A Cortical-Inspired Contour Completion Model Based on Contour Orientation and Thickness.

An extended four-dimensional version of the traditional Petitot-Citti-Sarti model on contour completion in the visual cortex is examined. The neural configuration space is considered as the group of similarity transformations, denoted as M=SIM(2). The left-invariant subbundle of the tangent bundle models possible directions for establishing neural communication.

Liouville Integrability in a Four-Dimensional Model of the Visual Cortex.

We consider a natural extension of the Petitot-Citti-Sarti model of the primary visual cortex. In the extended model, the curvature of contours is taken into account. The occluded contours are completed via sub-Riemannian geodesics in the four-dimensional space M of positions, orientations, and curvatures.

Fourier Transform on the Homogeneous Space of 3D Positions and Orientations for Exact Solutions to Linear PDEs.

Fokker-Planck PDEs (including diffusions) for stable Lévy processes (including Wiener processes) on the joint space of positions and orientations play a major role in mechanics, robotics, image analysis, directional statistics and probability theory. Exact analytic designs and solutions are known in the 2D case, where they have been obtained using Fourier transform on S E ( 2 ) . Here, we extend these approaches to 3D using Fourier transform on the Lie group S E ( 3 ) of rigid body motions.

Tracking of Lines in Spherical Images via Sub-Riemannian Geodesics in .

In order to detect salient lines in spherical images, we consider the problem of minimizing the functional for a curve on a sphere with fixed boundary points and directions. The total length is free, denotes the spherical arclength, and denotes the geodesic curvature of  . Here the smooth external cost is obtained from spherical data.