Digital image processing is a field that has diverse applications, such as remote sensing, computer vision, medical imaging, computer graphics, graphic arts, pattern recognition, and industrial inspection. There have been many books that cover the general topics of digital image processing in varying depths and applications (e.g., [86, 165, 262, 351, 363, 456, 457, 594, 752, 776, 807, 841]). Readers are encouraged to consult these books for various operations and algorithms for digital image processing. Most of the books deal with monochromatic images. When dealing with color images, there are several concepts that are inherently quite different. For example, if we treat the RGB signals at a pixel as a three-dimensional vector, a color image becomes a vector field, while a monochromatic image is a scalar field. Typical operations, such as the gradient of an image, have to be thought over again because simply repeating the same scalar operation three times is often not the best thing to do. Another important reason for much of the required rethinking is that our visual perception of a color image is usually described in terms of luminance–chrominance color attributes, not RGB color channels. A color image simply provides much more information than a monochromatic image about the scene, its material properties and its illumination. We have to think and rethink about how to extract the additional information more effectively for the applications we have in mind. In this chapter, we will study some basic issues and explore some new concepts for formulating old problems which we might have encountered when working on monochromatic image processing.