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We present a technique to estimate the egomotion of an RGB-D sensor based on rotations of functions defined on the unit sphere. In contrast to traditional approaches, our technique is not based on image features and does not require correspondences to be generated between frames of data. Instead, consecutive functions are correlated using spherical harmonic analysis. An Extended Gaussian Image (EGI), created from the local normal estimates of a point cloud, defines each function. Correlations are efficiently computed using Fourier transformations, resulting in a 3 Degree of Freedom (3-DoF) rotation estimate. An Iterative Closest Point (ICP) process then refines the initial rotation estimate and adds a translational component, yielding a full 6-DoF egomotion estimate. The focus of this work is to investigate the merits of using spherical harmonic analysis for egomotion estimation by comparison with alternative 6-DoF methods. We compare the performance of the proposed technique with that of stand-alone ICP and image feature based methods. As with other egomotion techniques, estimation errors accumulate and degrade results, necessitating correction mechanisms for robust localization. For this report, however, we use the raw estimates; no filtering or smoothing processes are applied. In-house and external benchmark data sets are analyzed for both runtime and accuracy. Results show that the algorithm is competitive in terms of both accuracy and runtime, and future work will aim to

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