Hierarchical Implicit Surface Joint Limits for Human Body Tracking

To increase the reliability of existing human motion tracking algorithms, we propose a method for imposing limits on the underlying hierarchical joint structures in a way that is true to life. Unlike most existing approaches, we explicitly represent dependencies between the various degrees of freedom and derive these limits from actual experimental data. To this end, we use quaternions to represent individual 3 DOF joint rotations and Euler angles for 2 DOF rotations, which we have experimentally sampled using an optical motion capture system. Each set of valid positions is bounded by an implicit surface and we handle hierarchical dependencies by representing the space of valid configurations for a child joint as a function of the position of its parent joint. This representation provides us with a metric in the space of rotations that readily lets us determine whether a posture is valid or not. As a result, it becomes easy to incorporate these sophisticated constraints into a motion tracking algorithm, using standard constrained optimization techniques. We demonstrate this by showing that doing so dramatically improves performance of an existing system when attempting to track complex and ambiguous upper body motions from low quality stereo data

Using biomechanical constraints to improve video-based motion capture

In motion capture applications whose aim is to recover human body postures from various input, the high dimensionality of the problem makes it desirable to reduce the size of the search-space by eliminating a priori impossible configurations. This can be carried out by constraining the posture recovery process in various ways. Most recent work in this area has focused on applying camera viewpoint-related constraints to eliminate erroneous solutions. When camera calibration parameters are available, they provide an extremely efficient tool for disambiguating not only posture estimation, but also 3D reconstruction and data segmentation. Increased robustness is indeed to be gained from enforcing such constraints, which we prove in the context of an optical motion capture framework. Our contribution in this respect resides in having applied such constraints consistently to each main step involved in a motion capture process, namely marker reconstruction and segmentation, followed by posture recovery. These steps are made inter-dependent, where each one constrains the other. A more application-independent approach is to encode constraints directly within the human body model, such as limits on the rotational joints. This being an almost unexplored research subject, our efforts were mainly directed at determining a new method for measuring, representing and applying such joint limits. To the present day, the few existing range of motion boundary representations present severe drawbacks that call for an alternative formulation. The joint limits paradigm we propose not only overcomes these drawbacks, but also allows to capture intra- and inter-joint rotation dependencies, these being essential to realistic joint motion representation. The range of motion boundary is defined by an implicit surface, its analytical expression enabling us to readily establish whether a given joint rotation is valid or not. Furthermore, its continuous and differentiable nature provides us with a means of elegantly incorporating such a constraint within an optimisation process for posture recovery. Applying constrained optimisation to our body model and stereo data extracted from video sequence, we demonstrate the clearly resulting decrease in posture estimation errors. As a bonus, we have integrated our joint limits representation in character animation packages to show how motion can be naturally constrained in this manner

Resource optimization and dynamic state management in a collaborative virtual environment.

