{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T00:55:43Z","timestamp":1780880143135,"version":"3.54.1"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2006,7,23]],"date-time":"2006-07-23T00:00:00Z","timestamp":1153612800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int J Comput Vision"],"published-print":{"date-parts":[[2007,4]]},"DOI":"10.1007\/s11263-006-8894-5","type":"journal-article","created":{"date-parts":[[2006,7,22]],"date-time":"2006-07-22T21:43:37Z","timestamp":1153604617000},"page":"79-102","source":"Crossref","is-referenced-by-count":87,"title":["Image Analysis and Reconstruction using a Wavelet Transform Constructed from a Reducible Representation of the Euclidean Motion Group"],"prefix":"10.1007","volume":"72","author":[{"given":"Remco","family":"Duits","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael","family":"Felsberg","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"G\u00f6sta","family":"Granlund","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bart ter Haar","family":"Romeny","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2006,7,23]]},"reference":[{"key":"8894_CR1","volume-title":"Coherent States, Wavelets and Their Generalizations","author":"S.T. Ali","year":"1999","unstructured":"Ali S.T., Antoine J.P. and Gazeau J.P. 1999. Coherent States, Wavelets and Their Generalizations. Springer Verlag, New York, Berlin, Heidelberg."},{"key":"8894_CR2","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1006\/acha.1998.0255","volume":"6","author":"J.P. Antoine","year":"1999","unstructured":"Antoine J.P. 1999. Directional wavelets revisited: Cauchy wavelets and symmetry detection in patterns. Applied and Computational Harmonic Analysis, 6:314\u2013345.","journal-title":"Applied and Computational Harmonic Analysis"},{"key":"8894_CR3","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1090\/S0002-9947-1950-0051437-7","volume":"68","author":"N. Aronszajn","year":"1950","unstructured":"Aronszajn, N. 1950. Theory of reproducing kernels. Trans. A.M.S., 68:337\u2013404.","journal-title":"Trans. A.M.S."},{"key":"8894_CR4","unstructured":"August J. and Zucker S.W. 2003. The curve indicator random field and markov processes. IEEE-PAMI, Pattern Recognition and Machine Intelligence, 25."},{"issue":"6","key":"8894_CR5","doi-asserted-by":"crossref","first-page":"2112","DOI":"10.1523\/JNEUROSCI.17-06-02112.1997","volume":"17","author":"W.H. Bosking","year":"1997","unstructured":"Bosking W.H., Zhang Y., Schofield B. and Fitzpatrick D. 1997. Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex. The Journal of Neuroscience, 17(6):2112\u20132127.","journal-title":"The Journal of Neuroscience"},{"key":"8894_CR6","unstructured":"Duits M. 2004. A functional Hilbert space approach to frame transforms and wavelet transforms. Master thesis in Applied Analysis group at the department of Mathematics and Computer Science at the Eindhoven University of Technology."},{"key":"8894_CR7","unstructured":"Duits, M. and Duits, R. 2004. A functional Hilbert space approach to the theory of wavelets. Technical report, TUE, Eindhoven, RANA\/CASA Report RANA-7-2004, available on the web: ftp:\/\/ftp.win.tue.nl\/pub\/rana\/rana04-07.pdf Department of Mathematics Eindhoven University of Technology."},{"key":"8894_CR8","unstructured":"Duits, R. 2005. Perceptual Organization in Image Analysis. PhD thesis, Eindhoven University of Technology, Department of Biomedical Engineering, The Netherlands. A digital version is available on the web: URL: http:\/\/www.bmi2.bmt.tue.nl\/Image-Analysis\/People\/RDuits\/THESISRDUITS.pdf ."},{"key":"8894_CR9","unstructured":"Duits, R. and van Almsick, M. 2005. The explicit solutions of the left invariant evolution equations on the Euclidean motion group. Eindhoven University of Technology, Eindhoven, 5\u201343. Available on the web http:\/\/yp.bmt.tue.nl\/pdfs\/6321.pdf . An improved version of which is recently submitted to the Quarterly of Applied Mathematics (journal of American Mathetical Society.)"},{"key":"8894_CR10","unstructured":"Duits, R., Duits, M. and van Almsick, M. 2004. Invertible orientation scores as an application of generalized wavelet theory. Technical report, TUE, Eindhoven. Technical Report 04-04, Biomedical Image and Analysis, Department of Biomedical Engineering, Eindhoven University of Technology."