Graph Spectral Image Processing

Recent advent of graph signal processing (GSP) has spurred intensive studies of signals that live naturally on irregular data kernels described by graphs (e.g., social networks, wireless sensor networks). Though a digital image contains pixels that reside on a regularly sampled 2D grid, if one can design an appropriate underlying graph connecting pixels with weights that reflect the image structure, then one can interpret the image (or image patch) as a signal on a graph, and apply GSP tools for processing and analysis of the signal in graph spectral domain. In this article, we overview recent graph spectral techniques in GSP specifically for image / video processing. The topics covered include image compression, image restoration, image filtering and image segmentation

Feature-preserving image restoration and its application in biological fluorescence microscopy

This thesis presents a new investigation of image restoration and its application to fluorescence cell microscopy. The first part of the work is to develop advanced image denoising algorithms to restore images from noisy observations by using a novel featurepreserving diffusion approach. I have applied these algorithms to different types of images, including biometric, biological and natural images, and demonstrated their superior performance for noise removal and feature preservation, compared to several state of the art methods. In the second part of my work, I explore a novel, simple and inexpensive super-resolution restoration method for quantitative microscopy in cell biology. In this method, a super-resolution image is restored, through an inverse process, by using multiple diffraction-limited (low) resolution observations, which are acquired from conventional microscopes whilst translating the sample parallel to the image plane, so referred to as translation microscopy (TRAM). A key to this new development is the integration of a robust feature detector, developed in the first part, to the inverse process to restore high resolution images well above the diffraction limit in the presence of strong noise. TRAM is a post-image acquisition computational method and can be implemented with any microscope. Experiments show a nearly 7-fold increase in lateral spatial resolution in noisy biological environments, delivering multi-colour image resolution of ~30 nm

Structure-aware image denoising, super-resolution, and enhancement methods

Denoising, super-resolution and structure enhancement are classical image processing applications. The motive behind their existence is to aid our visual analysis of raw digital images. Despite tremendous progress in these fields, certain difficult problems are still open to research. For example, denoising and super-resolution techniques which possess all the following properties, are very scarce: They must preserve critical structures like corners, should be robust to the type of noise distribution, avoid undesirable artefacts, and also be fast. The area of structure enhancement also has an unresolved issue: Very little efforts have been put into designing models that can tackle anisotropic deformations in the image acquisition process. In this thesis, we design novel methods in the form of partial differential equations, patch-based approaches and variational models to overcome the aforementioned obstacles. In most cases, our methods outperform the existing approaches in both quality and speed, despite being applicable to a broader range of practical situations.Entrauschen, Superresolution und Strukturverbesserung sind klassische Anwendungen der Bildverarbeitung. Ihre Existenz bedingt sich in dem Bestreben, die visuelle Begutachtung digitaler Bildrohdaten zu unterstützen. Trotz erheblicher Fortschritte in diesen Feldern bedürfen bestimmte schwierige Probleme noch weiterer Forschung. So sind beispielsweise Entrauschungsund Superresolutionsverfahren, welche alle der folgenden Eingenschaften besitzen, sehr selten: die Erhaltung wichtiger Strukturen wie Ecken, Robustheit bezüglich der Rauschverteilung, Vermeidung unerwünschter Artefakte und niedrige Laufzeit. Auch im Gebiet der Strukturverbesserung liegt ein ungelöstes Problem vor: Bisher wurde nur sehr wenig Forschungsaufwand in die Entwicklung von Modellen investieret, welche anisotrope Deformationen in bildgebenden Verfahren bewältigen können. In dieser Arbeit entwerfen wir neue Methoden in Form von partiellen Differentialgleichungen, patch-basierten Ansätzen und Variationsmodellen um die oben erwähnten Hindernisse zu überwinden. In den meisten Fällen übertreffen unsere Methoden nicht nur qualitativ die bisher verwendeten Ansätze, sondern lösen die gestellten Aufgaben auch schneller. Zudem decken wir mit unseren Modellen einen breiteren Bereich praktischer Fragestellungen ab

