Use of the quaternion exponential form in the analysis of RGB and HSV images

The thesis investigated the effect of changes made to a colour image on its phase components. Each pixel of an RGB/HSV image is represented as a unit quaternion whose phase components are expressed by Euler angles. The theoretical part presents the mathematical foundations of the quaternion exponential representation. The experimental part involved developing a computer program and carrying out a series of experiments on three test images. All of them were subjected to selected transformations: brightening, darkening, blurring, sharpening and saturation enhancement. The implemented program made it possible to determine the differences between the phase angles of the original and modified images. Possible practical applications of the developed method are proposed.