Model Checking Spatial Logics for Closure Spaces

Spatial aspects of computation are becoming increasingly relevant in Computer Science, especially in the field of collective adaptive systems and when dealing with systems distributed in physical space. Traditional formal verification techniques are well suited to analyse the temporal evolution of programs; however, properties of space are typically not taken into account explicitly. We present a topology-based approach to formal verification of spatial properties depending upon physical space. We define an appropriate logic, stemming from the tradition of topological interpretations of modal logics, dating back to earlier logicians such as Tarski, where modalities describe neighbourhood. We lift the topological definitions to the more general setting of closure spaces, also encompassing discrete, graph-based structures. We extend the framework with a spatial surrounded operator, a propagation operator and with some collective operators. The latter are interpreted over arbitrary sets of points instead of individual points in space. We define efficient model checking procedures, both for the individual and the collective spatial fragments of the logic and provide a proof-of-concept tool

Robust Temporally Coherent Laplacian Protrusion Segmentation of 3D Articulated Bodies

In motion analysis and understanding it is important to be able to fit a suitable model or structure to the temporal series of observed data, in order to describe motion patterns in a compact way, and to discriminate between them. In an unsupervised context, i.e., no prior model of the moving object(s) is available, such a structure has to be learned from the data in a bottom-up fashion. In recent times, volumetric approaches in which the motion is captured from a number of cameras and a voxel-set representation of the body is built from the camera views, have gained ground due to attractive features such as inherent view-invariance and robustness to occlusions. Automatic, unsupervised segmentation of moving bodies along entire sequences, in a temporally-coherent and robust way, has the potential to provide a means of constructing a bottom-up model of the moving body, and track motion cues that may be later exploited for motion classification. Spectral methods such as locally linear embedding (LLE) can be useful in this context, as they preserve "protrusions", i.e., high-curvature regions of the 3D volume, of articulated shapes, while improving their separation in a lower dimensional space, making them in this way easier to cluster. In this paper we therefore propose a spectral approach to unsupervised and temporally-coherent body-protrusion segmentation along time sequences. Volumetric shapes are clustered in an embedding space, clusters are propagated in time to ensure coherence, and merged or split to accommodate changes in the body's topology. Experiments on both synthetic and real sequences of dense voxel-set data are shown. This supports the ability of the proposed method to cluster body-parts consistently over time in a totally unsupervised fashion, its robustness to sampling density and shape quality, and its potential for bottom-up model constructionComment: 31 pages, 26 figure

Learning quadrangulated patches for 3D shape parameterization and completion

We propose a novel 3D shape parameterization by surface patches, that are oriented by 3D mesh quadrangulation of the shape. By encoding 3D surface detail on local patches, we learn a patch dictionary that identifies principal surface features of the shape. Unlike previous methods, we are able to encode surface patches of variable size as determined by the user. We propose novel methods for dictionary learning and patch reconstruction based on the query of a noisy input patch with holes. We evaluate the patch dictionary towards various applications in 3D shape inpainting, denoising and compression. Our method is able to predict missing vertices and inpaint moderately sized holes. We demonstrate a complete pipeline for reconstructing the 3D mesh from the patch encoding. We validate our shape parameterization and reconstruction methods on both synthetic shapes and real world scans. We show that our patch dictionary performs successful shape completion of complicated surface textures.Comment: To be presented at International Conference on 3D Vision 2017, 201

Community structure detection in the evolution of the United States airport network

This is the post-print version of the Article. Copyright © 2013 World Scientific PublishingThis paper investigates community structure in the US Airport Network as it evolved from 1990 to 2010 by looking at six bi-monthly intervals in 1990, 2000 and 2010, using data obtained from the Bureau of Transportation Statistics of the US Department of Transport. The data contained monthly records of origin-destination pairs of domestic airports and the number of passengers carried. The topological properties and the volume of people traveling are both studied in detail, revealing high heterogeneity in space and time. A recently developed community structure detection method, accounting for the spatial nature of these networks, is applied and reveals a picture of the communities within. The patterns of communities plotted for each bi-monthly interval reveal some interesting seasonal variations of passenger flows and airport clusters that do not occupy a single US region. The long-term evolution of the network between those years is explored and found to have consistently improved its stability. The more recent structure of the network (2010) is compared with migration patterns among the four US macro-regions (West, Midwest, Northeast and South) in order to identify possible relationships and the results highlight a clear overlap between US domestic air travel and migration

