Vertical and oblique fault detection in explicit surfaces
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.
scientific article; zbMATH DE number 1758447