New Set of Quaternion Moments for Color Images Representation and Recognition

In this paper, a new set of quaternion radial-substituted Chebyshev moments (QRSCMs) is proposed for color image representation and recognition. These new moments are circular moments defined over a unit disk by using a new set of orthogonal basis functions called radial-substituted Chebyshev functions. A new hybrid method is proposed for highly accurate computation of QRSCMs in polar coordinates. In this method, the angular kernel is exactly computed by analytical integration of Fourier function over circular pixels. The radial kernel is computed using a recurrence relation which completely eliminates the coefficient matrix associated with the radial-substituted Chebyshev functions. Rotation, scaling, and translation (RST) invariances for QRSCMs are proved. Numerical experiments were conducted where the results of these experiments show better performance of QRSCMs over existing quaternion moments in terms of image reconstruction capabilities, RST invariances, robust to different noises, and CPU elapsed times.

[1]  Jian Zou,et al.  Generic orthogonal moments: Jacobi-Fourier moments for invariant image description , 2007, Pattern Recognit..

[2]  C Camacho-Bello,et al.  High-precision and fast computation of Jacobi-Fourier moments for image description. , 2014, Journal of the Optical Society of America. A, Optics, image science, and vision.

[3]  Gang Chen,et al.  Quaternion Zernike moments and their invariants for color image analysis and object recognition , 2012, Signal Process..

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

[5]  César Camacho-Bello,et al.  Reconstruction of color biomedical images by means of quaternion generic Jacobi-Fourier moments in the framework of polar pixels , 2016, Journal of medical imaging.

[6]  Ziliang Ping,et al.  Image description with Chebyshev-Fourier moments. , 2002, Journal of the Optical Society of America. A, Optics, image science, and vision.

[7]  Bin Xiao,et al.  Radial shifted Legendre moments for image analysis and invariant image recognition , 2014, Image Vis. Comput..

[8]  Tengfei Yang,et al.  Robust circularly orthogonal moment based on Chebyshev rational function , 2017, Digit. Signal Process..

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

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

[11]  Khalid M. Hosny.  Accurate Orthogonal Circular Moment Invariants of Gray-Level Images , 2011 .

[12]  William Rowan Hamilton,et al.  Elements of Quaternions , 1969 .

[13]  Miroslaw Pawlak,et al.  Accurate Computation of Zernike Moments in Polar Coordinates , 2007, IEEE Transactions on Image Processing.

[14]  Xiangyang Wang,et al.  Quaternion Exponent Moments and Their Invariants for Color Image , 2016, Fundam. Informaticae.

[15]  John Harris,et al.  Handbook of mathematics and computational science , 1998 .

[16]  Cordelia Schmid,et al.  A maximum entropy framework for part-based texture and object recognition , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

[17]  Xingming Sun,et al.  Color Face Recognition Using Quaternion Representation of Color Image , 2012 .

[18]  J. Faires,et al.  Numerical Methods , 2002 .

[19]  Cordelia Schmid,et al.  Semi-Local Affine Parts for Object Recognition , 2004, BMVC.

[20]  Ming Zhu,et al.  Quaternion Fourier-Mellin moments for color images , 2011, Pattern Recognit..

[21]  Jan Flusser,et al.  Affine Moment Invariants of Color Images , 2009, CAIP.

[22]  Khalid M. Hosny,et al.  Highly accurate and numerically stable higher order QPCET moments for color image representation , 2017, Pattern Recognit. Lett..

[23]  Xudong Jiang,et al.  Two-Dimensional Polar Harmonic Transforms for Invariant Image Representation , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[24]  Wang Xiang-yang,et al.  Invariant quaternion radial harmonic Fourier moments for color image retrieval , 2015 .

[25]  Mandyam D. Srinath,et al.  Orthogonal Moment Features for Use With Parametric and Non-Parametric Classifiers , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[26]  Xiangyang Wang,et al.  Quaternion polar complex exponential transform for invariant color image description , 2015, Appl. Math. Comput..

[27]  Min Wang,et al.  Fast computation of Zernike moments in polar coordinates , 2012 .

[28]  Khalid M. Hosny,et al.  Fast computation of orthogonal Fourier–Mellin moments in polar coordinates , 2009, Journal of Real-Time Image Processing.

[29]  Hui-Ping Wang,et al.  Statistical analysis of process parameters to eliminate hot cracking of fiber laser welded aluminum alloy , 2015 .

[30]  Ziliang Ping,et al.  Multidistortion-invariant image recognition with radial harmonic Fourier moments. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.