{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T16:04:27Z","timestamp":1742918667433,"version":"3.40.3"},"publisher-location":"Cham","reference-count":34,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319707419"},{"type":"electronic","value":"9783319707426"}],"license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017]]},"DOI":"10.1007\/978-3-319-70742-6_4","type":"book-chapter","created":{"date-parts":[[2017,12,30]],"date-time":"2017-12-30T15:59:36Z","timestamp":1514649576000},"page":"37-47","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Modelling of the Poggendorff Illusion via Sub-Riemannian Geodesics in the Roto-Translation Group"],"prefix":"10.1007","author":[{"given":"B.","family":"Franceschiello","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"Mashtakov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G.","family":"Citti","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"Sarti","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,12,31]]},"reference":[{"key":"4_CR1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-06404-7","volume-title":"Control Theory From the Geometric Viewpoint","author":"AA Agrachev","year":"2004","unstructured":"Agrachev, A.A., Sachkov, Y.: Control Theory From the Geometric Viewpoint, vol. 87. Springer-Verlag, Berlin Heidelberg (2004)"},{"key":"4_CR2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-4413-5_15","volume-title":"Perceptual Organization for Artificial Vision Systems","author":"J August","year":"2000","unstructured":"August, J., Zucker, S.W.: The curve indicator random field: curve organization via edge correlation. In: Boyer, K.L., Sarkar, S. (eds.) Perceptual Organization for Artificial Vision Systems. Springer, Heidelberg (2000). https:\/\/doi.org\/10.1007\/978-1-4615-4413-5_15"},{"issue":"4","key":"4_CR3","doi-asserted-by":"publisher","first-page":"2740","DOI":"10.1137\/15M1018460","volume":"8","author":"EJ Bekkers","year":"2015","unstructured":"Bekkers, E.J., Duits, R., Mashtakov, A., Sanguinetti, G.R.: A PDE approach to data-driven sub-riemannian geodesics in SE (2). SIAM J. Imaging Sci. 8(4), 2740\u20132770 (2015)","journal-title":"SIAM J. Imaging Sci."},{"key":"4_CR4","doi-asserted-by":"publisher","first-page":"1263","DOI":"10.1109\/TPAMI.2011.262","volume":"34","author":"G Ben-Yosef","year":"2012","unstructured":"Ben-Yosef, G., Ben-Shahar, O.: A tangent bundle theory for visual curve completion. IEEE Trans. Pattern Anal. Mach. Intell. 34, 1263\u20131280 (2012)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"1","key":"4_CR5","doi-asserted-by":"publisher","first-page":"212","DOI":"10.1137\/15M1013572","volume":"9","author":"G Citti","year":"2016","unstructured":"Citti, G., Franceschiello, B., Sanguinetti, G., Sarti, A.: Sub-riemannian mean curvature flow for image processing. SIAM J. Imaging Sci. 9(1), 212\u2013237 (2016)","journal-title":"SIAM J. Imaging Sci."},{"issue":"3","key":"4_CR6","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."},{"issue":"1","key":"4_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1090\/S0273-0979-1992-00266-5","volume":"27","author":"MG Crandall","year":"1992","unstructured":"Crandall, M.G., Ishii, H., Lions, P.L.: User\u2019s guide to viscosity solutions of second order partial differential equations. Bull. AMS 27(1), 1\u201367 (1992)","journal-title":"Bull. AMS"},{"issue":"1","key":"4_CR8","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1090\/S0002-9947-1983-0690039-8","volume":"277","author":"MG Crandall","year":"1983","unstructured":"Crandall, M.G., Lions, P.L.: Viscosity solutions of Hamilton-Jacobi equations. Trans. Am. Math. Soc. 277(1), 1\u201342 (1983)","journal-title":"Trans. Am. Math. Soc."},{"issue":"7","key":"4_CR9","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":"4","key":"4_CR10","doi-asserted-by":"publisher","first-page":"537","DOI":"10.1111\/j.2044-8295.1976.tb01545.x","volume":"67","author":"R Day","year":"1976","unstructured":"Day, R., Dickinson, R.: The components of the poggendorff illusion. Br. J. Psychol. 67(4), 537\u2013552 (1976)","journal-title":"Br. J. Psychol."},{"issue":"10","key":"4_CR11","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1016\/0166-2236(95)94496-R","volume":"18","author":"GC DeAngelis","year":"1995","unstructured":"DeAngelis, G.C., Ohzawa, I., Freeman, R.D.: Receptive-field dynamics in the central visual pathways. Trends Neurosci. 18(10), 451\u2013458 (1995)","journal-title":"Trends Neurosci."},{"issue":"4","key":"4_CR12","doi-asserted-by":"publisher","first-page":"713","DOI":"10.3934\/dcds.2007.17.713","volume":"17","author":"F Dragoni","year":"2007","unstructured":"Dragoni, F.: Metric Hopf-Lax formula with semicontinuous data. Discrete Continuous Dyn. Syst. 17(4), 713 (2007)","journal-title":"Discrete Continuous Dyn. Syst."},{"issue":"12","key":"4_CR13","doi-asserted-by":"publisher","first-page":"920","DOI":"10.1038\/35104092","volume":"2","author":"DM Eagleman","year":"2001","unstructured":"Eagleman, D.M.: Visual illusions and neurobiology. Nat. Rev. Neurosci. 2(12), 920\u2013926 (2001)","journal-title":"Nat. Rev. Neurosci."},{"issue":"11","key":"4_CR14","doi-asserted-by":"publisher","first-page":"694","DOI":"10.1037\/h0047037","volume":"15","author":"JJ Gibson","year":"1960","unstructured":"Gibson, J.J.: The concept of the stimulus in psychology. Am. Psychol. 15(11), 694 (1960)","journal-title":"Am. Psychol."},{"key":"4_CR15","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1007\/978-3-0348-9210-0_2","volume-title":"Sub-Riemannian Geometry","author":"M Gromov","year":"1996","unstructured":"Gromov, M.: Carnot-Carath\u00e9odory spaces seen from within. In: Bella\u00efche, A., Risler, J.J. (eds.) Sub-Riemannian Geometry, pp. 79\u2013323. Springer, Heidelberg (1996). https:\/\/doi.org\/10.1007\/978-3-0348-9210-0_2"},{"key":"4_CR16","unstructured":"Hering, E.: Beitr\u00e4ge zur Physiologie. I. Vom Ortsinne der Nethaut. Leipzig, Germany: Engelmann (1861)"},{"key":"4_CR17","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10851-009-0167-9","volume":"36","author":"R Hladky","year":"2010","unstructured":"Hladky, R., Pauls, S.: Minimal surfaces in the roto-translation group with applications to a neuro-biological image completion model. JMIV 36, 1\u201327 (2010)","journal-title":"JMIV"},{"issue":"2","key":"4_CR18","first-page":"137","volume":"32","author":"WC Hoffman","year":"1989","unstructured":"Hoffman, W.C.: The visual cortex is a contact bundle. Appl. Math. Comput. 32(2), 137\u2013167 (1989)","journal-title":"Appl. Math. Comput."},{"issue":"1","key":"4_CR19","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1113\/jphysiol.1962.sp006837","volume":"160","author":"DH Hubel","year":"1962","unstructured":"Hubel, D.H., Wiesel, T.N.: Receptive fields, binocular interaction and functional architecture in the cat\u2019s visual cortex. J. Physiol. 160(1), 106\u2013154 (1962)","journal-title":"J. Physiol."},{"issue":"6","key":"4_CR20","doi-asserted-by":"publisher","first-page":"1233","DOI":"10.1152\/jn.1987.58.6.1233","volume":"58","author":"JP Jones","year":"1987","unstructured":"Jones, J.P., Palmer, L.A.: An evaluation of the two-dimensional gabor filter model of simple receptive fields in cat striate cortex. J. Neurophysiol. 58(6), 1233\u20131258 (1987)","journal-title":"J. Neurophysiol."},{"issue":"6","key":"4_CR21","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."},{"key":"4_CR22","doi-asserted-by":"crossref","first-page":"95","DOI":"10.4208\/nmtma.2013.mssvm05","volume":"6","author":"A Mashtakov","year":"2013","unstructured":"Mashtakov, A., Ardentov, A., Sachkov, Y.: Parallel algorithm and software for image inpainting via sub-riemannian minimizers on the group of rototranslations. Numer. Math. Theory Methods Appl. 6, 95\u2013115 (2013)","journal-title":"Numer. Math. Theory Methods Appl."},{"issue":"4","key":"4_CR23","doi-asserted-by":"publisher","first-page":"1573","DOI":"10.1137\/120861667","volume":"52","author":"JM Mirebeau","year":"2014","unstructured":"Mirebeau, J.M.: Anisotropic fast-marching on cartesian grids using lattice basis reduction. SIAM J. Numer. Anal. 52(4), 1573\u20131599 (2014)","journal-title":"SIAM J. Numer. Anal."},{"key":"4_CR24","unstructured":"Montgomery, R.: A Tour of Subriemannian Geometries, Their Geodesics and Applications. Mathematical Surveys and Monographs (2002). http:\/\/bookstore.ams.org\/surv-91-s"},{"key":"4_CR25","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. Informatique et Sci. Humaines 145, 5\u2013102 (1999)","journal-title":"Math. Informatique et Sci. Humaines"},{"key":"4_CR26","volume-title":"The Psychology of Visual Illusion","author":"JO Robinson","year":"2013","unstructured":"Robinson, J.O.: The Psychology of Visual Illusion. Courier Corporation, Chelmsford (2013)"},{"key":"4_CR27","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1051\/cocv\/2010005","volume":"17","author":"Y Sachkov","year":"2011","unstructured":"Sachkov, Y.: Cut locus and optimal synthesis in the sub-riemannian problem on the group of motions of a plane. ESAIM C. Opt. Calc. Var. 17, 293\u2013321 (2011)","journal-title":"ESAIM C. Opt. Calc. Var."