We present the details of a multi-resolution method which we proposed in Taormina in 1993 (see [6]) which is suitable for fitting functions or data on the sphere. The method is based on tensor products of polynomial splines and trigonometric splines, and produces surfaces which are tangent plane continuous. The result is a convenient compression algorithm for dealing with large amounts of data ...

Finding an implicit polynomial that fits a set of observations X is the goal of many researches in recent years. However, most existing algorithms assume the knowledge of the degree of the implicit polynomial that best represents the points. This paper presents two main contributions. First, a new distance measure between X and the implicit polynomial is defined. Second, this distance is used t...

We propose the use of the bootstrap technique for estimating the test error in the context of surface reconstruction from noisy point sets. Validation experiments with polynomial fittings of locally parametrized neighborhoods of noisy point sets give evidence that, in agreement with the theory, the training error underestimates the test error while leave-one-out error overestimates it. Based on...

Algebraic invariants extracted from coefficients of implicit polynomials (IPs) have been attractive because of its convenience for solving the recognition problem in computer vision. However, traditional IP fitting methods fixed the polynomial degree and thus lead to the difficulty for obtaining appropriate invariants according to the complexity of an object. In this paper, we propose a multile...

Trivariate C macro-elements defined in terms of polynomials of degree 8r + 1 on tetrahedra are analyzed. For r = 1, 2, these spaces reduce to well-known macro-element spaces used in data fitting and in the finite-element method. We determine the dimension of these spaces, and describe stable local minimal determining sets and nodal minimal determining sets. We also show that the spaces approxim...

The singularly perturbed parabolic boundary value problem is considered. Difference scheme is obtained by using cubic spline difference scheme on Shishkin’s mesh in space and classical discretization on uniform mesh in time. To obtain better stability and simpler matrix the fitting factor in polynomial form is used. The uniform convergence is achieved. Numerical results are presented. AMS Mathe...

Aiming at the requirement of the autonomous time synchronization in BeiDou Navigation Satellite System (BDS), an algorithm for inter-satellite autonomous time synchronization and ranging is proposed. Based on the establishment of the inter-satellite link length model of the BDS, a series of simulation has been carried out through the use of STK (Satellite Tool Kit), which includes the simulatio...

RESEARCH ARTICLE Modelling of Friction Coefficient for Shoes Type LL By Means of Polynomial Fitting L. Cantone and A. Ottati Department of Engineering for Enterprise “Mario Lucertini" University of Rome “Tor Vergata”, via del Politecnico, 1, 00133 Rome, Italy Tecnologie Meccaniche e Sistemi Frenanti Ingegneria Rotabili e Tecnologie di Base, Direzione Tecnica TRENITALIA, Viale Spartaco Lavagnini...

This paper presents a vision based road boundary detection based on the combination of dynamic programming and 2nd order polynomial approximation. The initial estimate of the most likely road boundaries are obtained by a modified dynamic programming on a cost field defined on the edge image. A second order polynomial is fit to the initial coarse estimate of road boundaries to obtain a refined e...

This work deals with 2D object description and recognition based on coefficients of implicit polynomials (IP). We first improve the description abilities of recently published Min-Max and Min-Var algorithms by replacing algebraic distances by geometric ones in the relevant cost function. We show that a recognizer based on a full set of recently published linear, quadrature, and angular rotation...