{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T19:57:48Z","timestamp":1780084668924,"version":"3.54.0"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2018,4,7]],"date-time":"2018-04-07T00:00:00Z","timestamp":1523059200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"Manet marie curie eu project","award":["607643"],"award-info":[{"award-number":["607643"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Math Imaging Vis"],"published-print":{"date-parts":[[2018,7]]},"DOI":"10.1007\/s10851-018-0803-3","type":"journal-article","created":{"date-parts":[[2018,4,7]],"date-time":"2018-04-07T15:01:42Z","timestamp":1523113302000},"page":"900-912","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["A Geometric Model of Multi-scale Orientation Preference Maps via Gabor Functions"],"prefix":"10.1007","volume":"60","author":[{"given":"Emre","family":"Baspinar","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Giovanna","family":"Citti","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alessandro","family":"Sarti","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2018,4,7]]},"reference":[{"issue":"3","key":"803_CR1","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1007\/s10851-013-0482-z","volume":"49","author":"D Barbieri","year":"2014","unstructured":"Barbieri, D., Citti, G., Cocci, G., Sarti, A.: A cortical-inspired geometry for contour perception and motion integration. J. Math. Imaging Vis. 49(3), 511\u2013529 (2014)","journal-title":"J. Math. Imaging Vis."},{"key":"803_CR2","unstructured":"Barbieri, D., Citti, G., Sanguinetti, G., Sarti, A.: Coherent states of the euclidean group and activation regions of primary visual cortex. arXiv preprint \n                    arXiv:1111.0669\n                    \n                   (2011)"},{"issue":"5","key":"803_CR3","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1016\/j.jphysparis.2012.03.001","volume":"106","author":"D Barbieri","year":"2012","unstructured":"Barbieri, D., Citti, G., Sanguinetti, G., Sarti, A.: An uncertainty principle underlying the functional architecture of v1. J. Physiol. Paris 106(5), 183\u2013193 (2012)","journal-title":"J. Physiol. Paris"},{"issue":"1","key":"803_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1002\/cpa.3160200102","volume":"20","author":"V Bargmann","year":"1967","unstructured":"Bargmann, V.: On a hilbert space of analytie functions and an associated integral transform. part II. A family of related function spaces application to distribution theory. Commun. Pure Appl. Math. 20(1), 1\u2013101 (1967)","journal-title":"Commun. Pure Appl. Math."},{"key":"803_CR5","first-page":"13","volume":"2","author":"JA Bednar","year":"2004","unstructured":"Bednar, J.A., Miikkulainen, R.: Constructing visual function through prenatal and postnatal learning. Neuroconstructivism Perspect. Prospects 2, 13\u201337 (2004)","journal-title":"Neuroconstructivism Perspect. Prospects"},{"issue":"6","key":"803_CR6","doi-asserted-by":"publisher","first-page":"2112","DOI":"10.1523\/JNEUROSCI.17-06-02112.1997","volume":"17","author":"WH Bosking","year":"1997","unstructured":"Bosking, W.H., Zhang, Y., Schofield, B., Fitzpatrick, D.: Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex. J. Neurosci. 17(6), 2112\u20132127 (1997)","journal-title":"J. Neurosci."},{"issue":"2","key":"803_CR7","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1016\/j.jphysparis.2003.09.017","volume":"97","author":"PC Bressloff","year":"2003","unstructured":"Bressloff, P.C., Cowan, J.D.: The functional geometry of local and horizontal connections in a model of v1. J. Physiol. Paris 97(2), 221\u2013236 (2003)","journal-title":"J. Physiol. Paris"},{"issue":"1438","key":"803_CR8","doi-asserted-by":"publisher","first-page":"1643","DOI":"10.1098\/rstb.2002.1109","volume":"358","author":"PC Bressloff","year":"2003","unstructured":"Bressloff, P.C., Cowan, J.D.: A spherical model for orientation and spatial-frequency tuning in a cortical hypercolumn. Philos. Trans. R. Soc. Lond. B Biol. Sci. 358(1438), 1643\u20131667 (2003)","journal-title":"Philos. Trans. R. Soc. Lond. B Biol. Sci."},{"issue":"1407","key":"803_CR9","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1098\/rstb.2000.0769","volume":"356","author":"PC Bressloff","year":"2001","unstructured":"Bressloff, P.C., Cowan, J.D., Golubitsky, M., Thomas, P.J., Wiener, M.C.: Geometric visual hallucinations, euclidean symmetry and the functional architecture of striate cortex. Philos. Trans. R. Soc. B Biol. Sci. 356(1407), 299\u2013330 (2001)","journal-title":"Philos. Trans. R. Soc. B Biol. Sci."},{"issue":"5","key":"803_CR10","doi-asserted-by":"publisher","first-page":"797","DOI":"10.1016\/j.neuron.2005.09.015","volume":"48","author":"J Cang","year":"2005","unstructured":"Cang, J., Renter\u00eda, R.C., Kaneko, M., Liu, X., Copenhagen, D.R., Stryker, M.P.: Development of precise maps in visual cortex requires patterned spontaneous activity in the retina. Neuron 48(5), 797\u2013809 (2005)","journal-title":"Neuron"},{"issue":"3","key":"803_CR11","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1007\/s10851-005-3630-2","volume":"24","author":"G Citti","year":"2006","unstructured":"Citti, G., Sarti, A.: A cortical based model of perceptual completion in the roto-translation space. J. Math. Imaging Vis. 24(3), 307\u2013326 (2006)","journal-title":"J. Math. Imaging Vis."},{"key":"803_CR12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-34444-2","volume-title":"Neuromathematics of Vision","author":"G Citti","year":"2014","unstructured":"Citti, G., Sarti, A.: Neuromathematics of Vision. Springer, Berlin (2014)"},{"issue":"6","key":"803_CR13","doi-asserted-by":"publisher","first-page":"1252","DOI":"10.1162\/NECO_a_00738","volume":"27","author":"G Cocci","year":"2015","unstructured":"Cocci, G., Barbieri, D., Citti, G., Sarti, A.: Cortical spatiotemporal dimensionality reduction for visual grouping. Neural Comput. 27(6), 1252\u20131293 (2015)","journal-title":"Neural Comput."},{"issue":"6534","key":"803_CR14","doi-asserted-by":"publisher","first-page":"780","DOI":"10.1038\/375780a0","volume":"375","author":"A Das","year":"1995","unstructured":"Das, A., Gilbert, C.D.: Long-range horizontal connections and their role in cortical reorganization revealed by optical recording of cat primary visual cortex. Nature 375(6534), 780 (1995)","journal-title":"Nature"},{"issue":"7","key":"803_CR15","doi-asserted-by":"publisher","first-page":"1160","DOI":"10.1364\/JOSAA.2.001160","volume":"2","author":"JG Daugman","year":"1985","unstructured":"Daugman, J.G.: Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters. JOSA A 2(7), 1160\u20131169 (1985)","journal-title":"JOSA A"},{"issue":"1253","key":"803_CR16","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1098\/rspb.1986.0060","volume":"228","author":"D Field","year":"1986","unstructured":"Field, D., Tolhurst, D.: The structure and symmetry of simple-cell receptive-field profiles in the cat\u2019s visual cortex. Proc. R. Soc. Lond. B Biol. Sci. 228(1253), 379\u2013400 (1986)","journal-title":"Proc. R. Soc. Lond. B Biol. Sci."},{"issue":"2","key":"803_CR17","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1016\/0042-6989(93)90156-Q","volume":"33","author":"DJ Field","year":"1993","unstructured":"Field, D.J., Hayes, A., Hess, R.F.: Contour integration by the human visual system: evidence for a local association field. Vis. Res. 33(2), 173\u2013193 (1993)","journal-title":"Vis. Res."},{"key":"803_CR18","volume-title":"Harmonic Analysis in Phase Space, (AM-122)","author":"GB Folland","year":"2016","unstructured":"Folland, G.B.: Harmonic Analysis in Phase Space, (AM-122), vol. 122. Princeton University Press, Princeton (2016)"},{"issue":"26","key":"803_CR19","first-page":"429","volume":"93","author":"D Gabor","year":"1946","unstructured":"Gabor, D.: Theory of communication. part 1: the analysis of information. J. Inst. Electr. Eng. Part III Radio Commun. Eng. 93(26), 429\u2013441 (1946)","journal-title":"J. Inst. Electr. Eng. Part III Radio Commun. Eng."