Error estimation of grain distribution function recovery for dependent orientations with allowance for grain sizes

he effect of the kernel on the smoothing of orientations in a kernel method was studied, and the influence of dependent orientations and the grain sizes on the resulting distribution was analyzed. Discrete central normal distributions on the group $\mathrm{SO}(3)$ were smoothed by the kernel method. This problem is motivated by the development of experimental tools for studying the texture of polycrystalline materials, especially electron microscopy, which makes it possible to measure the orientations of individual grains.