Graph-based evidence accumulation for clustering 3D orientation measurements in planetary surface mapping under relational constraints

Groups of structural measurements based on orientation similarity are indicative of deformation mechanisms and are important measures to infer the deformation history of planetary surfaces. Despite methods for defining groups based only on orientation or spatial proximity, a general framework for defining orientation-based groups under multiple constraints is lacking. A second challenge pertains to the computational challenge of clustering large structural data due to the large volume and velocity of the data collected as a part of field-based, earth-observing, and planetary missions. In this paper, we propose a general clustering framework for defining groups in angular data based on orientation similarity that can be constrained with relational constraints, such as spatial proximity or prior knowledge of geologic units. We represent the similarity of geologic measurements with a similarity graph where similarity links (graph edges) are defined via the clustering evidence accumulated by re-clustering of data with varying parameters. We showcase the use of a spectral gap measure to define the optimal number of clusters for the evidence graph. We apply the proposed method to define groups of compaction bands using field data collected from the Valley of Fire, NV. We compare our results to a state-of-the-art Bingham mixture model. Results indicate the realism of the proposed method in terms of mapping distinct structural groups under different spatial proximity constraints.