where r is the distance from the point and dω is the round metric on the sphere. If X is an arbitrary manifold with boundary, the class of conic metrics on X is modeled on this special case. Namely, a conic metric is a Riemannian metric on the interior of X such that for some choice of the defining function x of the boundary (x ∈ C∞(X) with ∂X = {x = 0}, x ≥ 0, dx 6= 0 on ∂X), the metric takes ...

This paper is an overview of three spline approaches of degree one, two and three. It represents the review and comparative study of Linear, conic and cubic splines for the vectorization of outlines of the planar images. It has various phases including extracting outlines of images, detecting corner points from the detected outlines, and curve fitting. The idea of simulated annealing has been i...

A T-conic (rational cubic with a quadratic denominator) spiral spline, with shape control parameters, will be discussed with the view to its application in Computer Graphics. An efficient scheme is presented which constructs a curve interpolating a set of given data points and allows subsequent interactive alteration of the shape of the curve by changing the shape control and shape preserving p...

PURPOSE The optical quality of retinal images is dependent on the refracting elements of the eye including the nominally aspheric cornea and crystalline lens. This paper presents a retrospective theoretical analysis of the impact of corneal asphericity on the quality of retinal images. Clinical data are from the VISX Incorporated CustomVue IDE. METHOD Topography, contrast sensitivity, and vis...

Consider the situation of a monocular image sequence with known ego-motion observing a 3D point moving simultaneously but along a path of up to second order, i.e. it can trace a line in 3D or a conic shaped path. We wish to reconstruct the 3D path from the projection of the tangent to the path at each time instance. This problem is analogue to the \trajectory triangulation" of lines and conic s...

Conic quadratic optimization is the problem of minimizing a linear function subject to the intersection of an affine set and the product of quadratic cones. The problem is a convex optimization problem and has numerous applications in engineering, economics, and other areas of science. Indeed, linear and convex quadratic optimization is a special case. Conic quadratic optimization problems can ...

Previous algorithms for recovering 3D geometry from an uncalibrated image sequence of a single axis motion of unknown rotation angles are mainly based on the computation of two-view fundamental matrices and three-view trifocal tensors. In this paper, we propose three new methods that are based on fitting a conic locus to corresponding image points over multiple views. The main advantage is that...

Polynomial optimization encompasses a very rich class of problems in which both the objective and constraints can be written in terms of polynomials on the decision variables. There is a well established body of research on quadratic polynomial optimization problems based on reformulations of the original problem as a conic program over the cone of completely positive matrices, or its conic dua...

We present a novel algorithm, Random Conic Pursuit, that solves semidefinite programs (SDPs) via repeated optimization over randomly selected two-dimensional subcones of the PSD cone. This scheme is simple, easily implemented, applicable to very general SDPs, scalable, and theoretically interesting. Its advantages are realized at the expense of an ability to readily compute highly exact solutio...