Tracking Human Body Pose on a Learned Smooth Space

Particle filtering is a popular method used in systems for tracking human body pose in video. One key difficulty in using particle filtering is caused by the curse of dimensionality: generally a very large number of particles is required to adequately approximate the underlying pose distribution in a high-dimensional state space. Although the number of degrees of freedom in the human body is quite large, in reality, the subset of allowable configurations in state space is generally restricted by human biomechanics, and the trajectories in this allowable subspace tend to be smooth. Therefore, a framework is proposed to learn a low-dimensional representation of the high-dimensional human poses state space. This mapping can be learned using a Gaussian Process Latent Variable Model (GPLVM) framework. One important advantage of the GPLVM framework is that both the mapping to, and mapping from the embedded space are smooth; this facilitates sampling in the low-dimensional space, and samples generated in the low-dimensional embedded space are easily mapped back into the original highdimensional space. Moreover, human body poses that are similar in the original space tend to be mapped close to each other in the embedded space; this property can be exploited when sampling in the embedded space. The proposed framework is tested in tracking 2D human body pose using a Scaled Prismatic Model. Experiments on real life video sequences demonstrate the strength of the approach. In comparison with the Multiple Hypothesis Tracking and the standard Condensation algorithm, the proposed algorithm is able to maintain tracking reliably throughout the long test sequences. It also handles singularity and self occlusion robustly.

On the Effectiveness of Genetic Search in Combinatorial Optimization

In this paper, we study the efficacy of genetic algorithms in the context of combinatorial optimization. In particular, we isolate the effects of cross-over, treated as the central component of genetic search. We show that for problems of nontrivial size and difficulty, the contribution of cross-over search is marginal, both synergistically when run in conjunction with mutation and selection, or when run with selection alone, the reference point being the search procedure consisting of just mutation and selection. The latter can be viewed as another manifestation of the Metropolis process. Considering the high computational cost of maintaining a population to facilitate cross-over search, its marginal benefit renders genetic search inferior to its singleton-population counterpart, the Metropolis process, and by extension, simulated annealing. This is further compounded by the fact that many problems arising in practice may inherently require a large number of state transitions for a near-optimal solution to be found, making genetic search infeasible given the high cost of computing a single iteration in the enlarged state-space.

Dynamic Programming for Optimal Control of Set-Up Scheduling with Neural Network Modifications

This paper demonstrates an optimal control solution to change of machine set-up scheduling based on dynamic programming average cost per stage value iteration as set forth by Cararnanis et. al. [2] for the 2D case. The difficulty with the optimal approach lies in the explosive computational growth of the resulting solution. A method of reducing the computational complexity is developed using ideas from biology and neural networks. A real time controller is described that uses a linear-log representation of state space with neural networks employed to fit cost surfaces.

Protein Docking by the Underestimation of Free Energy Funnels in the Space of Encounter Complexes

Similarly to protein folding, the association of two proteins is driven by a free energy funnel, determined by favorable interactions in some neighborhood of the native state. We describe a docking method based on stochastic global minimization of funnel-shaped energy functions in the space of rigid body motions (SE(3)) while accounting for flexibility of the interface side chains. The method, called semi-definite programming-based underestimation (SDU), employs a general quadratic function to underestimate a set of local energy minima and uses the resulting underestimator to bias further sampling. While SDU effectively minimizes functions with funnel-shaped basins, its application to docking in the rotational and translational space SE(3) is not straightforward due to the geometry of that space. We introduce a strategy that uses separate independent variables for side-chain optimization, center-to-center distance of the two proteins, and five angular descriptors of the relative orientations of the molecules. The removal of the center-to-center distance turns out to vastly improve the efficiency of the search, because the five-dimensional space now exhibits a well-behaved energy surface suitable for underestimation. This algorithm explores the free energy surface spanned by encounter complexes that correspond to local free energy minima and shows similarity to the model of macromolecular association that proceeds through a series of collisions. Results for standard protein docking benchmarks establish that in this space the free energy landscape is a funnel in a reasonably broad neighborhood of the native state and that the SDU strategy can generate docking predictions with less than 5 � ligand interface Ca root-mean-square deviation while achieving an approximately 20-fold efficiency gain compared to Monte Carlo methods.

Articulated Pose Estimation in a Learned Smooth Space of Feasible Solutions

A learning based framework is proposed for estimating human body pose from a single image. Given a differentiable function that maps from pose space to image feature space, the goal is to invert the process: estimate the pose given only image features. The inversion is an ill-posed problem as the inverse mapping is a one to many process. Hence multiple solutions exist, and it is desirable to restrict the solution space to a smaller subset of feasible solutions. For example, not all human body poses are feasible due to anthropometric constraints. Since the space of feasible solutions may not admit a closed form description, the proposed framework seeks to exploit machine learning techniques to learn an approximation that is smoothly parameterized over such a space. One such technique is Gaussian Process Latent Variable Modelling. Scaled conjugate gradient is then used find the best matching pose in the space of feasible solutions when given an input image. The formulation allows easy incorporation of various constraints, e.g. temporal consistency and anthropometric constraints. The performance of the proposed approach is evaluated in the task of upper-body pose estimation from silhouettes and compared with the Specialized Mapping Architecture. The estimation accuracy of the Specialized Mapping Architecture is at least one standard deviation worse than the proposed approach in the experiments with synthetic data. In experiments with real video of humans performing gestures, the proposed approach produces qualitatively better estimation results.

Synchronized Oscillations During Cooperative Feature Linking in a Cortical Model of Visual Perception

A neural network model of synchronized oscillator activity in visual cortex is presented in order to account for recent neurophysiological findings that such synchronization may reflect global properties of the stimulus. In these recent experiments, it was reported that synchronization of oscillatory firing responses to moving bar stimuli occurred not only for nearby neurons, but also occurred between neurons separated by several cortical columns (several mm of cortex) when these neurons shared some receptive field preferences specific to the stimuli. These results were obtained not only for single bar stimuli but also across two disconnected, but colinear, bars moving in the same direction. Our model and computer simulations obtain these synchrony results across both single and double bar stimuli. For the double bar case, synchronous oscillations are induced in the region between the bars, but no oscillations are induced in the regions beyond the stimuli. These results were achieved with cellular units that exhibit limit cycle oscillations for a robust range of input values, but which approach an equilibrium state when undriven. Single and double bar synchronization of these oscillators was achieved by different, but formally related, models of preattentive visual boundary segmentation and attentive visual object recognition, as well as nearest-neighbor and randomly coupled models. In preattentive visual segmentation, synchronous oscillations may reflect the binding of local feature detectors into a globally coherent grouping. In object recognition, synchronous oscillations may occur during an attentive resonant state that triggers new learning. These modelling results support earlier theoretical predictions of synchronous visual cortical oscillations and demonstrate the robustness of the mechanisms capable of generating synchrony.