi-class object detection. International Journal of Computer Vision, 80(1).","DOI":"10.1007\/s11263-008-0139-3"},{"issue":"1","key":"762_CR34","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1115\/1.2826116","volume":"117","author":"FC Park","year":"1995","unstructured":"Park, F. C. (1995). Distance metrics on the rigid-body motions with applications to mechanism design. Journal of Mechanical Design, 117(1), 48\u201354.","journal-title":"Journal of Mechanical Design"},{"issue":"3","key":"762_CR35","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1145\/256157.256160","volume":"16","author":"FC Park","year":"1997","unstructured":"Park, F. C., & Ravani, B. (1997). Smooth invariant interpolation of rotations. ACM Transactions on Graphics, 16(3), 277\u2013295.","journal-title":"ACM Transactions on Graphics"},{"key":"762_CR36","doi-asserted-by":"crossref","unstructured":"Parzen, E. (1962). 1962. The Annals of Mathematical Statistics, 33(3), 1065\u20131076.","DOI":"10.1214\/aoms\/1177704472"},{"issue":"3","key":"762_CR37","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1016\/j.spl.2005.04.004","volume":"73","author":"B Pelletier","year":"2005","unstructured":"Pelletier, B. (2005). Kernel density estimation on Riemannian manifolds. Statistics Probability Letters, 73(3), 297\u2013304.","journal-title":"Statistics Probability Letters"},{"key":"762_CR38","unstructured":"Pennec, X. (1998). Computing the mean of geometric features application to the mean rotation. Tech. Rep. RR-3371, INRIA."},{"issue":"1","key":"762_CR39","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/s10851-006-6228-4","volume":"25","author":"X Pennec","year":"2006","unstructured":"Pennec, X. (2006). Intrinsic statistics on Riemannian manifolds: Basic tools for geometric measurements. JMIV, 25(1), 127\u2013154.","journal-title":"JMIV"},{"key":"762_CR40","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1023\/A:1008270110193","volume":"9","author":"X Pennec","year":"1998","unstructured":"Pennec, X., & Ayache, N. (1998). Uniform distribution, distance and expectation problems for geometric features processing. Journal of Mathematical Imaging and Vision, 9, 49\u201367.","journal-title":"Journal of Mathematical Imaging and Vision"},{"issue":"3","key":"762_CR41","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1023\/A:1007976002485","volume":"25","author":"X Pennec","year":"1997","unstructured":"Pennec, X., & Thirion, J. P. (1997). A framework for uncertainty and validation of 3D registration methods based on points and frames. International Journal of Computer Vision, 25(3), 203\u2013229.","journal-title":"International Journal of Computer Vision"},{"key":"762_CR42","doi-asserted-by":"crossref","unstructured":"Pham, M. T., Woodford, O. J., Perbet, F., Maki, A., Stenger, B., & Cipolla, R. (2011). A new distance for scale-invariant 3D shape recognition and registration. In: Proceedings of the international conference on computer vision.","DOI":"10.1109\/ICCV.2011.6126236"},{"key":"762_CR43","unstructured":"Pham, M. T., Woodford, O. J., Perbet, F., Maki, A., & Stenger, B. (2012). Toshiba CAD model point clouds dataset. http:\/\/www.toshiba.eu\/eu\/Cambridge-Research-Laboratory\/Computer-Vision-Group\/Stereo-Points\/"},{"key":"762_CR44","doi-asserted-by":"crossref","unstructured":"Poincar\u00e9, H. (1882). Th\u00e9orie des groupes fuchsiens. Almqvist & Wiksells.","DOI":"10.1007\/BF02592124"},{"issue":"3","key":"762_CR45","first-page":"460","volume":"105","author":"B Ravani","year":"1983","unstructured":"Ravani, B., & Roth, B. (1983). Motion synthesis using kinematic mappings. Journal of Mechanical Design, 105(3), 460\u2013467.","journal-title":"Journal of Mechanical Design"},{"issue":"3","key":"762_CR46","doi-asserted-by":"crossref","first-page":"832","DOI":"10.1214\/aoms\/1177728190","volume":"27","author":"M Rosenblatt","year":"1956","unstructured":"Rosenblatt, M. (1956). Remarks on some nonparametric estimates of a density function. The Annals of Mathematical Statistics, 27(3), 832\u2013837.","journal-title":"The Annals of Mathematical