• Corpus ID: 196471072

Visual Curve Completion and Rotational Surfaces of Constant Negative Curvature

  title={Visual Curve Completion and Rotational Surfaces of Constant Negative Curvature},
  author={{\'A}lvaro P{\'a}mpano},
  journal={arXiv: Differential Geometry},
  • Á. Pámpano
  • Published 27 June 2019
  • Mathematics
  • arXiv: Differential Geometry
If a piece of the contour of a picture is missing to the eye vision, then the brain tends to complete it using some kind of sub-Riemannian geodesics of the unit tangent bundle of the plane, R2xS1. These geodesics can be obtained by lifting extremal curves of a total curvature type energy in the plane. We completely solve this variational problem, geometrically. Moreover, we also show a way of constructing rotational surfaces of constant negative curvature in R3 by evolving these extremal curves… 

Figures from this paper

Rotational surfaces of constant astigmatism in space forms


Curvature-dependent energies minimizers and visual curve completion
Geometrical actions often used to describe elastic properties of elastic rods and fluid membranes have been proposed recently to explain functional mechanism of the primary visual cortex V1. These
A Tangent Bundle Theory for Visual Curve Completion
This work exploits the observation that curve completion is an early visual process to formalize the problem in the unit tangent bundle R2 × S1, which abstracts the primary visual cortex (V1) and facilitates exploration of basic principles from which perceptual properties are later derived rather than imposed.
Tangent Bundle Elastica and Computer Vision
This work proposes and develops a biologically plausible theory of elastica in the tangent bundle that provides not only perceptually superior completion results but also a rigorous computational prediction that inducer curvatures greatly affects the shape of the completed curve.
The neurogeometry of pinwheels as a sub-Riemannian contact structure
Knotted Elastic Curves in R3
One of the oldest topics in the calculus of variations is the study of the elastic rod which, according to Daniel Bernoulli's idealization, minimizes total squared curvature among curves of the same
Association Fields via Cuspless Sub-Riemannian Geodesics in SE(2)
S-parametrization simplifies the exponential map, the curvature formulas, the cusp-surface, and the boundary value problem, and shows that sub-Riemannian geodesics solve Petitot’s circle bundle model.
Binormal Motion of Curves with Constant Torsion in 3-Spaces
We study curve motion by the binormal flow with curvature and torsion depending velocity and sweeping out immersed surfaces. Using the Gauss-Codazzi equations, we obtain filaments evolving with
A direct variational approach to a problem arising in image reconstruction
Many problems in digital image processing require the ability to recover missing parts of an image or to remove spurious or undesired objects. One can mention for instance the removal of scratches in
The total squared curvature of closed curves