Journal
JOURNAL OF MATHEMATICAL IMAGING AND VISION
Volume 24, Issue 3, Pages 307-326Publisher
SPRINGER
DOI: 10.1007/s10851-005-3630-2
Keywords
visual cortex; perceptual completion; cognitive neuroscience; Lie group; partial differential equation
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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.
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