},{"key":"4_CR28","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"366","DOI":"10.1007\/978-3-319-25751-8_44","volume-title":"Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications","author":"G Sanguinetti","year":"2015","unstructured":"Sanguinetti, G., Bekkers, E., Duits, R., Janssen, M.H.J., Mashtakov, A., Mirebeau, J.-M.: Sub-riemannian fast marching in SE(2). In: Pardo, A., Kittler, J. (eds.) Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications. LNCS, vol. 9423, pp. 366\u2013374. Springer, Cham (2015). https:\/\/doi.org\/10.1007\/978-3-319-25751-8_44"},{"issue":"8","key":"4_CR29","first-page":"46","volume":"2","author":"G Sanguinetti","year":"2008","unstructured":"Sanguinetti, G., Citti, G., Sarti, A.: Image completion using a diffusion driven mean curvature flowin a sub-riemannian space. VISAPP 2(8), 46\u201353 (2008)","journal-title":"VISAPP"},{"key":"4_CR30","volume-title":"Level Set Methods and Fast Marching Methods","author":"JA Sethian","year":"1999","unstructured":"Sethian, J.A.: Level Set Methods and Fast Marching Methods, 2nd edn. Cambridge University Press, Cambridge (1999)","edition":"2"},{"key":"4_CR31","doi-asserted-by":"crossref","unstructured":"Talasli, U., Inan, A.B.: Applying Emmert\u2019s law to the Poggendorff illusion. Front. Hum. Neurosci. 9, October 2015. Article no. 531","DOI":"10.3389\/fnhum.2015.00531"},{"issue":"4","key":"4_CR32","doi-asserted-by":"publisher","first-page":"257","DOI":"10.3758\/BF03212818","volume":"10","author":"DJ Weintraub","year":"1971","unstructured":"Weintraub, D.J., Krantz, D.H.: The Poggendorff illusion: amputations, rotations, and other perturbations. Percept. Psychophys. 10(4), 257\u2013264 (1971)","journal-title":"Percept. Psychophys."},{"issue":"20","key":"4_CR33","doi-asserted-by":"publisher","first-page":"2128","DOI":"10.1016\/j.visres.2008.05.016","volume":"48","author":"G Westheimer","year":"2008","unstructured":"Westheimer, G.: Illusions in the spatial sense of the eye: geometrical-optical illusions and the neural representation of space. Vis. Res. 48(20), 2128\u20132142 (2008)","journal-title":"Vis. Res."},{"issue":"4","key":"4_CR34","doi-asserted-by":"publisher","first-page":"837","DOI":"10.1162\/neco.1997.9.4.837","volume":"9","author":"LR Williams","year":"1997","unstructured":"Williams, L.R., Jacobs, D.W.: Stochastic completion fields: a neural model of illusory contour shape and salience. Neural Comput. 9(4), 837\u2013858 (1997)","journal-title":"Neural Comput."}],"container-title":["Lecture Notes in Computer Science","New Trends in Image Analysis and Processing \u2013 ICIAP 2017"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-70742-6_4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,1,9]],"date-time":"2022-01-09T01:03:26Z","timestamp":1641690206000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-70742-6_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"ISBN":["9783319707419","9783319707426"],"references-count":34,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-70742-6_4","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2017]]},"assertion":[{"value":"31 December 2017","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ICIAP","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Image Analysis and Processing","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Catania","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Italy","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2017","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"11 September 2017","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"15 September 2017","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"19","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"iciap2017","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/www.iciap2017.com","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}