Yim-Pan Chui.Thesis (M.Phil.)--Chinese University of Hong Kong, 2001.Includes bibliographical references (leaves 126-132).Abstracts in English and Chinese.Abstract --- p.iiAcknowledgments --- p.vChapter 1 --- Introduction --- p.1Chapter 1.1 --- Introduction to Collaborative Virtual Environments --- p.1Chapter 1.2 --- Barriers to Resource Management and Optimization --- p.3Chapter 1.3 --- Thesis Contributions --- p.5Chapter 1.4 --- Application of this Research Work --- p.6Chapter 1.5 --- Thesis Organization --- p.6Chapter 2 --- Resource Optimization - Intelligent Server Partitioning --- p.9Chapter 2.1 --- Introduction --- p.9Chapter 2.2 --- Server Partitioning --- p.13Chapter 2.2.1 --- Related Works --- p.15Chapter 2.2.2 --- Global Optimization Approaches --- p.17Chapter 2.3 --- Hybrid Genetic Algorithm Paradigm --- p.17Chapter 2.3.1 --- Drawbacks of traditional GA --- p.18Chapter 2.3.2 --- Problem Modeling --- p.19Chapter 2.3.3 --- Discussion --- p.24Chapter 2.4 --- Results --- p.25Chapter 2.5 --- Concluding Remarks --- p.28Chapter 3 --- Dynamic State Management - Dead Reckoning of Attitude --- p.32Chapter 3.1 --- Introduction to Dynamic State Management --- p.32Chapter 3.2 --- The Dead Reckoning Approach --- p.35Chapter 3.3 --- Attitude Dead Reckoning by Quaternion --- p.37Chapter 3.3.1 --- Modeling of the Paradigm --- p.38Chapter 3.3.2 --- Prediction Step --- p.39Chapter 3.3.3 --- Convergence Step --- p.40Chapter 3.3.4 --- Overall Algorithm --- p.46Chapter 3.4 --- Results --- p.47Chapter 3.5 --- Conclusion --- p.51Chapter 4 --- Polynomial Attitude Extrapolation --- p.52Chapter 4.1 --- Introduction --- p.52Chapter 4.2 --- Related Works on Kalman Filtering --- p.53Chapter 4.3 --- Historical Propagation of Quaternion --- p.54Chapter 4.3.1 --- Cumulative Extrapolation --- p.54Chapter 4.3.2 --- Method I. Vandemonde Approach --- p.55Chapter 4.3.3 --- Method II. Lagrangian Approach --- p.58Chapter 4.4 --- History-Based Attitude Management --- p.60Chapter 4.4.1 --- Multi-order Prediction --- p.60Chapter 4.4.2 --- Adaptive Attitude Convergence --- p.63Chapter 4.4.3 --- Overall Algorithm --- p.67Chapter 4.5 --- Results --- p.69Chapter 4.6 --- Conclusion --- p.77Chapter 5 --- Forward Difference Approach on State Estimation --- p.78Chapter 5.1 --- Introduction --- p.78Chapter 5.2 --- Positional Forward Differencing --- p.79Chapter 5.3 --- Forward Difference on Quaternion Space --- p.80Chapter 5.3.1 --- Attitude Forward Differencing --- p.83Chapter 5.3.2 --- Trajectory Blending --- p.84Chapter 5.4 --- State Estimation --- p.86Chapter 5.5 --- Computational Efficiency --- p.87Chapter 5.6 --- Results --- p.88Chapter 5.7 --- Conclusion --- p.96Chapter 6 --- Predictive Multibody Kinematics --- p.98Chapter 6.1 --- Introduction --- p.98Chapter 6.2 --- Dynamic Management of Multibody System --- p.100Chapter 6.2.1 --- Multibody Representation --- p.100Chapter 6.2.2 --- Paradigm Overview --- p.101Chapter 6.3 --- Motion Estimation by Joint Extrapolation --- p.102Chapter 6.3.1 --- Individual Joint Extrapolation --- p.102Chapter 6.3.2 --- Forward Propagation of Joint State --- p.104Chapter 6.3.3 --- Pose Correction --- p.107Chapter 6.4 --- Limitations on Predictive Articulated State Management --- p.108Chapter 6.5 --- Implementation and Results --- p.109Chapter 6.6 --- Conclusion --- p.112Chapter 7 --- Complete System Architecture --- p.113Chapter 7.1 --- Server Cluster Model --- p.113Chapter 7.1.1 --- Peer-Server Systems --- p.114Chapter 7.1.2 --- Server Hierarchies --- p.114Chapter 7.2 --- Multi-Level Resource Management --- p.115Chapter 7.3 --- Aggregation of State Updates --- p.116Chapter 7.4 --- Implementation Issues --- p.117Chapter 7.4.1 --- Medical Visualization --- p.117Chapter 7.4.2 --- Virtual Walkthrough Application --- p.118Chapter 7.5 --- Conclusion --- p.119Chapter 8 --- Conclusions and Future directions --- p.121Chapter 8.1 --- Conclusion --- p.121Chapter 8.2 --- Future Research Directions --- p.122Chapter A --- Quaternion Basis --- p.124Chapter A.1 --- Basic Quaternion Mathematics --- p.124Chapter A.2 --- The Exponential and Logarithmic Maps --- p.125Bibliography --- p.12