Fast Polar and Spherical Fourier Descriptors for Feature Extraction

Polar Fourier Descriptor(PFD) and Spherical Fourier Descriptor(SFD) are rotation invariant feature descriptors for two dimensional(2D) and three dimensional(3D) image retrieval and pattern recognition tasks. They are demonstrated to show superiorities compared with other methods on describing rotation invariant features of 2D and 3D images. However in order to increase the computation speed, fast computation method is needed especially for machine vision applications like realtime systems, limited computing environments and large image databases. This paper presents fast computation method for PFD and SFD that are deduced based on mathematical properties of trigonometric functions and associated Legendre polynomials. Proposed fast PFD and SFD are 8 and 16 times faster than direct calculation that significantly boost computation process. Furthermore, the proposed methods are also compact for memory requirements for storing PFD and SFD basis in lookup tables. The experimental results on both synthetic and real data are given to illustrate the efficiency of the proposed method.

[1]  Guojun Lu,et al.  A Comparative Study of Fourier Descriptors for Shape Representation and Retrieval , 2002 .

[2]  T. J. Dennis,et al.  3D model representation using spherical harmonics , 1997 .

[3]  King-Sun Fu,et al.  Shape Discrimination Using Fourier Descriptors , 1977, IEEE Transactions on Pattern Analysis and Machine Intelligence.

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

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

[6]  Fillia Makedon,et al.  A Novel Surface Registration Algorithm With Biomedical Modeling Applications , 2007, IEEE Transactions on Information Technology in Biomedicine.

[7]  Ari Visa,et al.  Multiscale Fourier descriptors for defect image retrieval , 2006, Pattern Recognit. Lett..

[8]  Larry C. Andrews,et al.  Special Functions Of Mathematics For Engineers , 2022 .

[9]  Didier Lemoine,et al.  The discrete Bessel transform algorithm , 1994 .

[10]  Guojun Lu,et al.  Shape-based image retrieval using generic Fourier descriptor , 2002, Signal Process. Image Commun..

[11]  Witold A. J. Kosmala,et al.  Advanced Calculus: A Friendly Approach , 1998 .

[12]  Rob H. Bisseling,et al.  The fast Hankel transform as a tool in the solution of the time dependent Schrödinger equation , 1985 .

[13]  Ilaria Bartolini,et al.  WARP: accurate retrieval of shapes using phase of Fourier descriptors and time warping distance , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.