Polar Linear Canonical Transform in Quaternion Domain

Nowadays, almost all images acquired are in color format. Traditional methods process color images by either transforming them into gray scale or dividing them into red, green, and blue components for independent processing, which is definitely not effective in representing color information. Recently, a novel Polar Linear Canonical Transform (PLCT) with parameters in SL(2,<) has been reported, which is a generalization of the well-known Polar Harmonic Transform (PHT). However, PLCT is defined on gray-scale images, so it cannot handle color images directly. To solve the problem, this paper generalizes PLCT from complex domain to hypercomplex domain using quaternion algebras, producing the Quaternion Polar Linear Canonical Transform (QPLCT). The performance of QPLCT is then evaluated with Quaternion Fractional Polar Exponential Transform (QPFrET) as an example. The experimental results show that the QPLCT performs better than the commonly used Quaternion form Zernike Moment (QZM) and pseudo-Zernike Moment (QPZM) in terms of image representation capability and numerical stability.