On parameterizing higher-order motion for behaviour recognition

•Optical flow field is disambiguated systematically into acceleration, jerk and snap fields and their components. Our acceleration algorithm achieves superior performance to the state of art on efficiency and preciseness.•We show generalised application of higher-order motion detection in a richer selection of imagery for not only the new approach but also the new basis, on synthetic and on real image sequences.•Jerk and snap flow are applied for detecting heel strikes and the results demonstrates that jerk can be adapted in gait analysis or other applications on real images.•We demonstrate the capability to discriminate violence using velocity and acceleration flow and show the advantages of using analysis of acceleration.