Identifying unique patterns of energy in ground penetrating radar images plays an important role in landmine/clutter discrimination. Many different geometric features, including size and the distribution of energy values in a radar image, can be exploited in mine detection and discrimination. The granulometry of a random set (image), computed by measuring the integral of a sequence of closings with elements from a family of increasing homothetic shapes, yields a size distribution that can be used for texture analysis or object detection and discrimination. An important complement to granulometries for discrimination is the compactometry, a feature we have identified that is computed by measuring the integral of a sequence of increasing concentric homothetic subsets of a random set. The compactometry yields a characterization of the concentration of the density distribution of the random set at a given point. This paper investigates the properties of compactometry and its derivative, the density spectrum, and demonstrates how they can be used together with granulometry to address the problem of landmine/clutter discrimination using ground-penetrating radar sensors.
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