Early Warning Analysis for Social Diffusion Events

There is considerable interest in developing predictive capabilities for social diffusion processes, for instance to permit early identification of emerging contentious situations, rapid detection of disease outbreaks, or accurate forecasting of the ultimate reach of potentially viral ideas or behaviors. This paper proposes a new approach to this predictive analytics problem, in which analysis of meso-scale network dynamics is leveraged to generate useful predictions for complex social phenomena. We begin by deriving a stochastic hybrid dynamical systems (S-HDS) model for diffusion processes taking place over social networks with realistic topologies; this modeling approach is inspired by recent work in biology demonstrating that S-HDS offer a useful mathematical formalism with which to represent complex, multi-scale biological network dynamics. We then perform formal stochastic reachability analysis with this S-HDS model and conclude that the outcomes of social diffusion processes may depend crucially upon the way the early dynamics of the process interacts with the underlying network's community structure and core-periphery structure. This theoretical finding provides the foundations for developing a machine learning algorithm that enables accurate early warning analysis for social diffusion events. The utility of the warning algorithm, and the power of network-based predictive metrics, are demonstrated through an empirical investigation of the propagation of political memes over social media networks. Additionally, we illustrate the potential of the approach for security informatics applications through case studies involving early warning analysis of large-scale protests events and politically-motivated cyber attacks

Doctor of Philosophy

dissertationImage segmentation entails the partitioning of an image domain, usually two or three dimensions, so that each partition or segment has some meaning that is relevant to the application at hand. Accurate image segmentation is a crucial challenge in many disciplines, including medicine, computer vision, and geology. In some applications, heterogeneous pixel intensities; noisy, ill-defined, or diffusive boundaries; and irregular shapes with high variability can make it challenging to meet accuracy requirements. Various segmentation approaches tackle such challenges by casting the segmentation problem as an energy-minimization problem, and solving it using efficient optimization algorithms. These approaches are broadly classified as either region-based or edge (surface)-based depending on the features on which they operate. The focus of this dissertation is on the development of a surface-based energy model, the design of efficient formulations of optimization frameworks to incorporate such energy, and the solution of the energy-minimization problem using graph cuts. This dissertation utilizes a set of four papers whose motivation is the efficient extraction of the left atrium wall from the late gadolinium enhancement magnetic resonance imaging (LGE-MRI) image volume. This dissertation utilizes these energy formulations for other applications, including contact lens segmentation in the optical coherence tomography (OCT) data and the extraction of geologic features in seismic data. Chapters 2 through 5 (papers 1 through 4) explore building a surface-based image segmentation model by progressively adding components to improve its accuracy and robustness. The first paper defines a parametric search space and its discrete formulation in the form of a multilayer three-dimensional mesh model within which the segmentation takes place. It includes a generative intensity model, and we optimize using a graph formulation of the surface net problem. The second paper proposes a Bayesian framework with a Markov random field (MRF) prior that gives rise to another class of surface nets, which provides better segmentation with smooth boundaries. The third paper presents a maximum a posteriori (MAP)-based surface estimation framework that relies on a generative image model by incorporating global shape priors, in addition to the MRF, within the Bayesian formulation. Thus, the resulting surface not only depends on the learned model of shapes,but also accommodates the test data irregularities through smooth deviations from these priors. Further, the paper proposes a new shape parameter estimation scheme, in closed form, for segmentation as a part of the optimization process. Finally, the fourth paper (under review at the time of this document) presents an extensive analysis of the MAP framework and presents improved mesh generation and generative intensity models. It also performs a thorough analysis of the segmentation results that demonstrates the effectiveness of the proposed method qualitatively, quantitatively, and clinically. Chapter 6, consisting of unpublished work, demonstrates the application of an MRF-based Bayesian framework to segment coupled surfaces of contact lenses in optical coherence tomography images. This chapter also shows an application related to the extraction of geological structures in seismic volumes. Due to the large sizes of seismic volume datasets, we also present fast, approximate surface-based energy minimization strategies that achieve better speed-ups and memory consumption

The State of the Art in Cartograms

Cartograms combine statistical and geographical information in thematic maps, where areas of geographical regions (e.g., countries, states) are scaled in proportion to some statistic (e.g., population, income). Cartograms make it possible to gain insight into patterns and trends in the world around us and have been very popular visualizations for geo-referenced data for over a century. This work surveys cartogram research in visualization, cartography and geometry, covering a broad spectrum of different cartogram types: from the traditional rectangular and table cartograms, to Dorling and diffusion cartograms. A particular focus is the study of the major cartogram dimensions: statistical accuracy, geographical accuracy, and topological accuracy. We review the history of cartograms, describe the algorithms for generating them, and consider task taxonomies. We also review quantitative and qualitative evaluations, and we use these to arrive at design guidelines and research challenges