Journal of Mathematical Imaging and Vision

, Volume 24, Issue 3, pp 307-326

First online:

A Cortical Based Model of Perceptual Completion in the Roto-Translation Space

  • G. CittiAffiliated withDepartment of Mathematics, University of Bologna Email author 
  • , A. SartiAffiliated withDepartment of Electronics, Information and Systems, University of Bologna

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


We present a mathematical model of perceptual completion and formation of subjective surfaces, which is at the same time inspired by the architecture of the visual cortex, and is the lifting in the 3-dimensional rototranslation group of the phenomenological variational models based on elastica functional. The initial image is lifted by the simple cells to a surface in the rototranslation group and the completion process is modeled via a diffusion driven motion by curvature. The convergence of the motion to a minimal surface is proved. Results are presented both for modal and amodal completion in classic Kanizsa images.


visual cortex perceptual completion cognitive neuroscience Lie group partial differential equation