This book shows how different types of motion can be disambiguated into their components in a richer way than that currently possible in computer vision. Previous research of motion analysis has generally not yet considered the basic nature of higher orders of motion such as acceleration. Hence, this book introduces an approximation of the acceleration field using established optical flow techniques. Further, acceleration is decomposed into radial and tangential based on geometry and propagated as a general motion descriptor; this book shows the capability for differentiating different types of motion both on synthesized data and real image sequences. Beyond acceleration, the higher orders of motion flow and their continuant parts are investigated for further revealing the chaotic motion fields. Naturally, it is possible to extend this notion further: to detect higher orders of image motion. In this respect, this book shows how jerk and snap can be obtained from image sequences. The derived results on test images and heel strike detection in gait analysis illustrate the ability of higher-order motion, which provide the basis for the following research and applications in the future. We hope that the publication of this book will bring a new perspective to researchers and graduate students in the field of video analysis in computer vision.