2D Quaternion Fourier Transform: The Spectrum Properties and its Application in Color Image Registration

We first investigate 2D quaternion Fourier transform (QFT) spectrum relationship between an image and its geometrically transformed counterpart from the aspects of gray images and color images respectively, and then propose a 2D QFT-based color image registration approach, which is able to handle large translation, rotation and scaling. Fourier transform (FT) can be utilized in gray image registration but can not process color images naturally. As the extended version of FT in multidimensional signal processing, QFT is capable of processing three color components of color images together as pure quaternions and is able to deal with color image registration.