Related papers: Conformal Point and the Calibrated Conic
Some geometry on non-singular cubic curves, mainly over finite fields, is surveyed. Such a curve has 9,3,1 or 0 points of inflexion, and cubic curves are classified accordingly. The group structure and the possible numbers of rational…
We show that the visual angle metric and the triangular ratio metric are comparable in convex domains. We also find the extremal points for the visual angle metric in the half space and in the ball by use of a construction based on…
The coherent states are viewed as a powerful tool in differential geometry. It is shown that some objects in differential geometry can be expressed using quantities which appear in the construction of the coherent states. The following…
We give geometric ways to determine the cross ratio of conics in a pencil using elementary projective geometry.
Optical surfaces represented by second-degree polynomials (quadratic or conics) are ubiquitous in optics. We revisit the equations of the conic shapes in the context of grazing incidence optics, gathering together the curves commonly used…
Accurate calibration of camera intrinsic parameters is crucial to various computer vision-based applications in the fields of intelligent systems, autonomous vehicles, etc. However, existing calibration schemes are incompetent for finding…
We describe and analyze an interior-point method to decide feasibility problems of second-order conic systems. A main feature of our algorithm is that arithmetic operations are performed with finite precision. Bounds for both the number of…
This is a brief introduction to the basic concepts of topology. It includes the basic constructions, discusses separation properties, metric and pseudometric spaces, and gives some applications arising from the use of topology in computing.
The purpose of this note is to report, in narrative rather than rigorous style, about the nice geometry of $6$-division points on the Fermat cubic $F$ and various conics naturally attached to them. Most facts presented here were derived by…
We analyse the axioms of Euclidean geometry according to standard object-oriented software development methodology. We find a perfect match: the main undefined concepts of the axioms translate to object classes. The result is a suite of C++…
The goal of inversion is to estimate the model which generates the data of observations with a specific modeling equation. One general approach to inversion is to use optimization methods which are algebraic in nature to define an objective…
Preparing appropriate images for camera calibration is crucial to obtain accurate results. In this paper, new suggestions for preparing such data to alleviate the adverse effect of radial distortion for a calibration procedure using…
In most computer vision and image analysis problems, it is necessary to define a similarity measure between two or more different objects or images. Template matching is a classic and fundamental method used to score similarities between…
The basic tool for solving problems in metric geometry and isotonic regression is the metric projection onto closed convex cones. Isotonicity of these projections with respect to a given order relation can facilitate finding the solutions…
The topics of Convexity and Concavity and Envelopes are central in Complex Analysis and extensively investigated. The aim of this paper is to find a possible counterpart in Algebraic Geometry. The article presents preliminary results on…
Image Processing, Optimization and Prediction of an Image play a key role in Computer Science. Image processing provides a way to analyze and identify an image .Many areas like medical image processing, Satellite images, natural images and…
There exist efficient algorithms to project a point onto the intersection of a convex cone and an affine subspace. Those conic projections are in turn the work-horse of a range of algorithms in conic optimization, having a variety of…
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
There are several notions of duality between lines and points. In this note, it is shown that all these can be studied in a unified way. Most interesting properties are independent of specific choices. It is also shown that either dual…
The theory of modular forms and spherical harmonic analysis are applied to establish new best bounds towards the counting and equidistribution of rational points on spheres and other higher dimensional ellipsoids, in what may be viewed as a…