Calculation of the orientation distribution function from a set of individual orientations on $\mathrm{SO}(3)$

Kernel and projection methods for recovering the density function on the rotation group $\mathrm{SO}(3)$ are considered. Numerical examples are presented in which the density function is estimated depending on the sample size, a smoothing parameter (in the case of kernel methods), the approximation kernel, and the error in the input data. A set of orientations is specified by normally distributed rotations on $\mathrm{SO}(3)$ derived by the Monte Carlo method.