High-Orders Motion Analysis: Computer Vision Methods

Preface
Contents
Abbreviations
1 Overview
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
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
4 Jerk and High-Order Motion in Computer Images’ Streams
	4.1 Overview
	4.2 Jerk, Snap and€Higher Order Motion in€Kinematics
	4.3 Jerk and€Snap Field Estimation
	4.4 Appling Multi-orders Flow Fields to€Synthetic and€Real Images
	4.5 Conclusion
5 Detecting Heel Strikes for€Gait Analysis Through Higher-Order Motion Flow
	5.1 Overview
	5.2 Detecting Heel Strikes Through Radial Acceleration
		5.2.1 Gait Analysis
		5.2.2 Heel Strikes 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 Conclusions
6 More Potential Applications Via High-Order Motion
	6.1 Scenes Segmentation
	6.2 Gait Analysis
References