Applied Graph Theory in Computer Vision and Pattern Recognition

This book will serve as a foundation for a variety of useful applications of graph theory to computer vision, pattern recognition, and related areas. It covers a representative set of novel graph-theoretic methods for complex computer vision and pattern recognition tasks. The first part of the book presents the application of graph theory to low-level processing of digital images such as a new method for partitioning a given image into a hierarchy of homogeneous areas using graph pyramids, or a study of the relationship between graph theory and digital topology. Part II presents graph-theoretic learning algorithms for high-level computer vision and pattern recognition applications, including a survey of graph based methodologies for pattern recognition and computer vision, a presentation of a series of computationally efficient algorithms for testing graph isomorphism and related graph matching tasks in pattern recognition and a new graph distance measure to be used for solving graph matching problems. Finally, Part III provides detailed descriptions of several applications of graph-based methods to real-world pattern recognition tasks. It includes a critical review of the main graph-based and structural methods for fingerprint classification, a new method to visualize time series of graphs, and potential applications in computer network monitoring and abnormal event detection.

From EEG dependency multichannel matching pursuit to sparse topographic EEG decomposition

In this work, we present a multichannel EEG decomposition model based on an adaptive topographic time-frequency approximation technique. It is an extension of the Matching Pursuit algorithm and called dependency multichannel matching pursuit (DMMP). It takes the physiologically explainable and statistically observable topographic dependencies between the channels into account, namely the spatial smoothness of neighboring electrodes that is implied by the electric leadfield. DMMP decomposes a multichannel signal as a weighted sum of atoms from a given dictionary where the single channels are represented from exactly the same subset of a complete dictionary. The decomposition is illustrated on topographical EEG data during different physiological conditions using a complete Gabor dictionary. Further the extension of the single-channel time-frequency distribution to a multichannel time-frequency distribution is given. This can be used for the visualization of the decomposition structure of multichannel EEG. A clustering procedure applied to the topographies, the vectors of the corresponding contribution of an atom to the signal in each channel produced by DMMP, leads to an extremely sparse topographic decomposition of the EEG.

Beyond the tree of texts: Building an empirical model of scribal variation through graph analysis of texts and stemmata

Stemmatology, or the reconstruction of the transmission history of texts, is a field that stands particularly to gain from digital methods. Many scholars already take stemmatic approaches that rely heavily on computational analysis of the collated text (e.g. Robinson and O’Hara 1996; Salemans 2000; Heikkilä 2005; Windram et al. 2008 among many others). Although there is great value in computationally assisted stemmatology, providing as it does a reproducible result and allowing access to the relevant methodological process in related fields such as evolutionary biology, computational stemmatics is not without its critics. The current state-of-the-art effectively forces scholars to choose between a preconceived judgment of the significance of textual differences (the Lachmannian or neo-Lachmannian approach, and the weighted phylogenetic approach) or to make no judgment at all (the unweighted phylogenetic approach). Some basis for judgment of the significance of variation is sorely needed for medieval text criticism in particular. By this, we mean that there is a need for a statistical empirical profile of the text-genealogical significance of the different sorts of variation in different sorts of medieval texts. The rules that apply to copies of Greek and Latin classics may not apply to copies of medieval Dutch story collections; the practices of copying authoritative texts such as the Bible will most likely have been different from the practices of copying the Lives of local saints and other commonly adapted texts. It is nevertheless imperative that we have a consistent, flexible, and analytically tractable model for capturing these phenomena of transmission. In this article, we present a computational model that captures most of the phenomena of text variation, and a method for analysis of one or more stemma hypotheses against the variation model. We apply this method to three ‘artificial traditions’ (i.e. texts copied under laboratory conditions by scholars to study the properties of text variation) and four genuine medieval traditions whose transmission history is known or deduced in varying degrees. Although our findings are necessarily limited by the small number of texts at our disposal, we demonstrate here some of the wide variety of calculations that can be made using our model. Certain of our results call sharply into question the utility of excluding ‘trivial’ variation such as orthographic and spelling changes from stemmatic analysis.

Comparison of physiological triggering schemes for diffusion-weighted magnetic resonance imaging in kidneys

To determine the potential benefit of combined respiratory-cardiac triggering for diffusion-weighted imaging (DWI) of kidneys compared to respiratory triggering alone (RT).