Fast Summation of Functions on the Rotation Group

Ralf Hielscher*, Jürgen Prestin, Antje Vollrath

*Corresponding author for this work
7 Citations (Scopus)


Computing with functions on the rotation group is a task carried out in various areas of application. When it comes to approximation, kernel based methods are a suitable tool to handle these functions. In this paper, we present an algorithm which allows us to evaluate linear combinations of functions on the rotation group as well as a truly fast algorithm to sum up radial functions on the rotation group. These approaches based on nonequispaced FFTs on SO(3) take O(M+N) arithmetic operations for M and N arbitrarily distributed source and target nodes, respectively. In this paper, we investigate a selection of radial functions and give explicit theoretical error bounds, as well as numerical examples of approximation errors. Moreover, we provide an application of our method, namely the kernel density estimation from electron back scattering diffraction (EBSD) data, a problem relevant in texture analysis.

Original languageEnglish
JournalMathematical Geosciences
Issue number7
Pages (from-to)773-794
Number of pages22
Publication statusPublished - 09.06.2010


Dive into the research topics of 'Fast Summation of Functions on the Rotation Group'. Together they form a unique fingerprint.

Cite this