Related papers: Fast Geometric Fit Algorithm for Sphere Using Exac…

We present efficient algorithms for detecting central and mirror symmetry for the case of algebraic curves defined by means of polynomial parametrizations. The algorithms are based on the existence of a linear relationship between two…

Spherical spin glasses are canonical models for smooth random functions in high dimensions. In this review, we survey several interrelated lines of research on their geometric structure. We begin with results concerning critical points and…

Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for…

We find a new method for looking for the static and spherically symmetric solutions in $F(R)$ theory of gravity. With this method, a number of new solutions in terms of the analytic functions are obtained. We hope this investigation may be…

In this work, we propose a parameterised quantum circuit learning approach to point set matching problem. In contrast to previous annealing-based methods, we propose a quantum circuit-based framework whose parameters are optimised via…

Keypoint matching can be slow and unreliable in challenging conditions such as repetitive textures or wide-baseline views. In such cases, known geometric relations (e.g., the fundamental matrix) can be used to restrict potential…

Jointly matching multiple, non-rigidly deformed 3D shapes is a challenging, $\mathcal{NP}$-hard problem. A perfect matching is necessarily cycle-consistent: Following the pairwise point correspondences along several shapes must end up at…

This paper provides a comprehensive survey on pioneer and state-of-the-art 3D scene geometry estimation methodologies based on single, two, or multiple images captured under the omnidirectional optics. We first revisit the basic concepts of…

Optimal error estimation is key to achieve accurate photometry and astrometry. Stellar fluxes and positions in high angular resolution images are typically measured with PSF fitting routines, such as StarFinder. However, the formal…

Recent advances in consumer depth sensors have created many opportunities for human body measurement and modeling. Estimation of 3D body shape is particularly useful for fashion e-commerce applications such as virtual try-on or fit…

We construct the solution to the periodic Cauchy problem of the Schr\"odinger flow on the sphere. Such construction of solutions is formulated explicitly and therefore a geometric algorithm of solving this periodic Cauchy problem follows.…

For dealing with the equal sphere packing problem, we propose a serial symmetrical relocation algorithm, which is effective in terms of the quality of the numerical results. We have densely packed up to 200 equal spheres in spherical…

The procedure of Least Square-Errors curve fitting is extensively used in many computer applications for fitting a polynomial curve of a given degree to approximate a set of data. Although various methodologies exist to carry out curve…

In this work, exact solutions of static and spherically symmetric space-times are analyzed in f(R) modified theories of gravity coupled to nonlinear electrodynamics. Firstly, we restrict the metric fields to one degree of freedom,…

The work develops further the theory of the following inversion problem, which plays the central role in the rapidly developing area of thermoacoustic tomography and has intimate connections with PDEs and integral geometry: {\it Reconstruct…

In this paper we present algorithms for a number of problems in geometric pattern matching where the input consist of a collections of segments in the plane. Our work consists of two main parts. In the first, we address problems and…

Many remarkably robust, rapid and spontaneous self-assembly phenomena in nature can be modeled geometrically starting from a collection of rigid bunches of spheres. This paper highlights the role of symmetry in sphere-based assembly…

We propose a computer-efficient and accurate method of estimation of spatially correlated errors in astrometric positions, parallaxes and proper motions obtained by space and ground-based astrometry missions. In our method, the simulated…

Improvement of the prediction accuracy of the Earth's rotation parameters (ERP) is one of the main problems of applied astrometry. In order to solve this problem, various approaches are used and in order to select the best one, comparison…

We investigate approximation algorithms for several fundamental optimization problems on geometric packing. The geometric objects considered are very generic, namely $d$-dimensional convex fat objects. Our main contribution is a versatile…