An Emergent Space for Distributed Data with Hidden Internal Order through Manifold Learning

Manifold-learning techniques are routinely used in mining complex spatiotemporal data to extract useful, parsimonious data representations/parametrizations; these are, in turn, useful in nonlinear model identification tasks. We focus here on the case of time series data that can ultimately be modelled as a spatially distributed system (e.g. a partial differential equation, PDE), but where we do not know the space in which this PDE should be formulated. Hence, even the spatial coordinates for the distributed system themselves need to be identified - to emerge from - the data mining process. We will first validate this emergent space reconstruction for time series sampled without space labels in known PDEs; this brings up the issue of observability of physical space from temporal observation data, and the transition from spatially resolved to lumped (order-parameter-based) representations by tuning the scale of the data mining kernels. We will then present actual emergent space discovery illustrations. Our illustrative examples include chimera states (states of coexisting coherent and incoherent dynamics), and chaotic as well as quasiperiodic spatiotemporal dynamics, arising in partial differential equations and/or in heterogeneous networks. We also discuss how data-driven spatial coordinates can be extracted in ways invariant to the nature of the measuring instrument. Such gauge-invariant data mining can go beyond the fusion of heterogeneous observations of the same system, to the possible matching of apparently different systems

Heterogeneous volumetric data mapping and its medical applications

With the advance of data acquisition techniques, massive solid geometries are being collected routinely in scientific tasks, these complex and unstructured data need to be effectively correlated for various processing and analysis. Volumetric mapping solves bijective low-distortion correspondence between/among 3D geometric data, and can serve as an important preprocessing step in many tasks in compute-aided design and analysis, industrial manufacturing, medical image analysis, to name a few. This dissertation studied two important volumetric mapping problems: the mapping of heterogeneous volumes (with nonuniform inner structures/layers) and the mapping of sequential dynamic volumes. To effectively handle heterogeneous volumes, first, we studied the feature-aligned harmonic volumetric mapping. Compared to previous harmonic mapping, it supports the point, curve, and iso-surface alignment, which are important low-dimensional structures in heterogeneous volumetric data. Second, we proposed a biharmonic model for volumetric mapping. Unlike the conventional harmonic volumetric mapping that only supports positional continuity on the boundary, this new model allows us to have higher order continuity $C^1$ along the boundary surface. This suggests a potential model to solve the volumetric mapping of complex and big geometries through divide-and-conquer. We also studied the medical applications of our volumetric mapping in lung tumor respiratory motion modeling. We were building an effective digital platform for lung tumor radiotherapy based on effective volumetric CT/MRI image matching and analysis. We developed and integrated in this platform a set of geometric/image processing techniques including advanced image segmentation, finite element meshing, volumetric registration and interpolation. The lung organ/tumor and surrounding tissues are treated as a heterogeneous region and a dynamic 4D registration framework is developed for lung tumor motion modeling and tracking. Compared to the previous 3D pairwise registration, our new 4D parameterization model leads to a significantly improved registration accuracy. The constructed deforming model can hence approximate the deformation of the tissues and tumor

Automatic landmark extraction from a class of hands using growing neural gas

A new method for automatically building statistical shape models from a set of training examples and in particular from a class of hands. In this method, landmark extraction is achieved using a self-organising neural network, the Growing Neural Gas (GNG), which is used to preserve the topology of any input space. Using GNG, the topological relations of a given set of deformable shapes can be learned. We describe how shape models can be built automatically by posing the correspondence problem on the behaviour of self-organising networks that are capable of adapting their topology to an input manifold, and due to their dynamic character to readapt it to the shape of the objects. Results are given for the training set of hand outlines, showing that the proposed method preserves accurate models

Data-Driven Shape Analysis and Processing

Data-driven methods play an increasingly important role in discovering geometric, structural, and semantic relationships between 3D shapes in collections, and applying this analysis to support intelligent modeling, editing, and visualization of geometric data. In contrast to traditional approaches, a key feature of data-driven approaches is that they aggregate information from a collection of shapes to improve the analysis and processing of individual shapes. In addition, they are able to learn models that reason about properties and relationships of shapes without relying on hard-coded rules or explicitly programmed instructions. We provide an overview of the main concepts and components of these techniques, and discuss their application to shape classification, segmentation, matching, reconstruction, modeling and exploration, as well as scene analysis and synthesis, through reviewing the literature and relating the existing works with both qualitative and numerical comparisons. We conclude our report with ideas that can inspire future research in data-driven shape analysis and processing.Comment: 10 pages, 19 figure

"Last-Mile" preparation for a potential disaster

Extreme natural events, like e.g. tsunamis or earthquakes, regularly lead to catastrophes with dramatic consequences. In recent years natural disasters caused hundreds of thousands of deaths, destruction of infrastructure, disruption of economic activity and loss of billions of dollars worth of property and thus revealed considerable deficits hindering their effective management: Needs for stakeholders, decision-makers as well as for persons concerned include systematic risk identification and evaluation, a way to assess countermeasures, awareness raising and decision support systems to be employed before, during and after crisis situations. The overall goal of this study focuses on interdisciplinary integration of various scientific disciplines to contribute to a tsunami early warning information system. In comparison to most studies our focus is on high-end geometric and thematic analysis to meet the requirements of small-scale, heterogeneous and complex coastal urban systems. Data, methods and results from engineering, remote sensing and social sciences are interlinked and provide comprehensive information for disaster risk assessment, management and reduction. In detail, we combine inundation modeling, urban morphology analysis, population assessment, socio-economic analysis of the population and evacuation modeling. The interdisciplinary results eventually lead to recommendations for mitigation strategies in the fields of spatial planning or coping capacity