Calculation of reference frames along a space curve
Graphics gems
Advanced animation and rendering techniques
Advanced animation and rendering techniques
Three-dimensional computer vision: a geometric viewpoint
Three-dimensional computer vision: a geometric viewpoint
Implicit surfaces for semi-automatic medical organ reconstruction
Computer graphics
Constrained optimal framings of curves and surfaces using quaternion Gauss maps
Proceedings of the conference on Visualization '98
The visual analysis of human movement: a survey
Computer Vision and Image Understanding
Animating rotation with quaternion curves
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Using Quaternions for Parametrizing 3-D Rotations in Unconstrained Nonlinear Optimization
VMV '01 Proceedings of the Vision Modeling and Visualization Conference 2001
Practical parameterization of rotations using the exponential map
Journal of Graphics Tools
Tracking People with Twists and Exponential Maps
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Shape Transformations Using Union of Spheres
Shape Transformations Using Union of Spheres
Articulated Soft Objects for Multiview Shape and Motion Capture
IEEE Transactions on Pattern Analysis and Machine Intelligence
An inverse kinematics architecture enforcing an arbitrary number of strict priority levels
The Visual Computer: International Journal of Computer Graphics - Special section on implicit surfaces
Learnt inverse kinematics for animation synthesis
Graphical Models - Special issue on the vision, video and graphics conference 2005
A survey of advances in vision-based human motion capture and analysis
Computer Vision and Image Understanding - Special issue on modeling people: Vision-based understanding of a person's shape, appearance, movement, and behaviour
Temporal motion models for monocular and multiview 3D human body tracking
Computer Vision and Image Understanding - Special issue on modeling people: Vision-based understanding of a person's shape, appearance, movement, and behaviour
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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.