  Topographic mapping in planetary environments relies on accurate 3D scan
registration methods. However, most global registration algorithms relying on
features such as FPFH and Harris-3D show poor alignment accuracy in these
settings due to the poor structure of the Mars-like terrain and variable
resolution, occluded, sparse range data that is hard to register without some
a-priori knowledge of the environment. In this paper, we propose an alternative
approach to 3D scan registration using the curvelet transform that performs
multi-resolution geometric analysis to obtain a set of coefficients indexed by
scale (coarsest to finest), angle and spatial position. Features are detected
in the curvelet domain to take advantage of the directional selectivity of the
transform. A descriptor is computed for each feature by calculating the 3D
spatial histogram of the image gradients, and nearest neighbor based matching
is used to calculate the feature correspondences. Correspondence rejection
using Random Sample Consensus identifies inliers, and a locally optimal
Singular Value Decomposition-based estimation of the rigid-body transformation
aligns the laser scans given the re-projected correspondences in the metric
space. Experimental results on a publicly available data-set of planetary
analogue indoor facility, as well as simulated and real-world scans from Neptec
Design Group's IVIGMS 3D laser rangefinder at the outdoor CSA Mars yard
demonstrates improved performance over existing methods in the challenging
sparse Mars-like terrain.
