The purpose of this paper is to extend, as much as possible, the modern theory of condition numbers for conic convex optimization: z∗ := minx ctx s.t. Ax− b ∈ CY x ∈ CX , to the more general non-conic format: (GPd) z∗ := minx ctx s.t. Ax− b ∈ CY x ∈ P , where P is any closed convex set, not necessarily a cone, which we call the groundset. Although any convex problem can be transformed to conic ...

In this paper we discuss the Kruppa’s equation, which is widely known as the first camera self-calibration method. The classical and the simplified version of the method are of our interest. We have analyzed it based on how it is derived. As Kruppa’s equation works based on the image of the absolute conic, which is an imaginary conic, we have found that the use of circular points at infinity wa...

We present a geometric de nition of conic sections in the oriented projective plane and describe some of their nice properties. This de nition leads to a very simple and unambiguous representation for a ne conics and conic arcs. A conic (of any type) is represented by the homogeneous coordinates of its foci and one point on it, hence, the metric plays a major role in this case as opposed to the...

A stable nanoscale thermal hot spot, with temperature approaching 100 °C, is shown to be sustained by localized Ohmic heating of a focused electric field at the tip of a slender conic nanopore. The self-similar (length-independent) conic geometry allows us to match the singular heat source at the tip to the singular radial heat loss from the slender cone to obtain a self-similar steady temperat...

The purpose of this survey article is to introduce the reader to a very elegant formulation of convex optimization problems called conic optimization and outline its many advantages. After a brief introduction to convex optimization, the notion of convex cone is introduced, which leads to the conic formulation of convex optimization problems. This formulation features a very symmetric dual prob...

A framework is developed for the design and analysis of single-viewpoint catadioptric cameras that use two or more mirrors. The use of multiple mirrors permits folding of the optics which leads to more compact camera designs than ones that use a single mirror. A dictionary of camera designs that use two conic mirrors is presented. We show that any folded system that uses conic mirrors has a geo...

A public key cryptosystem scheme is proposed that are based on conic curves over the ring Zn. Our scheme is motivated by KMOV scheme on elliptic curves, but our scheme remove some restrictive condition from KMOV scheme and constructed on conic curves. Its security bases on the difficulty of factoring a composite number n, just like RSA. It can resist some of the known attacks on RSA. We also co...

We show that the complexity of a parabolic or conic spline approximating a sufficiently smooth curve with non-vanishing curvature to within Hausdorff distance ε is c1ε +O(1), if the spline consists of parabolic arcs, and c2ε + O(1), if it is composed of general conic arcs of varying type. The constants c1 and c2 are expressed in the Euclidean and affine curvature of the curve. We also show that...

In this paper it is shown how to use corresponding conics in two images to estimate the epipolar geometry, the fundamental/essential matrix and reconstruct the scene. The corresponding conics can be images of either a planar conic or silhouettes of a quadric. It is shown that one conic correspondence gives two constraints on the fundamental matrix and a method to estimate the fundamental matrix...

We propose a new p-norm linear discrimination model that generalizes the model of Bennett and Mangasarian (1992) and reduces to linear programming problem with p-order conic constraints. We demonstrate that the developed model possesses excellent methodological and computational properties (e.g., it does not allow for a null separating hyperplane when the sets are linearly separable, etc). The ...