Singularity Analysis for Image Processing and Anomaly Enhancement

Local structural property of an image is often considered in image enhancement with various high/low pass filters. Spatial association indexes (autocorrelation, covariance, and variogram) have been commonly used to characterize the local structure of surfaces for data interpolation in kriging. Singularity is another index measuring the scaling invariant property of measures from a multifractal point view. Comparing with spatial association indexes, the singularity has not yet been generally known by the community of image processing and geostatistics. Spatial association and scaling invariant are two different aspects of local structure of surfaces. Both must be taken into account in data interpolation and image enhancement. Recent studies of multifractal modeling have shown that the local singularity exponent involved in multifractal modeling can quantify the local scaling invariant property characterizing the concave/convex properties of the neighborhood values. In dealing with geochemical maps these properties may correspond to “depletion” and “enrichment”. A method proposed by the author incorporating both the singularity and spatial association has been used for image enhancement and data interpolation. A case study of the geochemical maps created from concentration values of trace elements As, Pb, Zn, and Cu in lake sediment samples from the southwestern Nova Scotia, Canada, was used to demonstrate the application of the method in geochemical anomaly enhancement. It has shown that the areas with significant singularity (enriched element concentration) are related either to gold mineralization and the occurrences of known deposits or to the local structures such as granitoid phase changes and intersections of linear structures. 32% of the known mineral deposits and occurrences in the area fall in those areas with enrichments of all four elements As, Cu, Pb and Zn and 97% in the areas with at least one element enrichment.