},{"issue":"1","key":"803_CR20","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1007\/BF02392081","volume":"119","author":"L H\u00f6rmander","year":"1967","unstructured":"H\u00f6rmander, L.: Hypoelliptic second order differential equations. Acta Mathematica 119(1), 147\u2013171 (1967)","journal-title":"Acta Mathematica"},{"issue":"10","key":"803_CR21","doi-asserted-by":"publisher","first-page":"1291","DOI":"10.1016\/j.neucom.2005.12.094","volume":"69","author":"S Jegelka","year":"2006","unstructured":"Jegelka, S., Bednar, J.A., Miikkulainen, R.: Prenatal development of ocular dominance and orientation maps in a self-organizing model of v1. Neurocomputing 69(10), 1291\u20131296 (2006)","journal-title":"Neurocomputing"},{"issue":"5","key":"803_CR22","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1007\/BF00336961","volume":"50","author":"JJ Koenderink","year":"1984","unstructured":"Koenderink, J.J.: The structure of images. Biol. Cybern. 50(5), 363\u2013370 (1984)","journal-title":"Biol. Cybern."},{"issue":"6","key":"803_CR23","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1007\/BF00318371","volume":"55","author":"JJ Koenderink","year":"1987","unstructured":"Koenderink, J.J., van Doorn, A.J.: Representation of local geometry in the visual system. Biol. Cybern. 55(6), 367\u2013375 (1987)","journal-title":"Biol. Cybern."},{"issue":"2","key":"803_CR24","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1023\/A:1008045108935","volume":"30","author":"T Lindeberg","year":"1998","unstructured":"Lindeberg, T.: Feature detection with automatic scale selection. Int. J. Comput. Vis. 30(2), 79\u2013116 (1998)","journal-title":"Int. J. Comput. Vis."},{"issue":"1","key":"803_CR25","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1007\/s10851-010-0242-2","volume":"40","author":"T Lindeberg","year":"2011","unstructured":"Lindeberg, T.: Generalized gaussian scale-space axiomatics comprising linear scale-space, affine scale-space and spatio-temporal scale-space. J. Math. Imaging Vis. 40(1), 36\u201381 (2011)","journal-title":"J. Math. Imaging Vis."},{"issue":"6","key":"803_CR26","doi-asserted-by":"publisher","first-page":"589","DOI":"10.1007\/s00422-013-0569-z","volume":"107","author":"T Lindeberg","year":"2013","unstructured":"Lindeberg, T.: A computational theory of visual receptive fields. Biol. Cybern. 107(6), 589\u2013635 (2013)","journal-title":"Biol. Cybern."},{"issue":"2","key":"803_CR27","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1016\/j.jphysparis.2003.10.010","volume":"97","author":"J Petitot","year":"2003","unstructured":"Petitot, J.: The neurogeometry of pinwheels as a sub-riemannian contact structure. J. Physiol. Paris 97(2), 265\u2013309 (2003)","journal-title":"J. Physiol. Paris"},{"key":"803_CR28","volume-title":"Neurog\u00e9om\u00e9trie de la vision. Modeles math\u00e9matiques et physiques des architectures fonctionelles","author":"J Petitot","year":"2008","unstructured":"Petitot, J.: Neurog\u00e9om\u00e9trie de la vision. Modeles math\u00e9matiques et physiques des architectures fonctionelles. \u00c9d. \u00c9cole Polytech, Paris (2008)"},{"key":"803_CR29","first-page":"5","volume":"145","author":"J Petitot","year":"1999","unstructured":"Petitot, J., Tondut, Y.: Vers une neurog\u00e9om\u00e9trie. fibrations corticales, structures de contact et contours subjectifs modaux. Math\u00e9matiques informatique et sciences humaines 145, 5\u2013102 (1999)","journal-title":"Math\u00e9matiques informatique et sciences humaines"},{"issue":"14","key":"803_CR30","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1167\/10.14.37","volume":"10","author":"G Sanguinetti","year":"2010","unstructured":"Sanguinetti, G., Citti, G., Sarti, A.: A model of natural image edge co-occurrence in the rototranslation group. J. Vis. 10(14), 37\u201337 (2010)","journal-title":"J. Vis."