Statistics"},{"issue":"1","key":"762_CR47","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02289451","volume":"31","author":"P Sch\u00f6nemann","year":"1966","unstructured":"Sch\u00f6nemann, P. (1966). A generalized solution of the orthogonal procrustes problem. Psychometrika, 31(1), 1\u201310.","journal-title":"Psychometrika"},{"key":"762_CR48","doi-asserted-by":"crossref","unstructured":"Schramm, E., & Schreck, P. (2003). Solving geometric constraints invariant modulo the similarity group. In: International conference on computational science and its applications (pp. 356\u2013365).","DOI":"10.1007\/3-540-44842-X_37"},{"issue":"7","key":"762_CR49","doi-asserted-by":"crossref","first-page":"1270","DOI":"10.1109\/TPAMI.2007.70772","volume":"30","author":"J Shotton","year":"2008","unstructured":"Shotton, J., Blake, A., & Cipolla, R. (2008). Multiscale categorical object recognition using contour fragments. IEEE Transactions on Pattern Analysis and Machine Intelligence, 30(7), 1270\u20131281.","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"issue":"2","key":"762_CR50","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1111\/j.2517-6161.1979.tb01076.x","volume":"41","author":"R Sibson","year":"1979","unstructured":"Sibson, R. (1979). Studies in the robustness of multidimensional scaling: Perturbational analysis of classical scaling. Journal of the Royal Statistical Society Series B, 41(2), 217\u2013229.","journal-title":"Journal of the Royal Statistical Society Series B"},{"key":"762_CR51","unstructured":"Sternberg, S. (1999). Lectures on differential geometry. AMS Chelsea Publishing Series. Chelsea Publishing Company"},{"issue":"3","key":"762_CR52","first-page":"5","volume":"2","author":"H Strasdat","year":"2010","unstructured":"Strasdat, H., Montiel, J., & Davison, A. J. (2010). Scale drift-aware large scale monocular slam. Robotics: Science and Systems., 2(3), 5.","journal-title":"Robotics: Science and Systems."},{"key":"762_CR53","doi-asserted-by":"crossref","unstructured":"Subbarao, R., & Meer, P. (2009). Nonlinear mean shift over Riemannian manifolds. International Journal of Computer Vision, 84(1).","DOI":"10.1007\/s11263-008-0195-8"},{"key":"762_CR54","doi-asserted-by":"crossref","unstructured":"Tombari, F., & Di Stefano, L. (2010). Object recognition in 3D scenes with occlusions and clutter by Hough voting. In: Proceedings of Pacific-Rim symposium on image and video technology (pp. 349\u2013355).","DOI":"10.1109\/PSIVT.2010.65"},{"key":"762_CR55","unstructured":"Vaccaro, C. (2012). Heat kernel methods in finance: The SABR model. Quantitative Finance Papers. http:\/\/arxiv.org\/ftp\/arxiv\/papers\/1201\/1201.1437.pdf"},{"key":"762_CR56","unstructured":"Woodford, O. J., Pham, M. T., Maki, A., Perbet, F., & Stenger, B. (2013). Demisting the Hough transform for 3D shape recognition and registration. In: International Journal of Computer Vision."},{"issue":"3","key":"762_CR57","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/S0010-4485(97)00060-2","volume":"30","author":"M Zefran","year":"1998","unstructured":"Zefran, M., & Kumar, V. (1998). Interpolation schemes for rigid body motions. Computer-Aided Design, 30(3), 179\u2013189.","journal-title":"Computer-Aided Design"}],"container-title":["International Journal of Computer Vision"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11263-014-0762-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11263-014-0762-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11263-014-0762-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,2]],"date-time":"2024-06-02T18:12:29Z","timestamp":1717351949000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11263-014-0762-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,9,20]]},"references-count":57,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2015,5]]}},"alternative-id":["762"],"URL":"https:\/\/doi.org\/10.1007\/s11263-014-0762-0","relation":{},"ISSN":["0920-5691","1573-1405"],"issn-type":[{"value":"0920-5691","type":"print"},{"value":"1573-1405","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,9,20]]}}}