Quaternion polar complex exponential transform for invariant color image description

Moments and moment invariants have been widely used as a basic feature descriptors in image analysis, pattern recognition, and image retrieval. However, they are mainly used to deal with the binary or gray-scale images, which lose some significant color information. Recently, quaternion techniques were introduced to conventional image moments (including Fourier-Mellin moments, Zernike/Pseudo Zernike moments, and Bessel-Fourier moments, etc.) for describing color images, and some quaternion moment and moment invariants were developed. But, the conventional image moments usually cannot effectively capture the image information, especially the edges. Besides, the kernel computation of them involves computation of a number of factorial terms, which inevitably cause the numerical stability of these moments. Based on effective polar complex exponential transform (PCET) and algebra of quaternions, we introduced the quaternion polar complex exponential transform (QPCET) for describing color images in this paper, which can be seen as the generalization of PCET for gray-level images. It is shown that the QPCETs can be obtained from the PCET of each color channel. We derived and analyzed the rotation, scaling, and translation (RST) invariant property of QPCET. We also discussed the problem of color image retrieval using QPCET. Experimental results are provided to illustrate the efficiency of the proposed color image descriptors.