We extend to a Engel type structure a cortically inspired model of perceptual completion initially proposed in the Lie group of positions and orientations with a sub-Riemannian metric. According to this model, a given image is lifted in the group and completed by a minimal surface. The main obstacle in extending the model to a higher dimensional group, which can code also curvatures, is the lack of a good definition of codimension 2 minimal surface. We present here this notion, and describe an application to image completion.
Citti G., Giovannardi G., Ritore M., Sarti A. (2021). Submanifolds of Fixed Degree in Graded Manifolds for Perceptual Completion. Cham : Springer [10.1007/978-3-030-80209-7_6].
Submanifolds of Fixed Degree in Graded Manifolds for Perceptual Completion
Citti G.;
2021
Abstract
We extend to a Engel type structure a cortically inspired model of perceptual completion initially proposed in the Lie group of positions and orientations with a sub-Riemannian metric. According to this model, a given image is lifted in the group and completed by a minimal surface. The main obstacle in extending the model to a higher dimensional group, which can code also curvatures, is the lack of a good definition of codimension 2 minimal surface. We present here this notion, and describe an application to image completion.| File | Dimensione | Formato | |
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