Mathematical and Data-driven Pattern Representation with Applications in Image Processing, Computer Graphics, and Infinite Dimensional Dynamical Data Mining

Patterns represent the spatial or temporal regularities intrinsic to various phenomena in nature, society, art, and science. From rigid ones with well-defined generative rules to flexible ones implied by unstructured data, patterns can be assigned to a spectrum. On one extreme, patterns are completely described by algebraic systems where each individual pattern is obtained by repeatedly applying simple operations on primitive elements. On the other extreme, patterns are perceived as visual or frequency regularities without any prior knowledge of the underlying mechanisms. In this thesis, we aim at demonstrating some mathematical techniques for representing patterns traversing the aforementioned spectrum, which leads to qualitative analysis of the patterns' properties and quantitative prediction of the modeled behaviors from various perspectives. We investigate lattice patterns from material science, shape patterns from computer graphics, submanifold patterns encountered in point cloud processing, color perception patterns applied in underwater image processing, dynamic patterns from spatial-temporal data, and low-rank patterns exploited in medical image reconstruction. For different patterns and based on their dependence on structured or unstructured data, we present suitable mathematical representations using techniques ranging from group theory to deep neural networks.Ph.D

Joint methods in imaging based on diffuse image representations

This thesis deals with the application and the analysis of different variants of the Mumford-Shah model in the context of image processing. In this kind of models, a given function is approximated in a piecewise smooth or piecewise constant manner. Especially the numerical treatment of the discontinuities requires additional models that are also outlined in this work. The main part of this thesis is concerned with four different topics. Simultaneous edge detection and registration of two images: The image edges are detected with the Ambrosio-Tortorelli model, an approximation of the Mumford-Shah model that approximates the discontinuity set with a phase field, and the registration is based on these edges. The registration obtained by this model is fully symmetric in the sense that the same matching is obtained if the roles of the two input images are swapped. Detection of grain boundaries from atomic scale images of metals or metal alloys: This is an image processing problem from materials science where atomic scale images are obtained either experimentally for instance by transmission electron microscopy or by numerical simulation tools. Grains are homogenous material regions whose atomic lattice orientation differs from their surroundings. Based on a Mumford-Shah type functional, the grain boundaries are modeled as the discontinuity set of the lattice orientation. In addition to the grain boundaries, the model incorporates the extraction of a global elastic deformation of the atomic lattice. Numerically, the discontinuity set is modeled by a level set function following the approach by Chan and Vese. Joint motion estimation and restoration of motion-blurred video: A variational model for joint object detection, motion estimation and deblurring of consecutive video frames is proposed. For this purpose, a new motion blur model is developed that accurately describes the blur also close to the boundary of a moving object. Here, the video is assumed to consist of an object moving in front of a static background. The segmentation into object and background is handled by a Mumford-Shah type aspect of the proposed model. Convexification of the binary Mumford-Shah segmentation model: After considering the application of Mumford-Shah type models to tackle specific image processing problems in the previous topics, the Mumford-Shah model itself is studied more closely. Inspired by the work of Nikolova, Esedoglu and Chan, a method is developed that allows global minimization of the binary Mumford-Shah segmentation model by solving a convex, unconstrained optimization problem. In an outlook, segmentation of flowfields into piecewise affine regions using this convexification method is briefly discussed

Information Extraction and Modeling from Remote Sensing Images: Application to the Enhancement of Digital Elevation Models

To deal with high complexity data such as remote sensing images presenting metric resolution over large areas, an innovative, fast and robust image processing system is presented. The modeling of increasing level of information is used to extract, represent and link image features to semantic content. The potential of the proposed techniques is demonstrated with an application to enhance and regularize digital elevation models based on information collected from RS images

Design and Evaluation of a Novel Lens-Based SPECT System Based on Laue Lens Gamma Diffraction: GEANT4/GAMOS Monte Carlo Study

Abstract While improvements in SPECT imaging techniques constitute a significant advance in biomedical science and cancer diagnosis, their limited spatial resolution has hindered their application to small animal research and early tumour detection. Using recent breakthroughs established by the high-energy astrophysics community, focusing X-ray optics provides a method to overcome the paradigm of low resolution and presents the possibility of imaging small objects with sub-millimetre resolution. This thesis aims to tackle the constraints associated with the current SPECT imaging designs by exploiting the notion of focusing high energy photons through Laue lens diffraction and developing a means of performing gamma rays imaging that would not rely on parallel or pinhole collimators. The gradual development of the novel system is discussed, starting from the single, modular, and multi-Laue lens-based SPECT. A customized 3D reconstruction algorithm was developed to reconstruct an accurate 3D radioactivity distribution from focused projections. A plug-in implementing the Laue diffraction concept was developed and used to model gamma rays focusing in the GEANT4 toolkit. The plug-in will be incorporated into GEANT4 upon final approval from its developers. The single lens-based, modular lens-based and multi lens-based SPECT models detected one hit per 42 source photons (sensitivity of 790 ⁄), three hits per 42 source photons (sensitivity of 2,373 ⁄), and one hit per 20 source photons (sensitivity of 1,670 ⁄), respectively. Based on the generated 3D reconstructed images, the achievable spatial resolution was found to be 0.1 full width at half maximum (FWHM). The proposed design’s performance parameters were compared against the existing SIEMENS parallel LEHR and multi-pinhole (5-MWB-1.0) Inveon SPECT. The achievable spatial resolution is decoupled from the sensitivity of the system, which is in stark contrast with the existing collimators that suffer from the resolution-sensitivity trade-off and are limited to a resolution of 2 . The proposed system allows discrimination between adjacent volumes as small as 0.113 , which is substantially smaller than what can be imaged by any existing SPECT or PET system. The proposed design could lay the foundation for a new SPECT imaging technology akin to a combination of tomosynthesis and lightfield imaging

Discrete Tomography by Convex-Concave Regularization using Linear and Quadratic Optimization

Discrete tomography concerns the reconstruction of objects that are made up from a few different materials, each of which comprising a homogeneous density distribution. Under the assumption that these densities are a priori known new algorithms can be developed which typically need less projection data to reveal appealing reconstruction results

Microscopy Conference 2021 (MC 2021) - Proceedings

Das Dokument enthält die Kurzfassungen der Beiträge aller Teilnehmer an der Mikroskopiekonferenz "MC 2021"

ReSCon '10, Research Student Conference: Book of Abstracts

The third SED Research Student Conference (ReSCon2010) was hosted over three days, 21-23 June 2010, in the Hamilton Centre at Brunel University. The conference consisted of oral and poster presentations, which showcased the high quality and diversity of the research being conducted within the School of Engineering and Design. The abstracts and presentations were the result of ongoing research by postgraduate research students from the School. The conference is held annually, and ReSCon plays a key role in contributing to research and innovations within the School