TWO‐DIMENSIONAL FILTERING AND THE SECOND DERIVATIVE METHOD

Publisher Website
Google Scholar
Abstract
The data‐processing operations of second derivative formulas are equivalent to two‐dimensional digital filtering operations. Therefore any coefficient set can be described unambiguously by its two‐dimensional frequency response. The frequency responses can be represented by surfaces over the two‐dimensional frequency plane. We have simplified the representation by giving some curves intersected from these surfaces by a) planes, b) cylindrical surfaces perpendicular to the frequency plane. The coefficient sets given by Elkins (1951), Henderson and Zietz (1949), Rosenbach (1953), and the “center‐point‐and‐one‐ring” method are analysed. These formulas, in order of increasing “average” accuracy of approximation, are Henderson and Zietz, Rosenbach, “center‐point‐and‐one‐ring” method, Elkins. Henderson and Zietz’s formula and the “center‐point‐and‐one‐ring” method have depended significantly on direction, while Rosenbach’s formula is nearly nondirectional. Elkins’ formula lies between them.

This publication has 0 references indexed in Scilit: