3D object detection using a fast voxel-wise local spherical Fourier tensor transformation

Authors:
Henrik Skibbe;Marco Reisert;Thorsten Schmidt;Klaus Palme;Olaf Ronneberger;Hans Burkhardt
Affiliations:
Department of Computer Science, University of Freiburg, Germany and Center for Biological Signalling Studies, University of Freiburg;Dept. of Diagnostic Radiology, Medical Physics, University Medical Center, Freiburg;Department of Computer Science, University of Freiburg, Germany and Center for Biological Signalling Studies, University of Freiburg;Institute of Biology II, Freiburg Institute for Advanced Studies and Center for Biological Signalling Studies, University of Freiburg;Department of Computer Science, University of Freiburg, Germany and Center for Biological Signalling Studies, University of Freiburg;Department of Computer Science, University of Freiburg, Germany and Center for Biological Signalling Studies, University of Freiburg
Venue:
Proceedings of the 32nd DAGM conference on Pattern recognition
Year:
2010

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Abstract

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 a-helices in cryo-EM density maps of secondary protein structures, leading to very promising results.