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.

Active Blobs

A new region-based approach to nonrigid motion tracking is described. Shape is defined in terms of a deformable triangular mesh that captures object shape plus a color texture map that captures object appearance. Photometric variations are also modeled. Nonrigid shape registration and motion tracking are achieved by posing the problem as an energy-based, robust minimization procedure. The approach provides robustness to occlusions, wrinkles, shadows, and specular highlights. The formulation is tailored to take advantage of texture mapping hardware available in many workstations, PC's, and game consoles. This enables nonrigid tracking at speeds approaching video rate.

Head Tracking via Robust Registration in Texture Map Images

A novel method for 3D head tracking in the presence of large head rotations and facial expression changes is described. Tracking is formulated in terms of color image registration in the texture map of a 3D surface model. Model appearance is recursively updated via image mosaicking in the texture map as the head orientation varies. The resulting dynamic texture map provides a stabilized view of the face that can be used as input to many existing 2D techniques for face recognition, facial expressions analysis, lip reading, and eye tracking. Parameters are estimated via a robust minimization procedure; this provides robustness to occlusions, wrinkles, shadows, and specular highlights. The system was tested on a variety of sequences taken with low quality, uncalibrated video cameras. Experimental results are reported.

Surface Reconstruction from Multiple Views using Rational B-Splines

A method for reconstructing 3D rational B-spline surfaces from multiple views is proposed. The method takes advantage of the projective invariance properties of rational B-splines. Given feature correspondences in multiple views, the 3D surface is reconstructed via a four step framework. First, corresponding features in each view are given an initial surface parameter value (s; t), and a 2D B-spline is fitted in each view. After this initialization, an iterative minimization procedure alternates between updating the 2D B-spline control points and re-estimating each feature's (s; t). Next, a non-linear minimization method is used to upgrade the 2D B-splines to 2D rational B-splines, and obtain a better fit. Finally, a factorization method is used to reconstruct the 3D B-spline surface given 2D B-splines in each view. This surface recovery method can be applied in both the perspective and orthographic case. The orthographic case allows the use of additional constraints in the recovery. Experiments with real and synthetic imagery demonstrate the efficacy of the approach for the orthographic case.

Foundational Theory for Understanding Policy Routing Dynamics

In this paper we introduce a theory of policy routing dynamics based on fundamental axioms of routing update mechanisms. We develop a dynamic policy routing model (DPR) that extends the static formalism of the stable paths problem (introduced by Griffin et al.) with discrete synchronous time. DPR captures the propagation of path changes in any dynamic network irrespective of its time-varying topology. We introduce several novel structures such as causation chains, dispute fences and policy digraphs that model different aspects of routing dynamics and provide insight into how these dynamics manifest in a network. We exercise the practicality of the theoretical foundation provided by DPR with two fundamental problems: routing dynamics minimization and policy conflict detection. The dynamics minimization problem utilizes policy digraphs, that capture the dependencies in routing policies irrespective of underlying topology dynamics, to solve a graph optimization problem. This optimization problem explicitly minimizes the number of routing update messages in a dynamic network by optimally changing the path preferences of a minimal subset of nodes. The conflict detection problem, on the other hand, utilizes a theoretical result of DPR where the root cause of a causation cycle (i.e., cycle of routing update messages) can be precisely inferred as either a transient route flap or a dispute wheel (i.e., policy conflict). Using this result we develop SafetyPulse, a token-based distributed algorithm to detect policy conflicts in a dynamic network. SafetyPulse is privacy preserving, computationally efficient, and provably correct.

Fast, Reliable Head Tracking under Varying Illumination

An improved technique for 3D head tracking under varying illumination conditions is proposed. The head is modeled as a texture mapped cylinder. Tracking is formulated as an image registration problem in the cylinder's texture map image. To solve the registration problem in the presence of lighting variation and head motion, the residual error of registration is modeled as a linear combination of texture warping templates and orthogonal illumination templates. Fast and stable on-line tracking is then achieved via regularized, weighted least squares minimization of the registration error. The regularization term tends to limit potential ambiguities that arise in the warping and illumination templates. It enables stable tracking over extended sequences. Tracking does not require a precise initial fit of the model; the system is initialized automatically using a simple 2-D face detector. The only assumption is that the target is facing the camera in the first frame of the sequence. The warping templates are computed at the first frame of the sequence. Illumination templates are precomputed off-line over a training set of face images collected under varying lighting conditions. Experiments in tracking are reported.

Fast, Reliable Head Tracking under Varying Illumination: An Approach Based on Registration of Texture-Mapped 3D Model

An improved technique for 3D head tracking under varying illumination conditions is proposed. The head is modeled as a texture mapped cylinder. Tracking is formulated as an image registration problem in the cylinder's texture map image. The resulting dynamic texture map provides a stabilized view of the face that can be used as input to many existing 2D techniques for face recognition, facial expressions analysis, lip reading, and eye tracking. To solve the registration problem in the presence of lighting variation and head motion, the residual error of registration is modeled as a linear combination of texture warping templates and orthogonal illumination templates. Fast and stable on-line tracking is achieved via regularized, weighted least squares minimization of the registration error. The regularization term tends to limit potential ambiguities that arise in the warping and illumination templates. It enables stable tracking over extended sequences. Tracking does not require a precise initial fit of the model; the system is initialized automatically using a simple 2D face detector. The only assumption is that the target is facing the camera in the first frame of the sequence. The formulation is tailored to take advantage of texture mapping hardware available in many workstations, PC's, and game consoles. The non-optimized implementation runs at about 15 frames per second on a SGI O2 graphic workstation. Extensive experiments evaluating the effectiveness of the formulation are reported. The sensitivity of the technique to illumination, regularization parameters, errors in the initial positioning and internal camera parameters are analyzed. Examples and applications of tracking are reported.