Improving filtering methods based on the fast Fourier transform to delineate objective relief domains: an application to Mare Ingenii lunar area

Abstract

A recent study has proven that high-pass filtering (HPF) based on the Fast Fourier Transform (FFT) is a rapid and efficient computational method for the semi-automated detection of geomorphic features from high-resolution digital elevation models (DEM). Although this new approach shows great potential for cartographic purposes using remote sensing data, some methodological improvements are still required in the following areas: (i) to develop a robust criteria for filter radius selection; (ii) to test the relationship between filter vectors and landscape form, and explore how DEM artefacts (vegetation, anthropic structures, etc.) can interfere with landform detection; and (iii) to explore filter response regarding generalisation and blurring effects when working with landscapes composed of landforms of different scales that are superimposed on one another. These topics are addressed here through two experiments (Experiment_1 and Experiment_2) with synthetic digital relief models inspired in the lunar landscape. Finally, the improved methodology was applied on the Mare Ingenii lunar relief (Experiment_3) using the Lunar Orbiter Laser Altimeter DEM and the results were tested against ground truths (GTs) developed using the extensive database available at Astropedia website and an ad hoc crater map. The analysis of existing frequencies in a 2D DEM signal through the true magnitude-true frequency plot provides an objective method for filter radius selection, and the use of a Butterworth transference function enables a more versatile filtering. Experiment_1 demonstrates a close correspondence between vectors obtained by filtering called Filtered Geomorphic References (FGRs) and the synthetic landform selected. The accuracy indicators from Experiment_1 and 2 show the good results obtained in the correspondence between FGRs and crater depressions, either from flat-bottomed to bowl shapes. Experiments 2 and 3 confirm that in landscapes generated by superimposed geomorphic features of different sizes, the smaller the crater, the better the filters detect its boundaries. Moreover, the spatial repeatability of FGRs can be used as a cartographic criterion in the identification of crater shape depressions or hills. Besides, the criterion is useful to assess true reality mapped in the GT employed. Finally, the objective geomorphic units obtained by combining the FGRs demonstrate their usefulness for the objective characterisation of the moonscape. Using the synthetic landscapes, the FGRs identify those relief domains composed of depressions and hills