Implementation of mathematical morphological operations for spatial data processing

Abstract

Mathematical morphology is a theory of image transformations which is based on set-theoretical, geometrical, and topological concepts. The methodology is useful particularly for the analysis of the geometrical structure in an image. Since many data types in the geosciences are related to spatial location, it is expected that the mathematical morphological operations are particularly important for geoscientific spatial data processing. In this paper, the binary mathematical morphological operations of dilation, erosion, opening, closing, hit/miss transform, and thinning are implemented using the C programming language and the PCIDSK C Toolbox. Dilation, erosion, opening, and closing operations are extended to gray-scale imagery. As an example, gray-scale image dilation and erosion operations are applied to an aeromagnetic image from the File Lake area, Manitoba, Canada for edge and linear feature detection. The detected edge and linear features are scaled into a binary image through thresholding, which allows for further binary morphological operations. Thinning operations are applied to binary images to obtain connected one-pixel thick skeletons. Trimming operations are tested to remove skeletal legs resulting from the thinning operation. Results from both binary and gray-scale images show that mathematical morphological operations can be applied efficiently to the processing of spatial data in the geosciences. The thinning operation makes it possible for edge and linear features to be vectorized and put directly into a geographic information system (GIS).