Abstract
We present a novel cortically-inspired image completion algorithm. It uses five-dimensional sub-Riemannian cortical geometry, modeling the orientation, spatial frequency and phase-selective behavior of the cells in the visual cortex. The algorithm extracts the orientation, frequency and phase information existing in a given two-dimensional corrupted input image via a Gabor transform and represents those values in terms of cortical cell output responses in the model geometry. Then, it performs completion via a diffusion concentrated in a neighborhood along the neural connections within the model geometry. The diffusion models the activity propagation integrating orientation, frequency and phase features along the neural connections. Finally, the algorithm transforms the diffused and completed output responses back to the two-dimensional image plane.
Highlights
Visual perception has drawn the attention of experts from fields of philosophy, psychology and neuroscience, as well as the attention of mathematicians and physicists working on perceptual modeling
With the boundary conditions given as u(q, z, t) = OI (q, z). The advantage of such approximation is that we perform the diffusion procedure in L three-dimensional spaces instead of in a five-dimensional geometry by still taking advantage of the frequency information extracted from the input image
The oputput responses are represented in the five-dimensional sub-Riemannian model geometry
Summary
Visual perception has drawn the attention of experts from fields of philosophy, psychology and neuroscience, as well as the attention of mathematicians and physicists working on perceptual modeling. We focus on amodal completion in the present work, and provide an approach which reconstructs the occluded parts in a compatible way with the law of good continuity and association fields, where those two notions are considered in an extended way based on position, orientation, frequency and phase alignment. They geometrically interpreted the association fields as the integration along the vector fields generating the contact geometry This setting was developed further by Citti and Sarti [33] to a framework in which they introduced a group-based approach to study the geometric modeling of V1 hypercolumnar architecture and the functional connectivity. It is different from the classical approach, in which a suitable geometry is assigned to the neural responses represented in terms of receptive profiles This extended model takes advantage of orientations, spatial frequencies and phases in a given 2D input image to encode the visual information. We give the main conclusions and some perspectives for related future research
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