Wavelet-based moment invariants for pattern recognition

Moment invariants have received a lot of attention as features for identification and inspection of two-dimensional shapes. In this paper, two sets of novel moments are proposed by using the auto-correlation of wavelet functions and the dual-tree complex wavelet functions. It is well known that the wavelet transform lacks the property of shift invariance. A little shift in the input signal will cause very different output wavelet coefficients. The autocorrelation of wavelet functions and the dual-tree complex wavelet functions, on the other hand, are shift-invariant, which is very important in pattern recognition. Rotation invariance is the major concern in this paper, while translation invariance and scale invariance can be achieved by standard normalization techniques. The Gaussian white noise is added to the noise-free images and the noise levels vary with different signal-to-noise ratios. Experimental results conducted in this paper show that the proposed wavelet-based moments outperform Zernike's moments and the Fourier-wavelet descriptor for pattern recognition under different rotation angles and different noise levels. It can be seen that the proposed wavelet-based moments can do an excellent job even when the noise levels are very high.

[1]  J. Flusser,et al.  Moments and Moment Invariants in Pattern Recognition , 2009 .

[2]  Raveendran Paramesran,et al.  Image analysis by Krawtchouk moments , 2003, IEEE Trans. Image Process..

[3]  Thomas Lengauer,et al.  Moment invariants as shape recognition technique for comparing protein binding sites , 2007, Bioinform..

[4]  Sim Heng Ong,et al.  Image Analysis by Tchebichef Moments , 2001, IEEE Trans. Image Process..

[5]  Nick G. Kingsbury,et al.  Multiscale classification using complex wavelets and hidden Markov tree models , 2000, Proceedings 2000 International Conference on Image Processing (Cat. No.00CH37101).

[6]  Adam Krzyzak,et al.  Invariant pattern recognition using radon, dual-tree complex wavelet and Fourier transforms , 2009, Pattern Recognit..

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

[8]  Gregory Dudek,et al.  Auto-correlation wavelet support vector machine , 2009, Image Vis. Comput..

[9]  Alireza Khotanzad,et al.  Rotation invariant image recognition using features selected via a systematic method , 1990, Pattern Recognition.

[10]  R. Mukundan,et al.  Moment Functions in Image Analysis: Theory and Applications , 1998 .

[11]  Naoki Saito,et al.  Multiresolution representations using the autocorrelation functions of compactly supported wavelets , 1993, IEEE Trans. Signal Process..

[12]  Ming-Kuei Hu,et al.  Visual pattern recognition by moment invariants , 1962, IRE Trans. Inf. Theory.

[13]  Nick G. Kingsbury,et al.  A dual-tree complex wavelet transform with improved orthogonality and symmetry properties , 2000, Proceedings 2000 International Conference on Image Processing (Cat. No.00CH37101).

[14]  Nick G. Kingsbury,et al.  Shift invariant properties of the dual-tree complex wavelet transform , 1999, 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258).

[15]  Adam Krzyzak,et al.  Rotation invariant feature extraction using Ridgelet and Fourier transforms , 2006, Pattern Analysis and Applications.

[16]  Yajun Li,et al.  Reforming the theory of invariant moments for pattern recognition , 1992, Pattern Recognit..

[17]  Richard J. Prokop,et al.  A survey of moment-based techniques for unoccluded object representation and recognition , 1992, CVGIP Graph. Model. Image Process..

[18]  Thomas H. Reiss,et al.  The revised Fundamental Theorem of Moment Invariants , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[19]  R. Mukundan,et al.  Some computational aspects of discrete orthonormal moments , 2004, IEEE Transactions on Image Processing.

[20]  Dong Xu,et al.  Geometric moment invariants , 2008, Pattern Recognit..

[21]  Prabir Bhattacharya,et al.  Invariant Pattern Recognition Using Ridgelet Packets and the Fourier Transform , 2009, Int. J. Wavelets Multiresolution Inf. Process..

[22]  Miroslaw Pawlak,et al.  On Image Analysis by Moments , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[23]  Dinggang Shen,et al.  Discriminative wavelet shape descriptors for recognition of 2-D patterns , 1999, Pattern Recognit..

[24]  Alireza Khotanzad,et al.  Invariant Image Recognition by Zernike Moments , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[25]  Nick G. Kingsbury,et al.  The dual-tree complex wavelet transform: A new efficient tool for image restoration and enhancement , 1998, 9th European Signal Processing Conference (EUSIPCO 1998).

[26]  Justin K. Romberg,et al.  Multiscale classification using complex wavelets , 2000 .

[27]  Robert B. McGhee,et al.  Aircraft Identification by Moment Invariants , 1977, IEEE Transactions on Computers.

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

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

[30]  Guangyi Chen,et al.  Invariant Fourier-wavelet descriptor for pattern recognition , 1999, Pattern Recognit..

[31]  Adam Krzyzak,et al.  Rotation invariant pattern recognition using ridgelets, wavelet cycle-spinning and Fourier features , 2005, Pattern Recognit..