Experimental study of combustion and scalar mixing in swirling jet flows

Turbulent mixing of passive scalar field and combustion of gaseous fuel were studied in the context of a non-premixed isothermal and reacting swirling jets discharged from a swirl-stabilised burner, as a function of swirl number. The rate of molecular mixing, which was quantified by the scalar dissipation rate was computed from measured scalar fields that were recorded by using Planar Laser Induced Fluorescence (PLIF) of acetone. The influence of the swirl number on the scalar mixing, unconditional and conditional scalar dissipation rate statistics was investigated. Scalar fields were measured with an average error of 3%. Scalar dissipation rate was measured with an average error of 12% after de-nosing. The influence of swirl number on combustion characteristics was examined by using Rayleigh scattering with accuracy of 90%. The flow fields in non-reacting and reacting swirling jets were investigated by using Particle Image Velocimetry (PIV). The effect of swirl number on a recirculation zone was shown and discussed. The flow structures were evaluated by using Proper Orthogonal Decomposition. Experimental assessment of presumed filtered density function and subgrid scale (SGS) scalar variance models that are being developed in the context of Large Eddy Simulation (LES) was performed by using the data obtained from measured scalar fields. Measurements were performed in a flow formed by discharging a central jet in the annular stream of swirling air. This is a typical geometry used in swirl-stabilised burners where the central jet is the flow. The measurements were performed at a constant Reynolds number of 28662, based on the area-averaged velocity of 8.46 (m/s) at the exit of the swirl-stabilised burner and the diameter of the annular swirling stream of 50.8(mm). Three swirl numbers S = {0.3, 0.58, 1.07} of the annular swirling stream were considered.Open Acces

Experimental study of combustion and scalar mixing in swirling jet flows

Turbulent mixing of passive scalar field and combustion of gaseous fuel were studied in the context of a non-premixed isothermal and reacting swirling jets discharged from a swirl-stabilised burner, as a function of swirl number. The rate of molecular mixing, which was quantified by the scalar dissipation rate was computed from measured scalar fields that were recorded by using Planar Laser Induced Fluorescence (PLIF) of acetone. The influence of the swirl number on the scalar mixing, unconditional and conditional scalar dissipation rate statistics was investigated. Scalar fields were measured with an average error of 3%. Scalar dissipation rate was measured with an average error of 12% after de-nosing. The influence of swirl number on combustion characteristics was examined by using Rayleigh scattering with accuracy of 90%. The flow fields in non-reacting and reacting swirling jets were investigated by using Particle Image Velocimetry (PIV). The effect of swirl number on a recirculation zone was shown and discussed. The flow structures were evaluated by using Proper Orthogonal Decomposition. Experimental assessment of presumed filtered density function and subgrid scale (SGS) scalar variance models that are being developed in the context of Large Eddy Simulation (LES) was performed by using the data obtained from measured scalar fields. Measurements were performed in a flow formed by discharging a central jet in the annular stream of swirling air. This is a typical geometry used in swirl-stabilised burners where the central jet is the flow. The measurements were performed at a constant Reynolds number of 28662, based on the area-averaged velocity of 8.46 (m/s) at the exit of the swirl-stabilised burner and the diameter of the annular swirling stream of 50.8(mm). Three swirl numbers S = {0.3, 0.58, 1.07} of the annular swirling stream were considered

Visualization and Analysis of Flow Fields based on Clifford Convolution

Vector fields from flow visualization often containmillions of data values. It is obvious that a direct inspection of the data by the user is tedious. Therefore, an automated approach for the preselection of features is essential for a complete analysis of nontrivial flow fields. This thesis deals with automated detection, analysis, and visualization of flow features in vector fields based on techniques transfered from image processing. This work is build on rotation invariant template matching with Clifford convolution as developed in the diploma thesis of the author. A detailed analysis of the possibilities of this approach is done, and further techniques and algorithms up to a complete segmentation of vector fields are developed in the process. One of the major contributions thereby is the definition of a Clifford Fourier transform in 2D and 3D, and the proof of a corresponding convolution theorem for the Clifford convolution as well as other major theorems. This Clifford Fourier transform allows a frequency analysis of vector fields and the behavior of vectorvalued filters, as well as an acceleration of the convolution computation as a fast transform exists. The depth and precision of flow field analysis based on template matching and Clifford convolution is studied in detail for a specific application, which are flow fields measured in the wake of a helicopter rotor. Determining the features and their parameters in this data is an important step for a better understanding of the observed flow. Specific techniques dealing with subpixel accuracy and the parameters to be determined are developed on the way. To regard the flow as a superposition of simpler features is a necessity for this application as close vortices influence each other. Convolution is a linear system, so it is suited for this kind of analysis. The suitability of other flow analysis and visualization methods for this task is studied here as well. The knowledge and techniques developed for this work are brought together in the end to compute and visualize feature based segmentations of flow fields. The resulting visualizations display important structures of the flow and highlight the interesting features. Thus, a major step towards robust and automatic detection, analysis and visualization of flow fields is taken