PURPOSE To explore the potential effect of ageing on the corneal curvature and corrected visual acuity in patients with long-term keratoconus because of the paucity of these patients older than 50 years. METHODS Records of keratoconic patients, who had initially presented to a specialized contact lens clinic and followed for more than 20 years after disease onset, were reviewed. Collected inf...

which is sharp as indicated in the Euclidean case. However even if M contains a small compact region where the Ricci curvature is not nonnegative, estimate (1.1) becomes very much different from (1.2) when r is large, due to the presence of the √ k term. Whether estimate (1.2) is stable under perturbation has been an open question for some time, in light of the known stability results on weaker...

We analyze 2-dimensional Ginzburg-Landau vortices at critical coupling, and establish asymptotic formulas for the tangent vectors of the vortex moduli space using theorems of Taubes and Bradlow. We then compute the corresponding Berry curvature and holonomy in the large area limit.

In this paper, we formally connect between vector median lters, morphological operators, and geometric partial diierential equations. Considering a lexicographic order, which permits to deene an order between vectors in IR N , we rst show that the vector median lter of a vector-valued image is equivalent to a collection of innmum-supremum morphological operations. We then proceed and study the ...

This paper presents a new technique for planar object recognition based on Hidden Markov Models. First, the contour of the object is processed to extract a sequence of high curvature points. These points are extracted from a new adaptively extracted curvature function which is resistant against noise and transformations. Each corner is characterized by its subtended angle and its distance to th...

In this paper we show the similarities and differences of two deep neural networks by comparing the manifolds composed of activation vectors in each fully connected layer of them. The main contribution of this paper includes 1) a new data generating algorithm which is crucial for determining the dimension of manifolds; 2) a systematic strategy to compare manifolds. Especially, we take Riemann c...

Discrete analogs of extrema of curvature and generalizations of the four-vertex theorem to the case of polygons and polyhedra are suggested and developed. Several interrelated approaches are considered. For smooth curves and polygonal lines in the plane, a formula relating the number of extrema of curvature to the winding numbers of the curves (polygonal lines) and their caustics is obtained. O...

Two special Finsler spaces have been introduced and investigated, namely R-recurrent Finsler space and concircularly recurrent Finsler space. The defining properties of these spaces are formulated in terms of the first curvature tensor of Cartan connection. The following three results constitute the main object of the present paper: (i) a concircularly flat Finsler manifold is necessarily of co...

A novel numerical method for solving three-dimensional two phase flow problems is presented. This method combines a quadrature free discontinuous Galerkin method for the level set equation with a pressure stabilized finite element method for the Navier Stokes equations. The main challenge in the computation of such flows is the accurate evaluation of surface tension forces. This involves the co...

This paper presents a new method for 3D object localization from a single image. It is known that single camera provide 2D image data, annihilating valuable 3D information about object and its localization in space. The main new idea is to match 2D image gradient to the reprojection of 3D curvature to retrieve objects position relative to the camera. The object parameters are a-priori known and...