Measures for comparing discrete models of single-valued surfaces (Q1759132)

Let us suppose that we have two plane Delaunay triangulation grids, \(g_1\) and \(g_2\), and two grid functions \(f_1\) and \(f_2\), captured for instance by a 3D scanner. The aim of the paper is to introduce a measure for comparing such functions, in order to determine the similarity/difference between them, and to develop the algorithm for its computation. In a previous paper by the same author [``An algorithm for calculating the similarity measures of surfaces represented as point clouds, Pattern Recognit'', Image Anal. 20, 495--504 (2010)] a previous measure was given, Nevertheless, if one of the grids is too sparse relative to the other, this measure can lead to gross errors. In the paper under review, a modified measure is proposed trying to solve this disadvantage because it takes into account only representative data. The algorithm to compute the measure is shown to be of linear complexity when the Delaunay triangulations associated to the grids grids \(g_1\) and \(g_2\) are constructed at the preprocessing stage.