3D Object Detection Using a Fast Voxel-Wise Local Spherical Fourier Tensor Transformation

In this paper we present a novel approach for expanding spherical 3D-tensor fields of arbitrary order in terms of a tensor valued local Fourier basis. For an efficient implementation, a two step approach is suggested combined with the use of spherical derivatives. Based on this new transformation we conduct two experiments utilizing the spherical tensor algebra for computing and using rotation invariant features for object detection and classification. The first experiment covers the successful detection of non-spherical root cap cells of Arabidopsis root tips presented in volumetric microscopical recordings. The second experiment shows how to use these features for successfully detecting α−helices in cryo-EM density maps of secondary protein structures, leading to very promising results.