A graphical method for a class of Branin trajectories
Journal of Optimization Theory and Applications
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
Statistics and Computing
Hyperdynamics Importance Sampling
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Implicit Probabilistic Models of Human Motion for Synthesis and Tracking
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Building Roadmaps of Local Minima of Visual Models
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
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
Consistency and Coupling in Human Model Likelihoods
FGR '02 Proceedings of the Fifth IEEE International Conference on Automatic Face and Gesture Recognition
Generative modeling for continuous non-linearly embedded visual inference
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Variational mixture smoothing for non-linear dynamical systems
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
Incremental Model-Based Estimation Using Geometric Constraints
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computational studies of human motion: part 1, tracking and motion synthesis
Foundations and Trends® in Computer Graphics and Vision
Human Motion Tracking with a Kinematic Parameterization of Extremal Contours
International Journal of Computer Vision
Twin Gaussian Processes for Structured Prediction
International Journal of Computer Vision
Finding multiple first order saddle points using a valley adaptive clearing genetic algorithm
CIRA'09 Proceedings of the 8th IEEE international conference on Computational intelligence in robotics and automation
Human posture analysis under partial self-occlusion
ICIAR'06 Proceedings of the Third international conference on Image Analysis and Recognition - Volume Part I
Hi-index | 0.00 |
Becoming trapped in suboptimal local minima is a perennial problem when optimizing visual models, particularly in applications like monocular human body tracking where complicated parametric models are repeatedly fitted to ambiguous image measurements. We show that trapping can be significantly reduced by building ‘roadmaps’ of nearby minima linked by transition pathways—paths leading over low ‘mountain 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 present two families of transition-state-finding algorithms based on local optimization. In eigenvector tracking, unconstrained Newton minimization is modified to climb uphill towards a transition state, while in hypersurface sweeping, a moving hypersurface is swept through the space and moving local minima within it are tracked using a constrained Newton method. These widely applicable numerical methods, which appear not to be known in vision and optimization, generalize methods from computational chemistry where finding transition states is critical for predicting reaction parameters. 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 numbers of minima that can exist in this and similar model based vision problems.