},{"key":"8894_CR11","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1023\/B:JMIV.0000024043.96722.aa","volume":"20","author":"R. Duits","year":"2004","unstructured":"Duits, R., Florack, L.M.J., de Graaf, J. and ter Haar Romeny, B. 2004. On the axioms of scale space theory. Journal of Mathematical Imaging and Vision, 20:267\u2013298.","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"8894_CR12","unstructured":"Duits, R., van Almsick, M., Duits, M., Franken, E. and Florack, L.M.J. 2004. Image processing via shift-twist invariant operations on orientation bundle functions. In Niemann Zhuralev et al. Geppener, Gurevich, editor, 7th International Conference on Pattern Recognition and Image Analysis: New Information Technologies, 193\u2013196, St. Petersburg. Extended version is to appear in special issue of the International Journal for Pattern Recognition and Image Analysis MAIK."},{"key":"8894_CR13","doi-asserted-by":"crossref","unstructured":"Dungey, N., ter Elst, A.F.M. and Robinson, D.W. 2003. Analysis on Lie groups with polynomial growth, volume 214. Birkhauser-Progress in Mathematics, Boston.","DOI":"10.1007\/978-1-4612-2062-6"},{"key":"8894_CR14","unstructured":"Eijndhoven, S.J.L. and de Graaf, J. 1982. Some results on hankel invariant distribution spaces. Proceedings of the Koninklijke Akademie van Wetenschapppen, Series A, 86(1):77\u201387."},{"key":"8894_CR15","volume-title":"Deux cours d\u2019analyse harmonique","author":"J. Faraut","year":"1984","unstructured":"Faraut, J. and Harzallah, K. 1984. Deux cours d\u2019analyse harmonique. Birkhaeuser, Tunis."},{"key":"8894_CR16","unstructured":"Felsberg, M., Forss\u00e9n, P.-E. and Scharr, H. 2004. Efficient robust smoothing of low-level signal features. Technical Report LiTH-ISY-R-2619, SE-581 83 Linkoping, Sweden."},{"issue":"2","key":"8894_CR17","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1109\/TPAMI.2006.29","volume":"28","author":"M. Felsberg","year":"2006","unstructured":"Felsberg, M., Forss\u00e9n, P.-E. and Scharr, H. 2006. Channel smoothing: Efficient robust smoothing of low-level signal features. IEEE Transactions on Pattern Analysis and Machine Intelligence, 28(2):209\u2013222.","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"8894_CR18","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-015-8845-4","volume-title":"Image Structure","author":"L.M.J. Florack","year":"1997","unstructured":"Florack, L.M.J., 1997. Image Structure. Kluwer Academic Publishers, Dordrecht, The Netherlands."},{"key":"8894_CR19","doi-asserted-by":"crossref","unstructured":"Forss\u00e9n, P.-E. and Granlund, G. H. 2000. Sparse feature maps in a scale hierarchy. In G. Sommer and Y.Y. Zeevi, editors, Proc. Int. Workshop on Algebraic Frames for the Perception-Action Cycle, volume 1888 of Lecture Notes in Computer Science, Kiel, Germany, Springer, Heidelberg.","DOI":"10.1007\/10722492_13"},{"key":"8894_CR20","unstructured":"Forss\u00e9n, P.E. 2004. Low and Medium Level Vision using Channel Representations. PhD thesis, Linkoping University, Dept. EE, Linkoping, Sweden."},{"key":"8894_CR21","unstructured":"van Ginkel, M. 2002. Image Analysis using Orientation Space based on Steerable Filters. PhD thesis, Delft University of Technology, Delft, Netherlands."},{"key":"8894_CR22","doi-asserted-by":"crossref","unstructured":"Granlund, G.H. 2000. An associative perception-action structure using a localized space variant information representation. In Proceedings of Algebraic Frames for the Perception-Action Cycle (AFPAC), Kiel, Germany, Also as Technical Report LiTH-ISY-R-2255.","DOI":"10.1007\/10722492_3"},{"key":"8894_CR23","doi-asserted-by":"crossref","first-page":"2473","DOI":"10.1063\/1.526761","volume":"26","author":"A. Grossmann","year":"1985","unstructured":"Grossmann, A., Morlet, J. and Paul, T. 1985. Integral transforms associated to square integrable representations. J.Math.Phys., 26:2473\u20132479.","journal-title":"J.Math.Phys."