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

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## Abstract

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.

## Keywords

visual cortex perceptual completion cognitive neuroscience Lie group partial differential equation## Preview

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