Two-Dimensional Polar Harmonic Transforms for Invariant Image Representation

This paper introduces a set of 2D transforms, based on a set of orthogonal projection bases, to generate a set of features which are invariant to rotation. We call these transforms Polar Harmonic Transforms (PHTs). Unlike the well-known Zernike and pseudo-Zernike moments, the kernel computation of PHTs is extremely simple and has no numerical stability issue whatsoever. This implies that PHTs encompass the orthogonality and invariance advantages of Zernike and pseudo-Zernike moments, but are free from their inherent limitations. This also means that PHTs are well suited for application where maximal discriminant information is needed. Furthermore, PHTs make available a large set of features for further feature selection in the process of seeking for the best discriminative or representative features for a particular application.

[1]  Jian Zou,et al.  Character Reconstruction with Radial-Harmonic-Fourier Moments , 2007, Fourth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2007).

[2]  Yoav Freund,et al.  Boosting the margin: A new explanation for the effectiveness of voting methods , 1997, ICML.

[3]  James Ze Wang,et al.  SIMPLIcity: Semantics-Sensitive Integrated Matching for Picture LIbraries , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[4]  Huazhong Shu,et al.  Moment-based approaches in imaging. Part 1, basic features. , 2007, IEEE engineering in medicine and biology magazine : the quarterly magazine of the Engineering in Medicine & Biology Society.

[5]  Roland T. Chin,et al.  On Image Analysis by the Methods of Moments , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[6]  Y. Sheng,et al.  Orthogonal Fourier–Mellin moments for invariant pattern recognition , 1994 .

[7]  A. Bhatia,et al.  On the circle polynomials of Zernike and related orthogonal sets , 1954, Mathematical Proceedings of the Cambridge Philosophical Society.

[8]  Glenn Healey,et al.  Using Zernike moments for the illumination and geometry invariant classification of multispectral texture , 1998, IEEE Trans. Image Process..

[9]  Huazhong Shu,et al.  Moment-based approaches in imaging part 3: computational considerations [A Look at...] , 2008, IEEE Engineering in Medicine and Biology Magazine.

[10]  A Look at . . . moment-based approaches in imaging part 2 : invariance , 2022 .

[11]  Miroslaw Pawlak,et al.  On the Accuracy of Zernike Moments for Image Analysis , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[12]  Limin Luo,et al.  Moment-Based Approaches in Imaging. 1. Basic Features [A Look At ...] , 2007, IEEE Engineering in Medicine and Biology Magazine.

[13]  Marcin Novotni,et al.  3D zernike descriptors for content based shape retrieval , 2003, SM '03.

[14]  Demetri Psaltis,et al.  Image Normalization by Complex Moments , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[15]  Xudong Jiang,et al.  Boosted complex moments for discriminant rotation invariant object recognition , 2008, 2008 19th International Conference on Pattern Recognition.

[16]  Hon-Son Don,et al.  3-D Moment Forms: Their Construction and Application to Object Identification and Positioning , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[17]  Demetri Psaltis,et al.  Recognitive Aspects of Moment Invariants , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[18]  M. Teague.  Image analysis via the general theory of moments , 1980 .

[19]  D. Jackson,et al.  fourier series and orthogonal polynomials , 1943, The Mathematical Gazette.

[20]  Sugata Ghosal,et al.  Detection of composite edges , 1994, IEEE Trans. Image Process..

[21]  D. R. Iskander,et al.  Optimal modeling of corneal surfaces with Zernike polynomials , 2001, IEEE Transactions on Biomedical Engineering.

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

[23]  Yoav Freund,et al.  A decision-theoretic generalization of on-line learning and an application to boosting , 1995, EuroCOLT.

[24]  Chee-Way Chong,et al.  A comparative analysis of algorithms for fast computation of Zernike moments , 2003, Pattern Recognit..

[25]  Heung-Kyu Lee,et al.  Invariant image watermark using Zernike moments , 2003, IEEE Trans. Circuits Syst. Video Technol..

[26]  Mandyam D. Srinath,et al.  Invariant character recognition with Zernike and orthogonal Fourier-Mellin moments , 2002, Pattern Recognit..

[27]  Mohammed Al-Rawi,et al.  Fast Zernike moments , 2008, Journal of Real-Time Image Processing.

[28]  Andrew Beng Jin Teoh,et al.  An efficient method for human face recognition using wavelet transform and Zernike moments , 2004, Proceedings. International Conference on Computer Graphics, Imaging and Visualization, 2004. CGIV 2004..

[29]  Yoshua Bengio,et al.  Gradient-based learning applied to document recognition , 1998, Proc. IEEE.

[30]  Jan Flusser,et al.  Construction of Complete and Independent Systems of Rotation Moment Invariants , 2003, CAIP.

[31]  Chin-Liang Wang,et al.  A new two-dimensional block adaptive FIR filtering algorithm and its application to image restoration , 1998, IEEE Trans. Image Process..

[32]  David P. Dobkin,et al.  A search engine for 3D models , 2003, TOGS.

[33]  Andrew Teoh Beng Jin,et al.  An efficient method for human face recognition using wavelet transform and Zernike moments , 2004 .

[34]  J Duvernoy,et al.  Circular-Fourier-radial-Mellin transform descriptors for pattern recognition. , 1986, Journal of the Optical Society of America. A, Optics and image science.