Related papers: Fast Geometric Fit Algorithm for Sphere Using Exac…
We analyze the problem of fitting a fonction en escalier or multi-step function to a curve in L^2 Hilbert space. We propose a two-stage optimization approach whereby the step positions are initially fixed, corresponding to a classic linear…
Sphere packing, Hilbert's eighteenth problem, asks for the densest arrangement of congruent spheres in n-dimensional Euclidean space. Although relevant to areas such as cryptography, crystallography, and medical imaging, the problem remains…
Given values of a piecewise smooth function $f$ on a square grid within a domain $\Omega$, we look for a piecewise adaptive approximation to $f$. Standard approximation techniques achieve reduced approximation orders near the boundary of…
This paper presents a geometric approach to the classical isoperimetric problem by analysing the efficiency of regular polygons in enclosing maximum area for a fixed perimeter. Using efficiency metrics, it proves that regular polygons…
We provide a method for fast and exact simulation of Gaussian random fields on spheres having isotropic covariance functions. The method proposed is then extended to Gaussian random fields defined over spheres cross time and having…
Symmetry detection and morphological classification of anatomical structures play pivotal roles in medical image analysis. The application of kinematic surface fitting, a method for characterizing shapes through parametric stationary…
The problem deals with an exact calculation of the intersection area of a circle arbitrary placed on a grid of square shaped elements with gaps between them (finite fill factor). Usually an approximation is used for the calculation of the…
A typical computational geometry problem begins: Consider a set P of n points in R^d. However, many applications today work with input that is not precisely known, for example when the data is sensed and has some known error model. What if…
This paper focuses on scattered data fitting problems on spheres. We study the approximation performance of a class of weighted spectral filter algorithms, including Tikhonov regularization, Landaweber iteration, spectral cut-off, and…
This article describes novel approaches to quickly estimate planar surfaces from RGBD sensor data. The approach manipulates the standard algebraic fitting equations into a form that allows many of the needed regression variables to be…
We present a fast algorithm for global rigid symmetry detection with approximation guarantees. The algorithm is guaranteed to find the best approximate symmetry of a given shape, to within a user-specified threshold, with very high…
Straight lines are common features in human made environments, which makes them a frequently explored feature for control applications. Many control schemes, like Visual Servoing, require the 3D parameters of the features to be estimated.…
Efficient and accurate particle tracking is crucial for measuring Standard Model parameters and searching for new physics. This task consists of two major computational steps: track finding, the identification of a subset of all hits that…
Orbital solutions for binary or multiple stellar systems that combine astrometry (e.g., position angles and angular separations) with spectroscopy (radial velocities) have important advantages over astrometric-only or spectroscopic-only…
We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…
The double Fourier sphere (DFS) method uses a clever trick to transform a function defined on the unit sphere to the torus and subsequently approximate it by a Fourier series, which can be evaluated efficiently via fast Fourier transforms.…
In this paper, we apply the classical Perron method to give a proof of the existence and uniqueness/rigidity result of a circle pattern on a closed surface equipped with conical spherical metric when prescribed measures of the angles of…
We present a novel area matching algorithm for merging two different 2D grid maps. There are many approaches to address this problem, nevertheless, most previous work is built on some assumptions, such as rigid transformation, or similar…
An explicit series solution is proposed for the inversion of the spherical mean Radon transform. Such an inversion is required in problems of thermo- and photo- acoustic tomography. Closed-form inversion formulae are currently known only…
An efficient technique to solve precision problems consists in using exact computations. For geometric predicates, using systematically expensive exact computations can be avoided by the use of filters. The predicate is first evaluated…