2-D Quaternion Discrete Fourier Transform in Color Image Enhancement
Research problems are related to developing enhancement methods using 2-D quaternion discrete Fourier transform, which preserve the color integrity of the image while processing. In all our proposed enhancement methods, the enhancement of the color image is done by moving color images to quaternion space and using transform based enhancement techniques. The quaternion number is a four-dimensional hyper-complex number and the Fourier transform in quaternion space are many and are primarily defined as right-sided, left-sided, and two-sided quaternion discrete Fourier transform. By developing fast algorithm for computing the four-dimensional 2-D quaternion Fourier transform we are able to use enhancement methods based on Fourier transform. Traditionally, color images are enhanced by applying the enhancement methods on each of the channels separately. This channel-by-channel approach does not consider color as a single unit and therefore such methods compromises the color identity of the image-objects. But, we have analyzed many enhancement methods which keeps intact the color identity of the image-object in images in RGB color models, and other color models such as XYZ, CMY, and CMYK. A few of the proposed enhancement methods implemented using the quaternion Fourier transform are alpha-rooting, alpha-rooting with spatial transformation, zonal-alpha-rooting, modified alpha-rooting, and retinex followed by the alpha-rooting method. Preliminary experimental results show that the proposed methods are effective when compared with component-wise enhancement methods. The enhancement is quantitatively measured by a proposed enhancement measure estimation. The optimum choice of alpha is determined by a genetic algorithm which is a robust optimization method. In our research, we also propose a few other quaternion based enhancement methods implemented in quaternion space in spatial domain including alpha-rooting in spatial domain which are found to be effective tools for processing color images. The application of enhancement methods specifically on medical images and underwater images show good results.