{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,30]],"date-time":"2026-06-30T21:48:17Z","timestamp":1782856097283,"version":"3.54.5"},"publisher-location":"Berlin, Heidelberg","reference-count":51,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783642128998","type":"print"},{"value":"9783642129001","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2010]]},"DOI":"10.1007\/978-3-642-12900-1_5","type":"book-chapter","created":{"date-parts":[[2010,4,19]],"date-time":"2010-04-19T14:38:27Z","timestamp":1271687907000},"page":"115-144","source":"Crossref","is-referenced-by-count":8,"title":["Statistical Analysis on Manifolds and Its Applications to Video Analysis"],"prefix":"10.1007","author":[{"given":"Pavan","family":"Turaga","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ashok","family":"Veeraraghavan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anuj","family":"Srivastava","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rama","family":"Chellappa","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","reference":[{"key":"5_CR1","doi-asserted-by":"crossref","DOI":"10.1515\/9781400830244","volume-title":"Optimization Algorithms on Matrix Manifolds","author":"P.A. Absil","year":"2008","unstructured":"Absil, P.A., Mahony, R., Sepulchre, R.: Optimization Algorithms on Matrix Manifolds. Princeton University Press, Princeton (2008)"},{"key":"5_CR2","doi-asserted-by":"crossref","unstructured":"Aggarwal, G., Roy-Chowdhury, A., Chellappa, R.: A system identification approach for video-based face recognition. In: International Conference on Pattern Recognition (ICPR) (2004)","DOI":"10.1109\/ICPR.2004.1333732"},{"key":"5_CR3","doi-asserted-by":"crossref","unstructured":"Begelfor, E., Werman, M.: Affine invariance revisited. In: IEEE International Conference on Computer Vision and Pattern Recognition, pp. 2087\u20132094 (2006)","DOI":"10.1109\/CVPR.2006.50"},{"key":"5_CR4","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1016\/S0378-3758(02)00268-9","volume":"108","author":"R. Bhattacharya","year":"2002","unstructured":"Bhattacharya, R., Patrangenaru, V.: Nonparametric estimation of location and dispersion on Riemannian manifolds. Journal for Statistical Planning and Inference\u00a0108, 23\u201336 (2002)","journal-title":"Journal for Statistical Planning and Inference"},{"issue":"1","key":"5_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1214\/aos\/1046294456","volume":"31","author":"R. Bhattacharya","year":"2003","unstructured":"Bhattacharya, R., Patrangenaru, V.: Large sample theory of intrinsic and extrinsic sample means on manifolds- I. The Annals of Statistics\u00a031(1), 1\u201329 (2003)","journal-title":"The Annals of Statistics"},{"key":"5_CR6","doi-asserted-by":"crossref","unstructured":"Bissacco, A., Chiuso, A., Ma, Y., Soatto, S.: Recognition of human gaits. In: IEEE International Conference on Computer Vision and Pattern Recognition (CVPR), vol.\u00a02, pp. 52\u201357 (2001)","DOI":"10.1109\/CVPR.2001.990924"},{"key":"5_CR7","series-title":"Lecture Notes in Computer Science","volume-title":"AVBPA 2003","author":"A. Bobick","year":"2003","unstructured":"Bobick, A., Tanawongsuwan: Performance analysis of time-distance gait parameters under different speeds. In: Kittler, J., Nixon, M.S. (eds.) AVBPA 2003. LNCS, vol.\u00a02688. Springer, Heidelberg (2003)"},{"key":"5_CR8","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1214\/ss\/1177013696","volume":"1","author":"F. Bookstein","year":"1986","unstructured":"Bookstein, F.: Size and shape spaces for landmark data in two dimensions. Statistical Science\u00a01, 181\u2013242 (1986)","journal-title":"Statistical Science"},{"key":"5_CR9","unstructured":"Boothby, W.M.: An introduction to differentiable manifolds and Riemannian geometry. Academic Press Inc., London (1975)"},{"key":"5_CR10","volume-title":"Systems and Control in the Twenty-First Century: Progress in Systems and Control","author":"R. Brockett","year":"1997","unstructured":"Brockett, R.: Notes on Stochastic Processes on Manifolds. In: Systems and Control in the Twenty-First Century: Progress in Systems and Control, vol.