Building Roadmaps of Local Minima of Visual Models

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.