Morphometric consistency with the Hausdorff-Besicovich dimension
Studies using different measurement resolutions on a single morphologic feature may yield vastly different measured values for the perimeter. Apparent internal inconsistencies such as these have greatly impeded the numerical taxonomy, description, and modeling of landforms. Fortunately, the underlying internal consistency of measurements can often be reestablished by introducing the Hausdorff-Besicovich dimension into the analysis. This is demonstrated here by the example of perimeter-area ratio measurements made on some of the complicated ejecta deposits that surround many Martian meteorite-impact craters.