Parameterization of Features on Spherical Surfaces

NASA’s Planetary Systems Laboratory (PSL) at the Goddard Spaceflight Center in Greenbelt, Maryland is tasked with the study of solar system objects. This work is frequently based on analysis of imagery from visiting spacecraft, orbiting telescopes, and ground-based sensors.
A consequence of this mission is the need to characterize features on the spherical surface of planets and moons, such characterization including the overall area of the feature, its center, its moments of inertia, its perimeter, its compactness, its major axis, its bounding box, its aspect ratio and its North-South orientation. Accurate assessment of these measures from a “flat” two-dimensional image is a challenge, since the scale of distance observed at the center of a spherical object distorts in any direction towards the horizon.
PSL has developed a technique to guarantee accurate and automated measurement at any point on the visible surface, by overlaying an imaginary grid of equal-area cells onto the two-dimensional image of the sphere. The technique is named Grid-Oriented Normalization for Analysis of Spherical Areas (GONASA).
This paper discusses the construction of the normalization grid and describes specific algorithms for feature parameterization. The algorithms are implemented in an accompanying Excel spreadsheet, both for clarity and ease of adoption, and to emphasize their aptness for automation. Finally, a concrete use case is offered where the GONASA grid and algorithms are used to characterize methane clouds on the Saturnian moon Titan.