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Quaternion Polar Harmonic Transforms for Color Images

Robust and compact content representation is a fundamental problem in image processing. The recently proposed polar harmonic transforms (PHTs) have provided a set of powerful tools for image representation. However, two-dimensional transforms cannot handle color image in a holistic manner. To extend the nice properties of PHTs to color image processing, we generalize PHTs from the complex field to hypercomplex field in this letter, and quaternion polar harmonic transforms (QPHTs) are developed based on quaternion algebra. Furthermore, the properties of QPHTs are studied via quaternion computation, including the orthogonality of quaternion kernels, the relationships between different transforms and their rotation invariance. Experimental results reveal that compared with complex PHTs, the quaternion transforms can make a more compact and discriminative representation of color image. Moreover, QPHTs can well capture the chromatic features and exploit the inter-channel redundancies of color image.