Map Comparison Methods for Three‐Dimensional Space and Time Voxel Data

Abstract

Map comparisons in three‐dimensional space (3D) and 3D time series (4D) are becoming a necessity with increased availability of multidimensional data and model simulation outputs. Therefore, this research study extends the two‐dimensional (2D) map comparison methods with the aim to propose a suite of 3D approaches such as 3D Kappa, 3D Fuzzy, and 4D Fuzzy Kappa coefficients specifically designed to perform with voxel data. These proposed approaches can account for fuzziness where small categorical differences in 3D space or space‐time are given a degree of similarity instead of a binary similarity value. The developed approaches are tested using different voxel data sets: (a) hypothetical with two and four classes to confirm the methods produce expected results, (b) voxelized LiDAR data to demonstrate the comparison of real 3D data sets, (c) soil horizon voxel data sets to conduct a sensitivity analysis of 3D voxel window sizes, (d) 4D outputs from an agent‐based forest‐fire smoke model to demonstrate the 4D Fuzzy Kappa coefficient and a sensitivity analysis of 4D voxel window size. The obtained results indicate that 3D and 4D voxel data comparisons are feasible allowing for further work on comparison of 3D data and evaluation of multidimensional models.