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We show that a color constancy image can be reconstructed as the solution of the associated inverse problem, which is a Poisson equation with heterogeneous differential operators. At the neural level the weights of short-range connectivity constitute the fundamental solution of the Poisson problem adapted point by point. A first demonstration of convergence of the result towards homogeneous reconstructions is proposed by means of homogenization techniques.<\/jats:p>","DOI":"10.1137\/23m1555958","type":"journal-article","created":{"date-parts":[[2024,2,21]],"date-time":"2024-02-21T04:02:40Z","timestamp":1708488160000},"page":"389-414","source":"Crossref","is-referenced-by-count":1,"title":["The Cortical V1 Transform as a Heterogeneous Poisson Problem"],"prefix":"10.1137","volume":"17","author":[{"given":"Alessandro","family":"Sarti","sequence":"first","affiliation":[{"name":"CAMS, EHESS, Paris, France."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8755-4740","authenticated-orcid":true,"given":"Mattia","family":"Galeotti","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica, Universit\u00e0 di Bologna, Bologna 40126, Italy."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Giovanna","family":"Citti","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica, Universit\u00e0 di Bologna, Bologna 40126, Italy."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2024,2,21]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2017.2761543"},{"key":"ref2","volume-title":"Nonlinear Analysis and Semilinear Elliptic Problems","author":"Ambrosetti A.","year":"2006"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1007\/s10851-013-0482-z"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.3389\/fncom.2022.775241"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1137\/15M1018460"},{"key":"ref6","volume-title":"Front-end Vision and Multi-scale Image Analysis","author":"ter Haar Romeny Bart M.","year":"2004"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-30961-3_4"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1186\/s13408-020-00089-6"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2021.09.024"},{"key":"ref10","volume":"15","author":"Bertoni F.","year":"2022","journal-title":"Front. 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