Efficient Algorithms for Robust Estimation

One of the most commonly encountered tasks in computer vision is the estimation of model parameters from image measurements. This scenario arises in a variety of applications -- for instance, in the estimation of geometric entities, such as camera pose parameters, from feature matches between images. The main challenge in this task is to handle the problem of outliers -- in other words, data points that do not conform to the model being estimated. It is well known that if these outliers are not properly accounted for, even a single outlier in the data can result in arbitrarily bad model estimates. Due to the widespread prevalence of problems of this nature, the field of robust estimation has been well studied over the years, both in the statistics community as well as in computer vision, leading to the development of popular algorithms like Random Sample Consensus (RANSAC). While recent years have seen exciting advances in this area, a number of important issues still remain open. In this dissertation, we aim to address some of these challenges. The main goal of this dissertation is to advance the state of the art in robust estimation techniques by developing algorithms capable of efficiently and accurately delivering model parameter estimates in the face of noise and outliers. To this end, the first contribution of this work is in the development of a coherent framework for the analysis of RANSAC-based robust estimators, which consolidates various improvements made over the years. In turn, this analysis leads naturally to the development of new techniques that combine the strengths of existing methods, and yields high-performance robust estimation algorithms, including for real-time applications. A second contribution of this dissertation is the development of an algorithm that explicitly characterizes the effects of estimation uncertainty in RANSAC. This uncertainty arises from small-scale measurement noise that affects the data points, and consequently, impacts the accuracy of model parameters. We show that knowledge of this measurement noise can be leveraged to develop an inlier classification scheme that is dependent on the model uncertainty, as opposed to a fixed inlier threshold, as in RANSAC. This has the advantage that, given a model with associated uncertainty, we can immediately identify a set of points that support this solution, which in turn leads to an improvement in computational efficiency. Finally, we have also developed an approach to addresses the issue of the inlier threshold, which is a user-supplied parameter that can vary depending on the estimation problem and the data being processed. Our technique is based on the intuition that the residual errors for good models are in some way consistent with each other, while bad models do not exhibit this consistency. In other words, looking at the relationship between \\subsets of models can reveal useful information about the validity of the models themselves. We show that it is possible to efficiently identify this consistent behaviour by exploiting residual ordering information coupled with simple non-parametric statistical tests, which leads to an effective algorithm for threshold-free robust estimation.Doctor of Philosoph

Atomic Interaction Networks in the Core of Protein Domains and Their Native Folds

Vastly divergent sequences populate a majority of protein folds. In the quest to identify features that are conserved within protein domains belonging to the same fold, we set out to examine the entire protein universe on a fold-by-fold basis. We report that the atomic interaction network in the solvent-unexposed core of protein domains are fold-conserved, extraordinary sequence divergence notwithstanding. Further, we find that this feature, termed protein core atomic interaction network (or PCAIN) is significantly distinguishable across different folds, thus appearing to be “signature” of a domain's native fold. As part of this study, we computed the PCAINs for 8698 representative protein domains from families across the 1018 known protein folds to construct our seed database and an automated framework was developed for PCAIN-based characterization of the protein fold universe. A test set of randomly selected domains that are not in the seed database was classified with over 97% accuracy, independent of sequence divergence. As an application of this novel fold signature, a PCAIN-based scoring scheme was developed for comparative (homology-based) structure prediction, with 1–2 angstroms (mean 1.61A) Cα RMSD generally observed between computed structures and reference crystal structures. Our results are consistent across the full spectrum of test domains including those from recent CASP experiments and most notably in the ‘twilight’ and ‘midnight’ zones wherein <30% and <10% target-template sequence identity prevails (mean twilight RMSD of 1.69A). We further demonstrate the utility of the PCAIN protocol to derive biological insight into protein structure-function relationships, by modeling the structure of the YopM effector novel E3 ligase (NEL) domain from plague-causative bacterium Yersinia Pestis and discussing its implications for host adaptive and innate immune modulation by the pathogen. Considering the several high-throughput, sequence-identity-independent applications demonstrated in this work, we suggest that the PCAIN is a fundamental fold feature that could be a valuable addition to the arsenal of protein modeling and analysis tools

RECON: Scale-Adaptive Robust Estimation via Residual Consensus

In this paper, we present a novel, threshold-free robust estimation framework capable of efficiently fitting models to contaminated data. While RANSAC and its many variants have emerged as popular tools for robust estimation, their performance is largely dependent on the availability of a reasonable prior estimate of the inlier threshold. In this work, we aim to remove this threshold dependency. We build on the observation that models generated from uncontaminated minimal subsets are “consistent ” in terms of the behavior of their residuals, while contaminated models exhibit uncorrelated behavior. By leveraging this observation, we then develop a very simple, yet effective algorithm that does not require apriori knowledge of either the scale of the noise, or the fraction of uncontaminated points. The resulting estimator, RECON (REsidual CONsensus), is capable of elegantly adapting to the contamination level of the data, and shows excellent performance even at low inlier ratios and high noise levels. We demonstrate the efficiency of our framework on a variety of challenging estimation problems. 1

Improved Resolution Scalability for Bi-Level Image Data in JPEG2000

In this paper, we address issues regarding bi-level image compression using JPEG2000. While JPEG2000 is designed to compress both bi-level and continuous tone imagery using a single unified framework, there exist significant limitations with respect to its use in the lossless compression of bi-level imagery. In particular, substantial degradation in image quality at low resolutions severely limits the resolution scalable features of the JPEG2000 code-stream. We analyze these effects and present two efficient methods to improve resolution scalability for bi-level imagery in JPEG2000. It may be noted that both proposed methods are compliant with Part-I of the JPEG2000 standard. I