Vertical and oblique fault detection in explicit surfaces
type: Item
instance of: scholarly article
title: Vertical and oblique fault detection in explicit surfaces
zbMATH Open document ID: 1019.65018
DOI: 10.1016/S0377-0427(01)00601-X
author: María Cruz López de Silanes
author: María Cruz Parra
author: Juan José Torrens
published in: Journal of Computational and Applied Mathematics
publication date: 2002-06-24T00:00:00Z
review text: The paper studies the detection of vertical and oblique faults in surfaces which are graphs of bivariate functions. The core of the investigations is a thorough study of the univariate case. The authors relate finite jump discontinuities of a univariate function to the divergence of certain sequences, which are related to the slopes of least-squares polynomial approximations of the function. These results can be applied to the detection of finite jump discontinuities of a univariate function and its first derivative, even if the function is only given by a finite set of scattered data values. It is then shown how to extend the results to the formulation of an algorithm which detects faults in graphs of bivariate functions. The bivariate function is given discretely with help of function values on a set of data points, which are distributed along lines. A number of examples shows the good performance of the proposed algorithms.
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 65D10
zbMATH DE Number: 1758447
zbMATH Keywords: discontinuity detection
zbMATH Keywords: fault detection
zbMATH Keywords: polynomial approximation
zbMATH Keywords: numerical examples
zbMATH Keywords: surfaces
zbMATH Keywords: least-squares
zbMATH Keywords: algorithm
reviewed by: Helmut Pottmann
MaRDI profile type: Publication
cites work: Detection of discontinuities in scattered data approximation
cites work: Inf-convolution spline pour l'approximation de données discontinues
cites work: Detection, Classification, and Measurement of Discontinuities
cites work: Singularity detection and processing with wavelets
cites work: Vertical fault detection from scattered data
cites work: Irregularity detection from noisy data in one and two dimensions
cites work: 2D-discontinuity detection from scattered data
full work available at URL: s0377-0427(01)00601-x
OpenAlex ID: W1996408427
description: scientific article; zbMATH DE number 1758447