Phone cameras are currently used in various medical fields for processing color images. Today they can play an important role in facilitating access to some diagnostic services because they are available to many people, including doctors and patients who do not have access to advanced imaging systems. Image enhancement via cell phones is a highly desired preprocessing tool because many pictures and images are poor in quality. Processing of color images in one of the known color models, such as RGB, XYZ, or HSV15 is a very difficult task and has attracted much research interest in the last decade. In traditional color image processing, each color channel (red, green, and blue in the RGB color space, for example) is separately considered, then the color image is composed. In such a simple approach, the inherent correlation between the components are not taken into account; this fact results in color artifacts. For another approach that simultaneously processes the color components of the image,19 the most promising tool is the theory of quaternion algebra with 2D quaternion transforms, such as the Fourier, Hadamard, and cosine transforms. The 2D discrete Fourier transform (DFT) is still the primary transform used in image enhancement and filtration. Therefore, we will focus on an extension of this transform in quaternion arithmetic. The color image as a three-component image is mapped into pure quaternion data and can be called a color-in-quaternion image. This quaternion-transform-based approach can effectively be used in different applications of color science. First introduced by Hamilton,quaternion numbers now are used in bioinformatics, navigation systems,6 image and video processing, and in a number of studies on quaternions in color image processing. Here, we note that since quaternion multiplication is not commutative, different definitions of quaternion Fourier transforms can be used in color image processing.
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