It is well known that the human visual system is very sensitive to gradients. An image gradient is a directional change in the intensity or color in the image. Image gradients have been used to create new images with “visualized edges." Moreover, image gradients are very important (or they are central building blocks) in many graphics, computer vision, robotics, imaging systems and visual surveillance applications. For instance, gradients can be used for extracting the useful information (structure, feature, and properties of objects) from images.
In this chapter, we cover the commonly used several gradient operators and introduce the human visual system based several new gradient operators for grayscale images, as well as for color images. New gradient operators in quaternion space, wherein the color images can be transferred, are also described and examples are given. The concepts of Weber-Fisher law-related visibility operators and images are presented and their applications in face recognition are described in Refs. 40 and 44. The extraction of features in the facial image representation is an important task in face recognition systems. Since the most information of the objects is in the contours of objects, different types of gradients are used to extract the edges, contours, and texture of objects. In face images, the important features of the size, shape, and face orientation are in points of the lines of eyes, nose, lips, and cheekbones. We also consider the application of visibility images related to the Michelson contrast, EME measure in face detection, and facial image representation. The grayscale facial image representation with the local binary patterns (LBP) is described and examples are given. The application of color image gradients and visibility images in extracting features for color face recognition is also presented. For that, the quaternion operation of the 2-D convolution of the quaternion image with the quaternion kernel is described and applied for quaternion gradient operations.
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