Ranks for Pairs of Spatial Fields via Metric Based on Grayscale Morphological Distances

Based on a set of morphological distances computed between the grayscale images (spatial fields) of similar size specifications, the ratios of selected morphological distances, and the ratios of areas of infima and suprema of grayscale images, a new metric to quantify the degree of similarity between the grayscale images is proposed. We denote the two spatial fields (grayscale images), respectively, with fⁱ and f^j, and the infima and suprema of these spatial fields with (fi ∧ f^j) and (fⁱ ⋁ f^j). The three morphology-based distances include: 1) dilation distance d( fⁱ, f^j); 2) erosion distance e(fⁱ, f^j); and 3) median-based distance MN(fⁱ, f^j). By employing these parameters, which play vital role in construction of parameter-specific interaction matrices, we provide a metric to designate every possible pair of images that can be considered out of a database consisting of a huge number of images. We demonstrate the whole approach on: 1) synthetic spatial fields; 2) a set of 12 similar-sized grayscale images representing cloud-top temperatures of a specific region for 12 different time instants; and 3) four spatial elevation fields to rank possible pairs of images.