Radial Basis Functions: Biomedical Applications and Parallelization

Radial basis function (RBF) is a real-valued function whose values depend only on the distances between an interpolation point and a set of user-specified points called centers. RBF interpolation is one of the primary methods to reconstruct functions from multi-dimensional scattered data. Its abilities to generalize arbitrary space dimensions and to provide spectral accuracy have made it particularly popular in different application areas, including but not limited to: finding numerical solutions of partial differential equations (PDEs), image processing, computer vision and graphics, deep learning and neural networks, etc. The present thesis discusses three applications of RBF interpolation in biomedical engineering areas: (1) Calcium dynamics modeling, in which we numerically solve a set of PDEs by using meshless numerical methods and RBF-based interpolation techniques; (2) Image restoration and transformation, where an image is restored from its triangular mesh representation or transformed under translation, rotation, and scaling, etc. from its original form; (3) Porous structure design, in which the RBF interpolation used to reconstruct a 3D volume containing porous structures from a set of regularly or randomly placed points inside a user-provided surface shape. All these three applications have been investigated and their effectiveness has been supported with numerous experimental results. In particular, we innovatively utilize anisotropic distance metrics to define the distance in RBF interpolation and apply them to the aforementioned second and third applications, which show significant improvement in preserving image features or capturing connected porous structures over the isotropic distance-based RBF method. Beside the algorithm designs and their applications in biomedical areas, we also explore several common parallelization techniques (including OpenMP and CUDA-based GPU programming) to accelerate the performance of the present algorithms. In particular, we analyze how parallel programming can help RBF interpolation to speed up the meshless PDE solver as well as image processing. While RBF has been widely used in various science and engineering fields, the current thesis is expected to trigger some more interest from computational scientists or students into this fast-growing area and specifically apply these techniques to biomedical problems such as the ones investigated in the present work

Hardware-accelerated algorithms in visual computing

This thesis presents new parallel algorithms which accelerate computer vision methods by the use of graphics processors (GPUs) and evaluates them with respect to their speed, scalability, and the quality of their results. It covers the fields of homogeneous and anisotropic diffusion processes, diffusion image inpainting, optic flow, and halftoning. In this turn, it compares different solvers for homogeneous diffusion and presents a novel \u27extended\u27 box filter. Moreover, it suggests to use the fast explicit diffusion scheme (FED) as an efficient and flexible solver for nonlinear and in particular for anisotropic parabolic diffusion problems on graphics hardware. For elliptic diffusion-like processes, it recommends to use cascadic FED or Fast Jacobi schemes. The presented optic flow algorithm represents one of the fastest yet very accurate techniques. Finally, it presents a novel halftoning scheme which yields state-of-the-art results for many applications in image processing and computer graphics.Diese Arbeit präsentiert neue parallele Algorithmen zur Beschleunigung von Methoden in der Bildinformatik mittels Grafikprozessoren (GPUs), und evaluiert diese im Hinblick auf Geschwindigkeit, Skalierungsverhalten, und Qualität der Resultate. Sie behandelt dabei die Gebiete der homogenen und anisotropen Diffusionsprozesse, Inpainting (Bildvervollständigung) mittels Diffusion, die Bestimmung des optischen Flusses, sowie Halbtonverfahren. Dabei werden verschiedene Löser für homogene Diffusion verglichen und ein neuer \u27erweiterter\u27 Mittelwertfilter präsentiert. Ferner wird vorgeschlagen, das schnelle explizite Diffusionsschema (FED) als effizienten und flexiblen Löser für parabolische nichtlineare und speziell anisotrope Diffusionsprozesse auf Grafikprozessoren einzusetzen. Für elliptische diffusionsartige Prozesse wird hingegen empfohlen, kaskadierte FED- oder schnelle Jacobi-Verfahren einzusetzen. Der vorgestellte Algorithmus zur Berechnung des optischen Flusses stellt eines der schnellsten und dennoch äußerst genauen Verfahren dar. Schließlich wird ein neues Halbtonverfahren präsentiert, das in vielen Bereichen der Bildverarbeitung und Computergrafik Ergebnisse produziert, die den Stand der Technik repräsentieren

ИНТЕЛЛЕКТУАЛЬНЫЙ числовым программным ДЛЯ MIMD-компьютер

For most scientific and engineering problems simulated on computers the solving of problems of the computational mathematics with approximately given initial data constitutes an intermediate or a final stage. Basic problems of the computational mathematics include the investigating and solving of linear algebraic systems, evaluating of eigenvalues and eigenvectors of matrices, the solving of systems of non-linear equations, numerical integration of initial- value problems for systems of ordinary differential equations.Для більшості наукових та інженерних задач моделювання на ЕОМ рішення задач обчислювальної математики з наближено заданими вихідними даними складає проміжний або остаточний етап. Основні проблеми обчислювальної математики відносяться дослідження і рішення лінійних алгебраїчних систем оцінки власних значень і власних векторів матриць, рішення систем нелінійних рівнянь, чисельного інтегрування початково задач для систем звичайних диференціальних рівнянь.Для большинства научных и инженерных задач моделирования на ЭВМ решение задач вычислительной математики с приближенно заданным исходным данным составляет промежуточный или окончательный этап. Основные проблемы вычислительной математики относятся исследования и решения линейных алгебраических систем оценки собственных значений и собственных векторов матриц, решение систем нелинейных уравнений, численного интегрирования начально задач для систем обыкновенных дифференциальных уравнений