},{"issue":"3","key":"8894_CR24","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1063\/1.529402","volume":"32","author":"C.J. Isham","year":"1991","unstructured":"Isham, C.J. and Klauder J.R. 1991. Coherent states for n-dimensional euclidean groups e(n) and their application. Journal of Mathematical Physics, 32(3):607\u2013620.","journal-title":"Journal of Mathematical Physics"},{"issue":"2\/3","key":"8894_CR25","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1023\/A:1008013815039","volume":"31","author":"S.N. Kalitzin","year":"1999","unstructured":"Kalitzin, S.N., ter Haar Romeny, B.M. and Viergever, M.A. 1999. Invertible apertured orientation filters in image analysis. International Journal of Computer Vision, 31(2\/3):145\u2013158.","journal-title":"International Journal of Computer Vision"},{"issue":"10","key":"8894_CR26","doi-asserted-by":"crossref","first-page":"959","DOI":"10.1109\/34.541406","volume":"18","author":"T.S. Lee","year":"1996","unstructured":"Lee T.S., 1996. Image representation using 2d gabor wavelets. IEEE-Transactions on Pattern Analysis and Machine Inteligence, 18(10):959\u2013971.","journal-title":"IEEE-Transactions on Pattern Analysis and Machine Inteligence"},{"key":"8894_CR27","volume-title":"Wavelets, Theory and Applications","author":"A.K. Louis","year":"1997","unstructured":"Louis, A.K., Maass, P. and Rieder, A. 1997. Wavelets, Theory and Applications. Wiley, New York."},{"key":"8894_CR28","unstructured":"Martens, F.J.L. 2004. Spaces of analytic functions on inductive\/projective limits of Hilbert Spaces. PhD thesis, University of Technology Eindhoven, Department of Mathematics and Computing Science, Eindhoven, The Netherlands, 1988. This PHD thesis is available on the webpages of the Technische Universiteit Eindhoven. Webpage in: http:\/\/alexandria.tue.nl\/extra3\/proefschrift\/PRF6A\/8810117.pdf ."},{"key":"8894_CR29","doi-asserted-by":"crossref","unstructured":"Mumford, D. 1994. Elastica and computer vision. Algebraic Geometry and Its Applications. Springer-Verlag, 491\u2013506.","DOI":"10.1007\/978-1-4612-2628-4_31"},{"key":"8894_CR30","unstructured":"van der Put, R.W. 2005. Methods for 3d orientation analysis and their application to the study of arterial remodelling. Master\u2019s thesis, Department of Biomedical Engineering Eindhoven University of Technology, Technical Report BMIA-0502."},{"key":"8894_CR31","unstructured":"Sugiura, M. 1990. Unitary representations and harmonic analysis. North-Holland Mathematical Library, 44., Amsterdam, Kodansha, Tokyo, second edition."},{"key":"8894_CR32","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1007\/s004220050282","volume":"75","author":"K.K. Thornber","year":"1996","unstructured":"Thornber, K.K. and Williams, L.R. 1996. Analytic solution of stochastic completion fields. Biological Cybernetics, 75:141\u2013 151.","journal-title":"Biological Cybernetics"},{"key":"8894_CR33","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1126\/science.2165630","volume":"249","author":"D.Y. Ts\u20190","year":"1990","unstructured":"Ts\u20190, D.Y., Frostig, R.D., Lieke, E.E. and Grinvald, A. 1990. Functional organization of primate visual cortex revealed by high resolution optical imaging. Science, 249:417\u201320.","journal-title":"Science"},{"key":"8894_CR34","doi-asserted-by":"crossref","unstructured":"Twareque Ali, S. 1998. A general theorem on square-integrability: Vector coherent states. Journal of Mathematical Physics, 39.","DOI":"10.1063\/1.532478"},{"key":"8894_CR35","doi-asserted-by":"crossref","unstructured":"van Almsick, M.A., Duits, R., Franken E. and ter Haar Romeny, B.M. 2005. From stochastic completion fields to tensor voting. In Proceedings DSSCC-workshop on Deep Structure Singularities and Computer Vision, Maastricht the Netherlands, Springer-Verlag.","DOI":"10.1007\/11577812_11"},{"key":"8894_CR36","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1007\/s00422-002-0370-x","volume":"88","author":"L.R. Williams","year":"2003","unstructured":"Williams, L.R. and Zweck, J.W. 2003. A rotation and translation invariant saliency network. Biological Cybernetics, 88:2\u201310.","journal-title":"Biological Cybernetics"}],"container-title":["International Journal of Computer Vision"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11263-006-8894-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11263-006-8894-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11263-006-8894-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T08:16:36Z","timestamp":1559376996000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11263-006-8894-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,7,23]]},"references-count":36,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2007,4]]}},"alternative-id":["8894"],"URL":"https:\/\/doi.org\/10.1007\/s11263-006-8894-5","relation":{},"ISSN":["0920-5691","1573-1405"],"issn-type":[{"value":"0920-5691","type":"print"},{"value":"1573-1405","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,7,23]]}}}