Related papers: On cylindrical regression in three-dimensional Euc…
The three-dimensional linear regression problem is a problem of finding a spacial straight line best fitting a group of points in three-dimensional Euclidean space. This problem is considered in the present paper and a solution to it is…
Given n points in Euclidean space E^d, we propose an algebraic algorithm to compute the best fitting (d-1)-cylinder. This algorithm computes the unknown direction of the axis of the cylinder. The location of the axis and the radius of the…
A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…
The Continuous p-Dispersion Problem (CpDP) with boundary constraints asks for the placement of a fixed number of points in a compact subset of Euclidean space such that the minimum distance between any two points, as well as the points and…
We will consider the resolution of the 3D non linear wave equation under the assumption of spherical symmetry on the euclidian space. For this purpose, we will build a non trivial measure on distributions such that there exists a set of…
We will consider the resolution of the 3D non linear wave equation under the assumption of spherical symmetry on the Euclidian space. For this purpose, we will build a non trivial measure on distributions such that there exists a set of…
Detecting the reflection symmetry plane of an object represented by a 3D point cloud is a fundamental problem in 3D computer vision and geometry processing due to its various applications, such as compression, object detection, robotic…
We propose an algorithm to detect approximate reflection symmetry present in a set of volumetrically distributed points belonging to $\mathbb{R}^d$ containing a distorted reflection symmetry pattern. We pose the problem of detecting…
Combinatorial optimization is a fertile testing ground for statistical physics methods developed in the context of disordered systems, allowing one to confront theoretical mean field predictions with actual properties of finite dimensional…
We consider the fundamental task of optimising a real-valued function defined in a potentially high-dimensional Euclidean space, such as the loss function in many machine-learning tasks or the logarithm of the probability distribution in…
Delaunay triangulations of a point set in the Euclidean plane are ubiquitous in a number of computational sciences, including computational geometry. Delaunay triangulations are not well defined as soon as 4 or more points are concyclic but…
In this paper, we present the point symmetry group of three-dimensional homogeneous Helmholtz equation, when we consider the cylindrical coordinate system. In continuation, we present a complete set of functionally independent invariants of…
The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this…
We propose a variational regularization approach based on a multiscale representation called cylindrical shearlets aimed at dynamic imaging problems, especially dynamic tomography. The intuitive idea of our approach is to integrate a…
The paper is devoted to the classification of entire solutions to the Cahn-Hilliard equation $-\Delta u = u-u^3-\delta$ in $\R^N$, with particular interest in those solutions whose nodal set is either bounded or contained in a cylinder. The…
A new method of root finding is formulated that uses a numerical iterative process involving three points. A given function y = f(x) whose roots are desired is fitted and approximated by a polynomial function of the form P(x)= a(x-b)^N that…
This paper enhances and develops bridges between statistics, mechanics, and geometry. For a given system of points in $\mathbb R^k$ representing a sample of full rank, we construct an explicit pencil of confocal quadrics with the following…
Two averaging algorithms are considered which are intended for choosing an optimal plane and an optimal circle approximating a group of points in three-dimensional Euclidean space.
Consider the problem of estimating the mean of a Gaussian random vector when the mean vector is assumed to be in a given convex set. The most natural solution is to take the Euclidean projection of the data vector on to this convex set; in…
In this paper we present methods for triangulation of infinite cylinders from image line silhouettes. We show numerically that linear estimation of a general quadric surface is inherently a badly posed problem. Instead we propose to…