Summed area table for rapid local singularity mapping

Abstract

The local singularity model based on multifractal theory suggested by Cheng has gained significant attention in characterizing mineralization and predicting mineral deposits. Chen et al. developed an iterative approach of local singularity analysis to get the final singularity index. However the computational efficiency need to be improved, because the moving average with several scales are calculated for each cell of an raster dataset in the conventional algorithm. Summed area table (SAT), also called as integral image, was first prominently used within the Viola-Jones object detection framework in computer vision. We introduced SAT in local singularity mapping in this study. Once computed using SAT, any one of the rectangular sum can be computed at any scale or location in constant time. SAT is used in geochemical stream sediment survey data applications. A wide variety of scale changes for non-iterative or iterative approach are adopted to calculate the singularity index values efficiently, and then we compare the results and generate optimal singularity mapping.