Density Estimation on the rotation group using Diffusive wavelets

This paper considers the problem of estimating probability density functions on the rotation group SO(3). Two distinct approaches are proposed, one based on characteristic functions and the other on wavelets using the heat kernel. Expressions are derived for their Mean Integrated Squared Errors. The performance of the estimators is studied numerically and compared with the performance of an existing technique using the De La Vallée Poussin kernel estimator. The heat-kernel wavelet approach appears to offer the best convergence, with faster convergence to the optimal bound and guaranteed positivity of the estimated probability density function. Index Terms Probability density estimation, Rotation group SO(3), Diffusive wavelets, Characteristic function, Kernel estimators, Mean Integrated Square Error (MISE), Mixture of densities.