Anomaly Detection in Noisy Images

Finding rare events in multidimensional data is an important detection problem that has applications in many fields, such as risk estimation in insurance industry, finance, flood prediction, medical diagnosis, quality assurance, security, or safety in transportation. The occurrence of such anomalies is so infrequent that there is usually not enough training data to learn an accurate statistical model of the anomaly class. In some cases, such events may have never been observed, so the only information that is available is a set of normal samples and an assumed pairwise similarity function. Such metric may only be known up to a certain number of unspecified parameters, which would either need to be learned from training data, or fixed by a domain expert. Sometimes, the anomalous condition may be formulated algebraically, such as a measure exceeding a predefined threshold, but nuisance variables may complicate the estimation of such a measure. Change detection methods used in time series analysis are not easily extendable to the multidimensional case, where discontinuities are not localized to a single point. On the other hand, in higher dimensions, data exhibits more complex interdependencies, and there is redundancy that could be exploited to adaptively model the normal data. In the first part of this dissertation, we review the theoretical framework for anomaly detection in images and previous anomaly detection work done in the context of crack detection and detection of anomalous components in railway tracks. In the second part, we propose new anomaly detection algorithms. The fact that curvilinear discontinuities in images are sparse with respect to the frame of shearlets, allows us to pose this anomaly detection problem as basis pursuit optimization. Therefore, we pose the problem of detecting curvilinear anomalies in noisy textured images as a blind source separation problem under sparsity constraints, and propose an iterative shrinkage algorithm to solve it. Taking advantage of the parallel nature of this algorithm, we describe how this method can be accelerated using graphical processing units (GPU). Then, we propose a new method for finding defective components on railway tracks using cameras mounted on a train. We describe how to extract features and use a combination of classifiers to solve this problem. Then, we scale anomaly detection to bigger datasets with complex interdependencies. We show that the anomaly detection problem naturally fits in the multitask learning framework. The first task consists of learning a compact representation of the good samples, while the second task consists of learning the anomaly detector. Using deep convolutional neural networks, we show that it is possible to train a deep model with a limited number of anomalous examples. In sequential detection problems, the presence of time-variant nuisance parameters affect the detection performance. In the last part of this dissertation, we present a method for adaptively estimating the threshold of sequential detectors using Extreme Value Theory on a Bayesian framework. Finally, conclusions on the results obtained are provided, followed by a discussion of possible future work.

Nurturing Change: Lilly Martin Spencer's Images of Children

This dissertation is the first full-length study to concentrate on American genre painter Lilly Martin Spencer's images of children, which constituted nearly one half of her saleable production during the height of her artistic career from 1848 to 1869. At this time, many young parents received advice regarding child rearing through books and other publications, having moved away from their families of origin in search of employment. These literatures, which gained in popularity from the 1830s onward, focused on spiritual, emotional, and disciplinary matters. My study considers four major themes from the period's writing on child nurture that changed over time, including depravity and innocence, parent/child bonding, standards of behavior and moral rectitude, and children's influence on adults. It demonstrates how Spencer's paintings, prints, and drawings featuring children supported and challenged these evolving ideologies, helping to shed light not only on the artist's reception of child-rearing advice, but also on its possible impact on her middle-class audience, to whom she closely catered. In four chapters, I investigate Spencer's images of sleeping children as visual equivalents of contemporary consolation literature during a time of high infant and child mortality rates; her paintings of parent/child interaction as promoting separation from mothers and emotional bonding with fathers; her prints of mischievous children as both considering changing ideals about children's behavior and comforting Anglo-American citizens afraid of what they saw as threatening minority groups; and her pictures with Civil War and Reconstruction subject matter as contending with the popular concept of the moral utility of children. By framing my interpretations of Spencer's output around key issues in the period's dynamic child-nurture literature, I advance new comprehensive readings of many of her most well-known paintings, including Domestic Happiness, Fi, Fo, Fum!, and The Pic Nic or the Fourth of July. I also consider work often overlooked by other art historians, but which received acclaim in Spencer's own time, including the lithographs of children made after her designs, and the allegorical painting Truth Unveiling Falsehood. Significantly, I provide the first in-depth analysis of a newly rediscovered Reconstruction-era painting, The Home of the Red, White, and Blue.