A general framework simultaneously addressing pose estimation, 2D segmentation, object recognition, and 3D reconstruction from a single image is introduced in this paper. The proposed approach partitions 3D space into voxels and estimates the voxel states that maximize a likelihood integrating two components: the object fidelity, that is, the probability that an object occupies the given voxels, here encoded as a 3D shape prior learned from 3D samples of objects in a class; and the image fidelity, meaning the probability that the given voxels would produce the input image when properly projected to the image plane. We derive a loop-less graphical model for this likelihood and propose a computationally efficient optimization algorithm that is guaranteed to produce the global likelihood maximum. Furthermore, we derive a multi-resolution implementation of this algorithm that permits to trade reconstruction and estimation accuracy for computation. The presentation of the proposed framework is complemented with experiments on real data demonstrating the accuracy of the proposed approach.

When accounting for structural fluctuations or measurement errors, a single rigid structure may not be sufficient to represent a protein. One approach to solve this problem is to represent the possible conformations as a discrete set of observed conformations, an ensemble. In this work, we follow a different richer approach, and introduce a framework for estimating probability density functions in very high dimensions, and then apply it to represent ensembles of folded proteins. This proposed approach combines techniques such as kernel density estimation, maximum likelihood, cross-validation, and bootstrapping. We present the underlying theoretical and computational framework and apply it to artificial data and protein ensembles obtained from molecular dynamics simulations. We compare the results with those obtained experimentally, illustrating the potential and advantages of this representation.

An approach for incremental learning of a 3D scene from a single static video camera is presented in this paper. In particular, we exploit the presence of casual people walking in the scene to infer relative depth, learn shadows, and segment the critical ground structure. Considering that this type of video data is so ubiquitous, this work provides an important step towards 3D scene analysis from single cameras in readily available ordinary videos and movies. On-line 3D scene learning, as presented here, is very important for applications such as scene analysis, foreground refinement, tracking, biometrics, automated camera collaboration, activity analysis, identification, and real-time computer-graphics applications. The main contributions of this work are then two-fold. First, we use the people in the scene to continuously learn and update the 3D scene parameters using an incremental robust (L1) error minimization. Secondly, models of shadows in the scene are learned using a statistical framework. A symbiotic relationship between the shadow model and the estimated scene geometry is exploited towards incremental mutual improvement. We illustrate the effectiveness of the proposed framework with applications in foreground refinement, automatic segmentation as well as relative depth mapping of the floor/ground, and estimation of 3D trajectories of people in the scene.