Receptive profiles of the primary visual cortex (V1) cortical cells are very heterogeneous and act by differentiating the stimulus image as operators changing from point to point. In this paper we aim to show that the distribution of cells in V1, although not complete to reconstruct the original image, is sufficient to reconstruct the perceived image with subjective constancy. 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.

Sarti, A., Galeotti, M., Citti, G. (2024). The Cortical V1 Transform as a Heterogeneous Poisson Problem. SIAM JOURNAL ON IMAGING SCIENCES, 17(1), 389-414 [10.1137/23m1555958].

The Cortical V1 Transform as a Heterogeneous Poisson Problem

Sarti, Alessandro;Galeotti, Mattia;Citti, Giovanna
2024

Abstract

Receptive profiles of the primary visual cortex (V1) cortical cells are very heterogeneous and act by differentiating the stimulus image as operators changing from point to point. In this paper we aim to show that the distribution of cells in V1, although not complete to reconstruct the original image, is sufficient to reconstruct the perceived image with subjective constancy. 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.
2024
Sarti, A., Galeotti, M., Citti, G. (2024). The Cortical V1 Transform as a Heterogeneous Poisson Problem. SIAM JOURNAL ON IMAGING SCIENCES, 17(1), 389-414 [10.1137/23m1555958].
Sarti, Alessandro; Galeotti, Mattia; Citti, Giovanna
File in questo prodotto:
File Dimensione Formato  
23m1555958.pdf

accesso aperto

Tipo: Versione (PDF) editoriale
Licenza: Licenza per accesso libero gratuito
Dimensione 10.18 MB
Formato Adobe PDF
10.18 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/964354
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? 0
social impact