Nonparametric Belief Propagation and Facial Appearance Estimation

In many applications of graphical models arising in computer vision, the hidden variables of interest are most naturally specified by continuous, non-Gaussian distributions. There exist inference algorithms for discrete approximations to these continuous distributions, but for the high-dimensional variables typically of interest, discrete inference becomes infeasible. Stochastic methods such as particle filters provide an appealing alternative. However, existing techniques fail to exploit the rich structure of the graphical models describing many vision problems. Drawing on ideas from regularized particle filters and belief propagation (BP), this paper develops a nonparametric belief propagation (NBP) algorithm applicable to general graphs. Each NBP iteration uses an efficient sampling procedure to update kernel-based approximations to the true, continuous likelihoods. The algorithm can accomodate an extremely broad class of potential functions, including nonparametric representations. Thus, NBP extends particle filtering methods to the more general vision problems that graphical models can describe. We apply the NBP algorithm to infer component interrelationships in a parts-based face model, allowing location and reconstruction of occluded features

Worst-case bounds on the quality of max-product fixed-points

We study worst-case bounds on the quality of any fixed point assignment of the max-product algorithm for Markov Random Fields (MRF). We start proving a bound independent of the MRF structure and parameters. Afterwards, we show how this bound can be improved for MRFs with particular structures such as bipartite graphs or grids. Our results provide interesting insight into the behavior of max-product. For example, we prove that max-product provides very good results (at least 90% of the optimal) on MRFs with large variable-disjoint cycles (MRFs in which all cycles are variable-disjoint, namely that they do not share any edge and in which each cycle contains at least 20 variables)

Geometric analysis of macromolecule organization within cryo-electron tomograms

Cryo-electron tomography (CET) provides unprecedented views into the native cellular environment at molecular resolution. While subtomogram analysis yields high-resolution native structures of molecular complexes, it also determines the precise positions and orientations of these macromolecules within the cell. Analyzing the geometric relationships between adjacent macromolecules can offer structural insights into molecular interactions and identify supramolecular ensembles. However, computation..

New Algorithms for Predicting Conformational Polymorphism and Inferring Direct Couplings for Side Chains of Proteins

