Quaternion higher-order spectra and their invariants for color image recognition

• Introducing the definition of quaternion higher-order spectra (QHOS).
• Deriving the equivalent form of QHOS in the frequency domain.
• Proposing the QHOS invariants generation method for color images.
• The derived QHOS invariants are rotation, translation, and scaling invariant.
• The derived QHOS invariants are highly immune to background noise.

This paper describes an invariants generation method for color images, which could be a useful tool in color object recognition tasks. First, by using the algebra of quaternions, we introduce the definition of quaternion higher-order spectra (QHOS) in the spatial domain and derive its equivalent form in the frequency domain. Then, QHOS invariants with respect to rotation, translation, and scaling transformations for color images are constructed using the central slice theorem and quaternion bispectral analysis. The feature data are further reduced to a smaller set using quaternion principal component analysis. The proposed method can deal with color images in a holistic manner, and the constructed QHOS invariants are highly immune to background noise. Experimental results show that the extracted QHOS invariants form compact and isolated clusters, and that a simple minimum distance classifier can yield high recognition accuracy.