},{"issue":"2","key":"803_CR31","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1007\/s10827-014-0540-6","volume":"38","author":"A Sarti","year":"2015","unstructured":"Sarti, A., Citti, G.: The constitution of visual perceptual units in the functional architecture of v1. J. Comput. Neurosci. 38(2), 285\u2013300 (2015)","journal-title":"J. Comput. Neurosci."},{"issue":"1","key":"803_CR32","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/s00422-007-0194-9","volume":"98","author":"A Sarti","year":"2008","unstructured":"Sarti, A., Citti, G., Petitot, J.: The symplectic structure of the primary visual cortex. Biol. Cybern. 98(1), 33\u201348 (2008)","journal-title":"Biol. Cybern."},{"issue":"1","key":"803_CR33","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/j.jphysparis.2009.05.004","volume":"103","author":"A Sarti","year":"2009","unstructured":"Sarti, A., Citti, G., Petitot, J.: Functional geometry of the horizontal connectivity in the primary visual cortex. J. Physiol. Paris 103(1), 37\u201345 (2009)","journal-title":"J. Physiol. Paris"},{"key":"803_CR34","doi-asserted-by":"crossref","unstructured":"Sarti, A., Piotrowski, D.: Individuation and semiogenesis: an interplay between geometric harmonics and structural morphodynamics. In: Sarti, A., Montanari, F. & Galofaro, F. (eds.) Morphogenesis and Individuation, pp. 49\u201373. Springer (2015)","DOI":"10.1007\/978-3-319-05101-7_3"},{"issue":"1","key":"803_CR35","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1016\/j.acha.2014.09.001","volume":"39","author":"U Sharma","year":"2015","unstructured":"Sharma, U., Duits, R.: Left-invariant evolutions of wavelet transforms on the similitude group. Appl. Comput. Harmon. Anal. 39(1), 110\u2013137 (2015)","journal-title":"Appl. Comput. Harmon. Anal."},{"issue":"3","key":"803_CR36","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1016\/S0896-6273(02)00577-9","volume":"33","author":"D Stellwagen","year":"2002","unstructured":"Stellwagen, D., Shatz, C.: An instructive role for retinal waves in the development of retinogeniculate connectivity. Neuron 33(3), 357\u2013367 (2002)","journal-title":"Neuron"},{"key":"803_CR37","volume-title":"Unitary Representations and Harmonic Analysis: An Introduction","author":"M Sugiura","year":"1990","unstructured":"Sugiura, M.: Unitary Representations and Harmonic Analysis: An Introduction, vol. 44. Elsevier, Amsterdam (1990)"},{"issue":"8","key":"803_CR38","doi-asserted-by":"publisher","first-page":"1363","DOI":"10.1016\/j.neunet.2004.06.014","volume":"17","author":"S Tanaka","year":"2004","unstructured":"Tanaka, S., Miyashita, M., Ribot, J.: Roles of visual experience and intrinsic mechanism in the activity-dependent self-organization of orientation maps: theory and experiment. Neural Netw. 17(8), 1363\u20131375 (2004)","journal-title":"Neural Netw."},{"key":"803_CR39","unstructured":"Wertheimer, M.: Laws of organization in perceptual forms. In: A Source Book of Gestalt Psychology. Harcourt Brace, New York (1923)"}],"container-title":["Journal of Mathematical Imaging and Vision"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10851-018-0803-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-018-0803-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-018-0803-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,7]],"date-time":"2019-04-07T04:16:25Z","timestamp":1554610585000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10851-018-0803-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,4,7]]},"references-count":39,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2018,7]]}},"alternative-id":["803"],"URL":"https:\/\/doi.org\/10.1007\/s10851-018-0803-3","relation":{},"ISSN":["0924-9907","1573-7683"],"issn-type":[{"value":"0924-9907","type":"print"},{"value":"1573-7683","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,4,7]]},"assertion":[{"value":"7 July 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 February 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 April 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}