Fast computation of 3D spherical Fourier harmonic descriptors - a complete orthonormal basis for a rotational invariant representation of three-dimensional objects

In this paper we propose to extend the well known spherical harmonic descriptors[6] (SHD) by adding an additional Fourier-like radial expansion to represent volumetric data. Having created an orthonormal basis on the ball with all the gentle properties known from the spherical harmonics theory and Fourier theory, we are able to compute efficiently a multi-scale representation of 3D objects that leads to highly discriminative rotation-invariant features, which will be called spherical Fourier harmonic descriptors (SFHD). Experiments on the challenging Princeton Shape Benchmark (PSB[16]) demonstrate the superiority of SFHD over the ordinary SHD.

[1]  Hans Burkhardt,et al.  Second order 3D shape features: An exhaustive study , 2006, Comput. Graph..

[2]  Hanns Schulz-Mirbach,et al.  Anwendung von Invarianzprinzipien zur Merkmalgewinnung in der Mustererkennung , 1995 .

[3]  Szymon Rusinkiewicz,et al.  Rotation Invariant Spherical Harmonic Representation of 3D Shape Descriptors , 2003, Symposium on Geometry Processing.

[4]  Steven G. Johnson,et al.  The Design and Implementation of FFTW3 , 2005, Proceedings of the IEEE.

[5]  Jack Dongarra,et al.  Special Issue on Program Generation, Optimization, and Platform Adaptation , 2005, Proc. IEEE.

[6]  Qing Wang,et al.  Rotational Invariance Based on Fourier Analysis in Polar and Spherical Coordinates , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[7]  Qing Wang,et al.  3D Invariants with High Robustness to Local Deformations for Automated Pollen Recognition , 2007, DAGM-Symposium.

[8]  Thomas A. Funkhouser,et al.  The Princeton Shape Benchmark , 2004, Proceedings Shape Modeling Applications, 2004..

[9]  Atilla Baskurt,et al.  Generalizations of angular radial transform for 2D and 3D shape retrieval , 2005, Pattern Recognit. Lett..

[10]  M. E. Rose.  Elementary Theory of Angular Momentum , 1957 .

[11]  Guoping Qiu,et al.  Human face detection using angular radial transform and support vector machines , 2003, Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429).

[12]  Hans Burkhardt,et al.  Efficient Tensor Voting with 3D tensorial harmonics , 2008, 2008 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops.

[13]  Daniel N. Rockmore,et al.  S2kit: A Lite Version of SpharmonicKit , 2004 .

[14]  Andrea J. van Doorn,et al.  Generic Neighborhood Operators , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[15]  Marco Reisert,et al.  Group integration techniques in pattern analysis - a kernel view , 2008, Ausgezeichnete Informatikdissertationen.

[16]  Nikolaos Canterakis,et al.  3D Zernike Moments and Zernike Affine Invariants for 3D Image Analysis and Recognition , 1999 .

[17]  Robin Green,et al.  Spherical Harmonic Lighting: The Gritty Details , 2003 .