This paper gives a new inpainting model based on curve and horizontal line evolution. By connecting the level lines that reach the edges and let the connected lines have minimum curvature, the model can finish the task successfully. What’s more, the algorithm has no request on the topology of the inpainting area and can deal with all areas simultaneously.

We present two comparison principles for viscosity suband supersolutions of Monge-Ampère-type equations associated to a family of vector fields. In particular, we obtain the uniqueness of a viscosity solution to the Dirichlet problem for the equation of prescribed horizontal Gauss curvature in a Carnot group.

Background DaVinci presentation is a physician friendly picture of scoliotic spine seen from the cephalad side in the horizontal plane. This presentation is complementary to the standard view of the spine in two planes: frontal (anterior-posterior) and sagittal (lateral). DaVinci presentation can be obtained by using a few techniques which allow for three-dimensional reconstructions: CT, MRI, E...

A linear theory is proposed for the focusing of internal waves generated by the oscillations of a horizontal annulus that is slender, namely of large aspect ratio, but otherwise arbitrary. The theory exploits the separation of scales and is applied to two configurations: a circular torus, and circular Gaussian topography at the ocean bottom. Both complete and partial annuli are considered. Focu...

In this paper, we construct and classify minimal surfaces foliated by horizontal constant curvature curves in M × R, where M is H, R or S. The main tool is the existence of a so called ”Shiffman” Jacobi field which characterize the property to be foliated in circles in these product manifolds.

The visual environment is distorted with respect to the physical environment. Luneburg [1947, Mathematical Analysis of Binocular Vision (Princeton, NJ: Princeton University Press)] assumed that visual space could be described by a Riemannian space of constant curvature. Such a space is described by a metric which defines the distance between any two points. It is uncertain, however, whether suc...

Gravitropism of oat (Avena sativa L.) and wheat (Triticum aestivum L.) coleoptiles was investigated in relation to the displacement angle or to the initially set stimulation angle (SA). We measured curvature rates at the early phase of curvature, before it was affected by the drop in SA resulting from the curvature response itself. The plot of the rates against the sines of initial SAs revealed...

In this paper, we generalize Liouville type theorems for some semilinear partial differential inequalities to sub-Riemannian manifolds satisfying a nonnegative generalized curvature-dimension inequality introduced by Baudoin and Garofalo in [5]. particular, our results apply all Sasakian with horizontal Webster-Tanaka-Ricci curvature. The key ingredient is construct class of “good” cut-off func...

Horizontal binocular disparities provide information about the distance of objects relative to the point of ocular fixation and must be combined with an estimate of viewing distance to recover the egocentric distance of an object. Vergence angle and the gradient of vertical disparities across the visual field are thought to provide independent sources of viewing distance information based on hu...

Experimental observations and theoretical studies show that nonlinear internal waves occur widely in shallow water and cause acoustic propagation effects including ducting and mode coupling. Horizontal ducting results when acoustic modes travel between internal wave fronts that form waveguide boundaries. For small grazing angles between a mode trajectory and a front, an interference pattern may...