Abstract: Highlights•Quaternion polar harmonic Fourier moments (QPHFM) is proposed.•Complex Chebyshev-Fourier moments (CHFM) is extended to quaternion QCHFM.•Comparison experiments between QPHFM and QZM, QPZM, QOFMM, QCHFM and QRHFM are conducted.•QPHFM performs superbly in image reconstruction and invariant object recognition.•The importance of phase information of QPHFM in image reconstruction are discussed.
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