Modeling and Halftoning for Multichannel Printers: A Spectral Approach

Printing has been has been the major communication medium for many centuries. In the last twenty years, multichannel printing has brought new opportunities and challenges. Beside of extended colour gamut of the multichannel printer, the opportunity was presented to use a multichannel printer for ‘spectral printing’. The aim of spectral printing is typically the same as for colour printing; that is, to match input signal with printing specific ink combinations. In order to control printers so that the combination or mixture of inks results in specific colour or spectra requires a spectral reflectance printer model that estimates reflectance spectra from nominal dot coverage. The printer models have one of the key roles in accurate communication of colour to the printed media. Accordingly, this has been one of the most active research areas in printing. The research direction was toward improvement of the model accuracy, model simplicity and toward minimal resources used by the model in terms of computational power and usage of material. The contribution of the work included in the thesis is also directed toward improvement of the printer models but for the multichannel printing. The thesis is focused primarily on improving existing spectral printer models and developing a new model. In addition, the aim was to develop and implement a multichannel halftoning method which should provide with high image quality. Therefore, the research goals of the thesis were: maximal accuracy of printer models, optimal resource usage and maximal image quality of halftoning and whole spectral reproduction system. Maximal colour accuracy of a model but with the least resources used is achieved by optimizing printer model calibration process. First, estimation of the physical and optical dot gain is performed with newly proposed method and model. Second, a custom training target is estimated using the proposed new method. These two proposed methods and one proposed model were at the same time the means of optimal resource usage, both in computational time and material. The third goal was satisfied with newly proposed halftoning method for multichannel printing. This method also satisfies the goal of optimal computational time but with maintaining high image quality. When applied in spectral reproduction workflow, this halftoning reduces noise induced in an inversion of the printer model. Finally, a case study was conducted on the practical use of multichannel printers and spectral reproduction workflow. In addition to a gamut comparison in colour space, it is shown that otherwise limited reach of spectral printing could potentially be used to simulate spectra and colour of textile fabrics

Procedural Generation and Rendering of Realistic, Navigable Forest Environments: An Open-Source Tool

Simulation of forest environments has applications from entertainment and art creation to commercial and scientific modelling. Due to the unique features and lighting in forests, a forest-specific simulator is desirable, however many current forest simulators are proprietary or highly tailored to a particular application. Here we review several areas of procedural generation and rendering specific to forest generation, and utilise this to create a generalised, open-source tool for generating and rendering interactive, realistic forest scenes. The system uses specialised L-systems to generate trees which are distributed using an ecosystem simulation algorithm. The resulting scene is rendered using a deferred rendering pipeline, a Blinn-Phong lighting model with real-time leaf transparency and post-processing lighting effects. The result is a system that achieves a balance between high natural realism and visual appeal, suitable for tasks including training computer vision algorithms for autonomous robots and visual media generation.Comment: 14 pages, 11 figures. Submitted to Computer Graphics Forum (CGF). The application and supporting configuration files can be found at https://github.com/callumnewlands/ForestGenerato

From rule-based to learning-based image-conditional image generation

Visual contents, such as movies, animations, computer games, videos and photos, are massively produced and consumed nowadays. Most of these contents are the combination of materials captured from real-world and contents synthesized by computers. Particularly, computer-generated visual contents are increasingly indispensable in modern entertainment and production. The generation of visual contents by computers is typically conditioned on real-world materials, driven by the imagination of designers and artists, or a combination of both. However, creating visual contents manually are both challenging and labor intensive. Therefore, enabling computers to automatically or semi-automatically synthesize needed visual contents becomes essential. Among all these efforts, a stream of research is to generate novel images based on given image priors, e.g., photos and sketches. This research direction is known as image-conditional image generation, which covers a wide range of topics such as image stylization, image completion, image fusion, sketch-to-image generation, and extracting image label maps. In this thesis, a set of novel approaches for image-conditional image generation are presented. The thesis starts with an exemplar-based method for facial image stylization in Chapter 2. This method involves a unified framework for facial image stylization based on a single style exemplar. A two-phase procedure is employed, where the first phase searches a dense and semantic-aware correspondence between the input and the exemplar images, and the second phase conducts edge-preserving texture transfer. While this algorithm has the merit of requiring only a single exemplar, it is constrained to face photos. To perform generalized image-to-image translation, Chapter 3 presents a data-driven and learning-based method. Inspired by the dual learning paradigm designed for natural language translation [115], a novel dual Generative Adversarial Network (DualGAN) mechanism is developed, which enables image translators to be trained from two sets of unlabeled images from two domains. This is followed by another data-driven method in Chapter 4, which learns multiscale manifolds from a set of images and then enables synthesizing novel images that mimic the appearance of the target image dataset. The method is named as Branched Generative Adversarial Network (BranchGAN) and employs a novel training method that enables unconditioned generative adversarial networks (GANs) to learn image manifolds at multiple scales. As a result, we can directly manipulate and even combine latent manifold codes that are associated with specific feature scales. Finally, to provide users more control over image generation results, Chapter 5 discusses an upgraded version of iGAN [126] (iGANHD) that significantly improves the art of manipulating high-resolution images through utilizing the multi-scale manifold learned with BranchGAN