\u00a022. Birkh\u00e4user, Basel (1997)"},{"issue":"2","key":"5_CR11","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1137\/0310021","volume":"10","author":"R.W. Brockett","year":"1972","unstructured":"Brockett, R.W.: System theory on group manifolds and coset spaces. SIAM Journal on Control\u00a010(2), 265\u2013284 (1972)","journal-title":"SIAM Journal on Control"},{"key":"5_CR12","series-title":"Lecture Notes in Statistics","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-21540-2","volume-title":"Statistics on special manifolds","author":"Y. Chikuse","year":"2003","unstructured":"Chikuse, Y.: Statistics on special manifolds. Lecture Notes in Statistics. Springer, Heidelberg (2003)"},{"key":"5_CR13","unstructured":"Cock, K.D., Moor, B.D.: Subspace angles and distances between ARMA models. In: Proceedings of the Intl. Symposium of Mathematical Theory of Networks and Systems, MTNS (2000)"},{"key":"5_CR14","volume-title":"Statistical shape analysis","author":"I. Dryden","year":"1998","unstructured":"Dryden, I., Mardia, K.: Statistical shape analysis. John Wiley and Sons, Chichester (1998)"},{"key":"5_CR15","volume-title":"Statistical Shape Analysis.","author":"I.L. Dryden","year":"1998","unstructured":"Dryden, I.L., Mardia, K.V.: Statistical Shape Analysis. John Wiley & Son, Chichester (1998)"},{"issue":"2","key":"5_CR16","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1137\/S0895479895290954","volume":"20","author":"A. Edelman","year":"1998","unstructured":"Edelman, A., Arias, T., Smith, S.T.: The geometry of algorithms with orthogonality constraints. SIAM Journal of Matrix Analysis and Applications\u00a020(2), 303\u2013353 (1998)","journal-title":"SIAM Journal of Matrix Analysis and Applications"},{"key":"5_CR17","doi-asserted-by":"crossref","unstructured":"Georghiades, A.S., Kriegman, D.J., Belhumeur, P.N.: Illumination cones for recognition under variable lighting: Faces. In: IEEE International Conference on Computer Vision and Pattern Recognition, pp. 52\u201359 (1998)","DOI":"10.1109\/CVPR.1998.698587"},{"key":"5_CR18","volume-title":"Probabilities on Algebraic Structures","author":"U. Grenander","year":"1963","unstructured":"Grenander, U.: Probabilities on Algebraic Structures. Wiley, Chichester (1963)"},{"key":"5_CR19","volume-title":"General Pattern Theory","author":"U. Grenander","year":"1993","unstructured":"Grenander, U.: General Pattern Theory. Oxford University Press, Oxford (1993)"},{"issue":"4","key":"5_CR20","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1090\/qam\/1668732","volume":"LVI","author":"U. Grenander","year":"1998","unstructured":"Grenander, U., Miller, M.I.: Computational anatomy: An emerging discipline. Quarterly of Applied Mathematics\u00a0LVI(4), 617\u2013694 (1998)","journal-title":"Quarterly of Applied Mathematics"},{"issue":"8","key":"5_CR21","doi-asserted-by":"publisher","first-page":"790","DOI":"10.1109\/34.709572","volume":"20","author":"U. Grenander","year":"1998","unstructured":"Grenander, U., Miller, M.I., Srivastava, A.: Hilbert-Schmidt lower bounds for estimators on matrix Lie groups for ATR. IEEE Transactions on Pattern Analysis and Machine Intelligence\u00a020(8), 790\u2013802 (1998)","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"5_CR22","doi-asserted-by":"crossref","unstructured":"Hartley, R.I., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. (2004)","DOI":"10.1017\/CBO9780511811685"},{"issue":"9","key":"5_CR23","doi-asserted-by":"publisher","first-page":"1163","DOI":"10.1109\/TIP.2004.832865","volume":"13","author":"A. Kale","year":"2004","unstructured":"Kale, A., Sundaresan, A., Rajagopalan, A., Cuntoor, N., Roy Cowdhury, A., Krueger, V., Chellappa, R.: Identification of humans using gait. IEEE Transactions on Image Processing\u00a013(9), 1163\u20131173 (2004)","journal-title":"IEEE Transactions on Image Processing"},{"key":"5_CR24","doi-asserted-by":"publisher","first-page":"509","DOI":"10.1002\/cpa.3160300502","volume":"30","author":"H. Karcher","year":"1977","unstructured":"Karcher, H.: Riemannian center of mass and mollifier smoothing. Communications on Pure and Applied Mathematics\u00a030, 509\u2013541 (1977)","journal-title":"Communications on Pure and Applied Mathematics"},{"key":"5_CR25","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1112\/blms\/16.2.81","volume":"16","author":"D. Kendall","year":"1984","unstructured":"Kendall, D.: Shape manifolds, procrustean metrics and complex projective spaces. Bulletin of London Mathematical society\u00a016, 81\u2013121 (1984)","journal-title":"Bulletin of London Mathematical society"},{"key":"5_CR26","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1112\/blms\/16.2.81","volume":"16","author":"D.G. Kendall","year":"1984","unstructured":"Kendall, D.G.: Shape manifolds, procrustean metrics and complex projective spaces. Bulletin of London Mathematical Society\u00a016, 81\u2013121 (1984)","journal-title":"Bulletin of London Mathematical Society"},{"issue":"3","key":"5_CR27","doi-asserted-by":"publisher","first-page":"372","DOI":"10.1109\/TPAMI.2004.1262333","volume":"26","author":"E. Klassen","year":"2004","unstructured":"Klassen, E., Srivastava, A., Mio, W., Joshi, S.: Analysis of planar shapes using geodesic paths on shape spaces. IEEE Transactions on Pattern Analysis and Machine Intelligence\u00a026(3), 372\u2013383 (2004)","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"issue":"3","key":"5_CR28","doi-asserted-by":"publisher","first-page":"1225","DOI":"10.1214\/aos\/1176349259","volume":"21","author":"H.L. Le","year":"1993","unstructured":"Le, H.L., Kendall, D.G.: The Riemannian structure of Euclidean shape spaces: a novel environment for statistics. Annals of Statistics\u00a021(3), 1225\u20131271 (1993)","journal-title":"Annals of Statistics"},{"issue":"6","key":"5_CR29","doi-asserted-by":"publisher","first-page":"863","DOI":"10.1109\/TPAMI.2006.122","volume":"28","author":"Z. Liu","year":"2006","unstructured":"Liu, Z., Sarkar, S.: Improved gait recognition by gait dynamics normalization. IEEE Transactions on Pattern Analysis and Machine Intelligence\u00a028(6), 863\u2013876 (2006)","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"5_CR30","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1007\/978-3-540-88688-4_4","volume-title":"Computer Vision \u2013 ECCV 2008","author":"Y.M. Lui","year":"2008","unstructured":"Lui, Y.M., Beveridge, J.R.: Grassmann registration manifolds for face recognition. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part II. LNCS, vol.\u00a05303, pp. 44\u201357. Springer, Heidelberg (2008)"},{"issue":"1\/2","key":"5_CR31","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1023\/A:1011161132514","volume":"41","author":"M.I. Miller","year":"2001","unstructured":"Miller, M.I., Younes, L.: Group actions, homeomorphisms, and matching: A general framework. International Journal on Computer Vision\u00a041(1\/2), 61\u201384 (2001)","journal-title":"International Journal on Computer Vision"},{"issue":"3","key":"5_CR32","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1007\/s11263-006-9968-0","volume":"73","author":"W. Mio","year":"2007","unstructured":"Mio, W., Srivastava, A., Joshi, S.: