text: 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.
  @cite_36: This paper presents HSM3D, an algorithm for global rigid 6DOF alignment of 3D point clouds. The algorithm works by projecting the two input sets into the Radon Hough domain, whose properties allow to decompose the 6DOF search into a series of fast one-dimensional cross-correlations. No planes or other particular features must be present in the input data, and the algorithm is provably complete in the case of noise-free input. The algorithm has been experimentally validated on publicly available data sets.
  @cite_19: We propose a novel technique for the registration of 3D point clouds which makes very few assumptions: we avoid any manual rough alignment or the use of landmarks, displacement can be arbitrarily large, and the two point sets can have very little overlap. Crude alignment is achieved by estimation of the 3D-rotation from two Extended Gaussian Images even when the data sets inducing them have partial overlap. The technique is based on the correlation of the two EGIs in the Fourier domain and makes use of the spherical and rotational harmonic transforms. For pairs with low overlap which fail a critical verification step, the rotational alignment can be obtained by the alignment of constellation images generated from the EGIs. Rotationally aligned sets are matched by correlation using the Fourier transform of volumetric functions. A fine alignment is acquired in the final step by running Iterative Closest Points with just few iterations.
summary: Another transformation found in the literature relies on finding a translation invariant Fourier transform on two Extended Gaussian Images (EGI) @cite_19 of laser scans, where the surface normals of an object are mapped onto the unit sphere. However, this approach can only be applied to smooth surfaces and fails to match surfaces with constant EGI (such as a sphere). @cite_36 proposed another approach to scan matching that projects the two scans into the Hough Radon domain @cite_36 defined on the unit sphere. Similar to the work of , a translation invariant spectrum is computed to find the rotation and cross-correlations are used to find the translation. Both EGI approaches and the ones based on transformation to Hough Radon domain are sensitive to the measurement noise and sampling density during the calculation of normals.