A generalized cross‐tabulation matrix to compare soft‐classified maps at multiple resolutions

TLDR

Geographic Information Science faces challenges in constructing cross‑tabulation matrices for soft‑classified pixels, with traditional Boolean, contemporary multiplication, and fuzzy minimum operators all encountering difficulties. The study aims to develop a cross‑tabulation matrix for soft‑classified pixels and extend it to multiple spatial resolutions. The authors derive equations for a composite‑operator cross‑tabulation matrix that works at multiple resolutions and link the method to GIS ontological foundations. The multiple‑resolution approach overcomes the limitations of existing methods and allows examination of how results vary across scales.

Abstract

This paper addresses two grand challenges in the development of methods for Geographic Information Science (GIS). First, this paper presents techniques to compute a cross‐tabulation matrix for soft‐classified pixels. Second, it shows how to compute the cross‐tabulation matrix at multiple scales. The traditional approach to construct the cross‐tabulation matrix uses a Boolean operator to analyse pixels that are hard‐classified. For soft‐classified pixels, the contemporary approach uses a Multiplication operator; the fuzzy approach uses a Minimum operator; whereas this paper proposes a multiple‐resolution approach that uses a Composite operator. There are difficulties with the traditional, contemporary, and fuzzy methods of computing the cross‐tabulation matrix. The proposed multiple‐resolution method resolves those difficulties. Furthermore, the proposed method facilitates multiple‐resolution analysis, so it can examine how results change as a function of scale. The paper derives the equations to compute cross‐tabulation matrices at multiple resolutions and connects those equations to ontological foundations of GIS.