On shape of plane elastic curves. International Journal on Computer Vision\u00a073(3), 307\u2013324 (2007)","journal-title":"International Journal on Computer Vision"},{"issue":"1","key":"5_CR33","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1023\/A:1008270110193","volume":"9","author":"X. Pennec","year":"1998","unstructured":"Pennec, X., Ayache, N.: Uniform distribution, distance and expectation problems for geometric features processing. Journal of Mathematical Imaging and Vision\u00a09(1), 49\u201367 (1998)","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"5_CR34","volume-title":"Fundamentals of speech recognition.","author":"L. Rabiner","year":"1993","unstructured":"Rabiner, L., Juang, B.: Fundamentals of speech recognition. Prentice-Hall, Englewood Cliffs (1993)"},{"key":"5_CR35","doi-asserted-by":"crossref","unstructured":"Sarkar, S., Phillips, P., Liu, Z., Vega, I., Grother, P., Bowyer, K.: The humanid gait challenge problem: data sets, performance, and analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence, 162\u2013177 (2005)","DOI":"10.1109\/TPAMI.2005.39"},{"key":"5_CR36","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4032-7","volume-title":"The Statistical Theory of Shape","author":"C.G. Small","year":"1996","unstructured":"Small, C.G.: The Statistical Theory of Shape. Springer, Heidelberg (1996)"},{"key":"5_CR37","doi-asserted-by":"crossref","unstructured":"Soatto, S., Doretto, G., Wu, Y.N.: Dynamic textures. In: IEEE International Conference on Computer Vision, vol.\u00a02, pp. 439\u2013446 (2001)","DOI":"10.1109\/ICCV.2001.937658"},{"key":"5_CR38","unstructured":"Spivak, M.: A Comprehensive Introduction to Differential Geometry, vol.\u00a01. Publish or Perish, Inc., Houston (1970)"},{"issue":"4","key":"5_CR39","doi-asserted-by":"publisher","first-page":"590","DOI":"10.1109\/TPAMI.2005.86","volume":"27","author":"A. Srivastava","year":"2005","unstructured":"Srivastava, A., Joshi, S., Mio, W., Liu, X.: Statistical shape analysis: Clustering, learning and testing. IEEE Transactions on Pattern Analysis and Machine Intelligence\u00a027(4), 590\u2013602 (2005)","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"issue":"2","key":"5_CR40","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1109\/78.978385","volume":"50","author":"A. Srivastava","year":"2001","unstructured":"Srivastava, A., Klassen, E.: Monte Carlo extrinsic estimators for manifold-valued parameters. IEEE Trans. on Signal Processing\u00a050(2), 299\u2013308 (2001)","journal-title":"IEEE Trans. on Signal Processing"},{"issue":"1","key":"5_CR41","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1239\/aap\/1077134463","volume":"36","author":"A. Srivastava","year":"2004","unstructured":"Srivastava, A., Klassen, E.: Bayesian, geometric subspace tracking. Journal for Advances in Applied Probability\u00a036(1), 43\u201356 (2004)","journal-title":"Journal for Advances in Applied Probability"},{"issue":"1","key":"5_CR42","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11263-008-0195-8","volume":"84","author":"R. Subbarao","year":"2009","unstructured":"Subbarao, R., Meer, P.: Nonlinear mean shift over riemannian manifolds. International Journal on Computer Vision\u00a084(1), 1\u201320 (2009)","journal-title":"International Journal on Computer Vision"},{"key":"5_CR43","doi-asserted-by":"crossref","unstructured":"Turaga, P., Chellappa, R.: Locally time-invariant models of human activities using trajectories on the grassmannian. In: IEEE International Conference on Computer Vision and Pattern Recognition, pp. 2435\u20132441 (2009)","DOI":"10.1109\/CVPR.2009.5206710"},{"issue":"3","key":"5_CR44","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1016\/j.cviu.2008.08.009","volume":"113","author":"P. Turaga","year":"2009","unstructured":"Turaga, P., Veeraraghavan, A., Chellappa, R.: Unsupervised view and rate invariant clustering of video sequences. Computer Vision and Image Understanding\u00a0113(3), 353\u2013371 (2009)","journal-title":"Computer Vision and Image Understanding"},{"key":"5_CR45","doi-asserted-by":"crossref","unstructured":"Turaga, P.K., Veeraraghavan, A., Chellappa, R.: Statistical analysis on Stiefel and Grassmann manifolds with applications in computer vision. In: IEEE International Conference on Computer Vision and Pattern Recognition (2008)","DOI":"10.1109\/CVPR.2008.4587733"},{"key":"5_CR46","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"589","DOI":"10.1007\/11744047_45","volume-title":"Computer Vision \u2013 ECCV 2006","author":"O. Tuzel","year":"2006","unstructured":"Tuzel, O., Porikli, F., Meer, P.: Region covariance: A fast descriptor for detection and classification. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol.\u00a03952, pp. 589\u2013600. Springer, Heidelberg (2006)"},{"issue":"10","key":"5_CR47","doi-asserted-by":"publisher","first-page":"1713","DOI":"10.1109\/TPAMI.2008.75","volume":"30","author":"O. Tuzel","year":"2008","unstructured":"Tuzel, O., Porikli, F., Meer, P.: Pedestrian detection via classification on Riemannian manifolds. IEEE Transactions on Pattern Analysis and Machine Intelligence\u00a030(10), 1713\u20131727 (2008)","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"issue":"12","key":"5_CR48","doi-asserted-by":"publisher","first-page":"1896","DOI":"10.1109\/TPAMI.2005.246","volume":"27","author":"A. Veeraraghavan","year":"2005","unstructured":"Veeraraghavan, A., Roy-Chowdhury, A., Chellappa, R.: Matching shape sequences in video with an application to human movement analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence\u00a027(12), 1896\u20131909 (2005)","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"issue":"6","key":"5_CR49","doi-asserted-by":"publisher","first-page":"1326","DOI":"10.1109\/TIP.2009.2017143","volume":"18","author":"A. Veeraraghavan","year":"2009","unstructured":"Veeraraghavan, A., Srivastava, A., Roy Chowdhury, A.K., Chellappa, R.: Rate-invariant recognition of humans and their activities. IEEE Transactions on Image Processing\u00a018(6), 1326\u20131339 (2009)","journal-title":"IEEE Transactions on Image Processing"},{"issue":"2","key":"5_CR50","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1016\/j.cviu.2006.07.013","volume":"104","author":"D. Weinland","year":"2006","unstructured":"Weinland, D., Ronfard, R., Boyer, E.: Free viewpoint action recognition using motion history volumes. Computer Vision and Image Understanding\u00a0104(2), 249\u2013257 (2006)","journal-title":"Computer Vision and Image Understanding"},{"key":"5_CR51","doi-asserted-by":"crossref","unstructured":"Zhong, H., Shi, J., Visontai, M.: Detecting unusual activity in video. In: IEEE International Conference on Computer Vision and Pattern Recognition, pp. 819\u2013826 (2004)","DOI":"10.1109\/CVPR.2004.1315249"}],"container-title":["Studies in Computational Intelligence","Video Search and Mining"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-12900-1_5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,24]],"date-time":"2020-11-24T02:58:11Z","timestamp":1606186691000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-12900-1_5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010]]},"ISBN":["9783642128998","9783642129001"],"references-count":51,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-12900-1_5","relation":{},"ISSN":["1860-949X","1860-9503"],"issn-type":[{"value":"1860-949X","type":"print"},{"value":"1860-9503","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010]]}}}