High-Orders Motion Analysis: Computer Vision Methods

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. 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