Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Updated Hessian matrix and the restricted step method for locating transition structures
Journal of Computational Chemistry
Optimal Structure from Motion: Local Ambiguities and Global Estimates
International Journal of Computer Vision
Tracking persons in monocular image sequences
Computer Vision and Image Understanding
Hyperdynamics Importance Sampling
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Partitioned Sampling, Articulated Objects, and Interface-Quality Hand Tracking
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part II
Stochastic Tracking of 3D Human Figures Using 2D Image Motion
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part II
Bundle Adjustment - A Modern Synthesis
ICCV '99 Proceedings of the International Workshop on Vision Algorithms: Theory and Practice
3-D model-based tracking of humans in action: a multi-view approach
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
Singularity Analysis for Articulated Object Tracking
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Global and local deformations of solid primitives
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
Model-based tracking of self-occluding articulated objects
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Consistency and Coupling in Human Model Likelihoods
FGR '02 Proceedings of the Fifth IEEE International Conference on Automatic Face and Gesture Recognition
Articulated Body Motion Capture by Stochastic Search
International Journal of Computer Vision
Hyperdynamics Importance Sampling
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Building Roadmaps of Minima and Transitions in Visual Models
International Journal of Computer Vision
Image-Based Rendering Using Image-Based Priors
International Journal of Computer Vision
Computational studies of human motion: part 1, tracking and motion synthesis
Foundations and Trends® in Computer Graphics and Vision
Fast mixing hyperdynamic sampling
Image and Vision Computing
Twin Gaussian Processes for Structured Prediction
International Journal of Computer Vision
Tracking human pose with multiple activity models
Pattern Recognition
Representation and matching of articulated shapes
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
Kinematic jump processes for monocular 3D human tracking
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Generalized darting Monte Carlo
Pattern Recognition
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Getting trapped in suboptimal local minima is a perennial problem in model based vision, especially in applications like monocular human body tracking where complex nonlinear parametric models are repeatedly fitted to ambiguous image data. We show that the trapping problem can be attacked by building 'roadmaps' of nearby minima linked by transition pathways -- paths leading over low 'cols' or 'passes' in the cost surface, found by locating the transition state (codimension-1 saddle point) at the top of the pass and then sliding downhill to the next minimum. We know of no previous vision or optimization work on numerical methods for locating transition states, but such methods do exist in computational chemistry, where transitions are critical for predicting reaction parameters. We present two families of methods, originally derived in chemistry, but here generalized, clarified and adapted to the needs of model based vision: eigenvector tracking is a modified form of damped Newton minimization, while hypersurface sweeping sweeps a moving hypersurface through the space, tracking minima within it. Experiments on the challenging problem of estimating 3D human pose from monocular images show that our algorithms find nearby transition states and minima very efficiently, but also underline the disturbingly large number of minima that exist in this and similar model based vision problems.