Invariant quaternion radial harmonic Fourier moments for color image retrieval

•A new color image descriptor, namely quaternion radial harmonic Fourier moments (QRHFMs), is introduced.•The invariant property of QRHFMs is derived and analyzed.•A QRHFMs based color image retrieval scheme is presented.

Moments and moment invariants have become a powerful tool in image processing owing to their image description capability and invariance property. But, conventional methods are mainly introduced to deal with the binary or gray-scale images, and the only approaches for color image always have poor color image description capability. Based on radial harmonic Fourier moments (RHFMs) and quaternion, we introduced the quaternion radial harmonic Fourier moments (QRHFMs) for representing color images in this paper, which can be seen as the generalization of RHFMs for gray-level images. It is shown that the QRHFMs can be obtained from the RHFMs of each color channel. We derived and analyzed the rotation, scaling, and translation (RST) invariant property of QRHFMs. We also discussed the problem of color image retrieval using invariant QRHFMs. Experimental results are provided to illustrate the efficiency of the proposed color image representation.