Chapter 1 Overview Chapter 2 Describing Motion in Computer Images' Stream: Optical Flow 2.1 Overview 2.2 Optical Flow 2.2.1 Data Term 2.2.2 Prior Term 2.2.3 Learning Methods 2.3 Selected Optical Flow Algorithms 2.3.1 Differential Method 2.3.2 Region-Based Method 2.3.3 Dense Optical Flow 2.3.4 DeepFlow 2.4 Preparation for Performance Quantify of Optical Flow Algorithms 2.4.1 Synthetic Images with Explicit Motion 2.4.2 Flow Visualization 2.4.3 Flow Error Measurements 2.5 Performance Comparison of Optical Flow Algorithms on Synthetic Images Chapter 3 Analysing Acceleration in Computer Images' Stream 3.1 Overview 3.2 Estimation of Acceleration Flow 3.2.1 Recovering Acceleration from Optical Flow 3.2.2 Approximating the Derivatives 3.2.3 Analysing Acceleration Algorithm on Image Sequences 3.3 Estimating Acceleration Flow via Other Flow Estimation Methods 3.3.1 A More Practical Approach 3.3.2 Evaluating Acceleration Algorithms on Synthetic Images 3.3.3 Comparison between Differential and Variational Acceleration 3.4 Tangential and Radial Acceleration 3.4.1 Decomposing the Resultant Acceleration 3.4.2 Radial and Tangential Acceleration Fields on Image Sequences 3.5 Conclusion Chapter 4 Jerk and High-Order Motion in Computer Images' Streams 4.1 Overview 4.2 Jerk, Snap and High-Order Motion in Kinematics 4.3 Jerk and Snap Field Estimation 4.4 Applying Multi-Order Flow Fields to Synthetic and Real Images 4.5 Conclusion Chapter 5 Detecting Heel Strikes for Gait Analysis through High-Order Motion Flow 5.1 Overview 5.2 Detecting Heel Strikes through Radial Acceleration 5.2.1 Gait Analysis 5.2.2 Heel Strike Detection for Gait Analysis 5.2.3 The Acceleration Pattern on Gait 5.2.4 Strike Position Estimation and Verification 5.3 Gait Databases 5.3.1 The Large Gait Database 5.3.2 CASIA Gait Database 5.3.3 The OU-ISIR Gait Database 5.4 Experimental Results 5.4.1 Key Frame Detection 5.4.2 Heel Strike Position Verification 5.4.3 Detection Performance 5.4.4 Robustness of Heel Strike Detection Approaches 5.4.5 Detecting Heel Strikes via Snap and Jerk 5.5 Discussion 5.6 Conclusion Chapter 6 More Potential Applications via High-Order Motion 6.1 Scene Segmentation 6.2 Gait Analysis References