Protein crystals populate diverse conformational ensembles. Despite much evidence that there is widespread conformational polymorphism in protein side chains, most of the xray crystallography data are modelled by single conformations in the Protein Data Bank. The ability to extract or to predict these conformational polymorphisms is of crucial importance, as it facilitates deeper understanding of protein dynamics and functionality. This dissertation describes a computational strategy capable of predicting side-chain polymorphisms. The applied approach extends a particular class of algorithms for side-chain prediction by modelling the side-chain dihedral angles more appropriately as continuous rather than discrete variables. Employing a new inferential technique known as particle belief propagation (PBP), we predict residue-speci c distributions that encode information about side-chain polymorphisms. The predicted polymorphisms are in relatively close agreement with results from a state-of-the-art approach based on x-ray crystallography data. This approach characterizes the conformational polymorphisms of side chains using electron density information, and has successfully discovered previously unmodelled conformations. Furthermore, it is known that coupled uctuations and concerted motions of residues can reveal pathways of communication used for information propagation in a molecule and hence, can help in understanding the \allostery" phenomenon in proteins. In order to characterize the coupled motions, most existing methods infer structural dependencies among a protein's residues. However, recent studies have highlighted the role of coupled side-chain uctuations alone in the allosteric behaviour of proteins, in contrast to a common belief that the backbone motions play the main role in allostery. These studies and the aforementioned recent discoveries about prevalent alternate side-chain conformations (conformational polymorphism) accentuate the need to devise new computational approaches that acknowledge side chains' roles. As well, these approaches must consider the polymorphic nature of the side chains, and incorporate e ects of this phenomenon (polymorphism) in the study of information transmission and functional interactions of residues in a molecule. Such frameworks can provide a more accurate understanding of the allosteric behaviour. Hence, as a topic related to the conformational polymorphism, this dissertation addresses the problem of inferring directly coupled side chains, as well. First, we present a novel approach to generate an ensemble of conformations and an e cient computational method to extract direct couplings of side chains in allosteric proteins. These direct couplings are used to provide sparse network representations of the coupled side chains. The framework is based on a fairly new statistical method, named graphical lasso (GLASSO), iii devised for sparse graph estimation. In the proposed GLASSO-based framework, the sidechain conformational polymorphism is taken into account. It is shown that by studying the intrinsic dynamics of an inactive structure alone, we are able to construct a network of functionally crucial residues. Second, we show that the proposed method is capable of providing a magni ed view of the coupled and conformationally polymorphic side chains. This model reveals couplings between the alternate conformations of a coupled residue pair. To the best of our knowledge, this is the rst computational method for extracting networks of side chains' alternate conformations. Such networks help in providing a detailed image of side-chain dynamics in functionally important and conformationally polymorphic sites, such as binding and/or allosteric sites. This information may assist in new drug-design alternatives. Side-chain conformations are commonly represented by multivariate angular variables. However, the GLASSO and other existing methods that can be applied to the aforementioned inference task are not capable of handling multivariate angular data. This dissertation further proposes a novel method to infer direct couplings from this type of data, and shows that this method is useful for identifying functional regions and their interactions in allosteric proteins. The proposed framework is a novel extension of canonical correlation analysis (CCA), which we call \kernelized partial CCA" (or simply KPCCA). Using the conformational information and uctuations of the inactive structure alone for allosteric proteins in the Ras and other Ras-like families, the KPCCA method identi ed allosterically important residues not only as strongly coupled ones but also in densely connected regions of the interaction graph formed by the inferred couplings. The results were in good agreement with other empirical ndings and outperformed those obtained by the GLASSO-based framework. By studying distinct members of the Ras, Rho, and Rab sub-families, we show further that KPCCA is capable of inferring common allosteric characteristics in the small G protein super-family

Efficient 3D Segmentation, Registration and Mapping for Mobile Robots

Sometimes simple is better! For certain situations and tasks, simple but robust methods can achieve the same or better results in the same or less time than related sophisticated approaches. In the context of robots operating in real-world environments, key challenges are perceiving objects of interest and obstacles as well as building maps of the environment and localizing therein. The goal of this thesis is to carefully analyze such problem formulations, to deduce valid assumptions and simplifications, and to develop simple solutions that are both robust and fast. All approaches make use of sensors capturing 3D information, such as consumer RGBD cameras. Comparative evaluations show the performance of the developed approaches. For identifying objects and regions of interest in manipulation tasks, a real-time object segmentation pipeline is proposed. It exploits several common assumptions of manipulation tasks such as objects being on horizontal support surfaces (and well separated). It achieves real-time performance by using particularly efficient approximations in the individual processing steps, subsampling the input data where possible, and processing only relevant subsets of the data. The resulting pipeline segments 3D input data with up to 30Hz. In order to obtain complete segmentations of the 3D input data, a second pipeline is proposed that approximates the sampled surface, smooths the underlying data, and segments the smoothed surface into coherent regions belonging to the same geometric primitive. It uses different primitive models and can reliably segment input data into planes, cylinders and spheres. A thorough comparative evaluation shows state-of-the-art performance while computing such segmentations in near real-time. The second part of the thesis addresses the registration of 3D input data, i.e., consistently aligning input captured from different view poses. Several methods are presented for different types of input data. For the particular application of mapping with micro aerial vehicles where the 3D input data is particularly sparse, a pipeline is proposed that uses the same approximate surface reconstruction to exploit the measurement topology and a surface-to-surface registration algorithm that robustly aligns the data. Optimization of the resulting graph of determined view poses then yields globally consistent 3D maps. For sequences of RGBD data this pipeline is extended to include additional subsampling steps and an initial alignment of the data in local windows in the pose graph. In both cases, comparative evaluations show a robust and fast alignment of the input data