Adaptive rational fractal interpolation function for image super-resolution via local fractal analysis

© 2019 Elsevier B.V. Image super-resolution aims to generate high-resolution image based on the given low-resolution image and to recover the details of the image. The common approaches include reconstruction-based methods and interpolation-based methods. However, these existing methods show difficulty in processing the regions of an image with complicated texture. To tackle such problems, fractal geometry is applied on image super-resolution, which demonstrates its advantages when describing the complicated details in an image. The common fractal-based method regards the whole image as a single fractal set. That is, it does not distinguish the complexity difference of texture across all regions of an image regardless of smooth regions or texture rich regions. Due to such strong presumption, it causes artificial errors while recovering smooth area and texture blurring at the regions with rich texture. In this paper, the proposed method produces rational fractal interpolation model with various setting at different regions to adapt to the local texture complexity. In order to facilitate such mechanism, the proposed method is able to segment the image region according to its complexity which is determined by its local fractal dimension. Thus, the image super-resolution process is cast to an optimization problem where local fractal dimension in each region is further optimized until the optimization convergence is reached. During the optimization (i.e. super-resolution), the overall image complexity (determined by local fractal dimension) is maintained. Compared with state-of-the-art method, the proposed method shows promising performance according to qualitative evaluation and quantitative evaluation

Stochastic Rounding for Image Interpolation and Scan Conversion

The stochastic rounding (SR) function is proposed to evaluate and demonstrate the effects of stochastically rounding row and column subscripts in image interpolation and scan conversion. The proposed SR function is based on a pseudorandom number, enabling the pseudorandom rounding up or down any non-integer row and column subscripts. Also, the SR function exceptionally enables rounding up any possible cases of subscript inputs that are inferior to a pseudorandom number. The algorithm of interest is the nearest-neighbor interpolation (NNI) which is traditionally based on the deterministic rounding (DR) function. Experimental simulation results are provided to demonstrate the performance of NNI-SR and NNI-DR algorithms before and after applying smoothing and sharpening filters of interest. Additional results are also provided to demonstrate the performance of NNI-SR and NNI-DR interpolated scan conversion algorithms in cardiac ultrasound videos.Comment: 10 pages, 17 figures, 3 tables. International Journal of Advanced Computer Science and Applications, 202

Multiple hazards risk profiling in West Africa : Assessment, Validation and Upscaling

Disasters, particularly recurring small-scale natural disasters of floods and droughts have been affecting West African (WA) communities, impacting particularly weak households. These losses have been significantly high over the last decade due to increasing climate variability and inherently depressed socio-economic systems. However, to date, few studies have attempted to understand the vulnerability profiles in WA to these multiple hazards across several scales. A considerable number of studies predict the impacts of droughts and floods hazards, but many do so at a very coarse scale and without any participatory process, as a result, they are unable to predict localized impacts. Despite many efforts put in vulnerability assessments, there has been limited success in simultaneously traversing scale and hierarchy and the need for upscaling risk indices is important to understand the effects of cross scale interactions. To address these gaps, this thesis (i) explored methods to involve at-risk populations in local communities in a bottom-up participatory process as opposed to the classical top-down, single scale approaches and (ii) assessed the risks from multi-hazard perspectives in a coupled Socio-Ecological System (SES). The thesis also (iii) explored appropriate methodologies that can reflect the spatial variability of flood hazard intensity at community level. Building on these investigations, the thesis finally (iv) introduced a novel risk index upscaling procedure to upscale risk and vulnerability indices across multiple scales. The thesis used several methods ranging from rural participatory methods, statistical, Geographic Information System (GIS), remote sensing and introduced the innovative concept of Community Impact Score (CIS). The results show that more than half of the designated local level indicators and over two thirds of the macro scale indicators are rarely used in present risk assessments in the region. Additionally, although an indicator may be common to three countries, their differential rankings will result in differences in explaining the risks faced by people in different societies. Empirical validation of a flood hazard map using the statistical confusion matrix and the principles of participatory GIS show that flood hazard areas could be mapped at an accuracy ranging from 77% to 81%. These high mapping accuracies notwithstanding, the flood index categories may change under conditions of very high rainfall intensities beyond the anomalies used to construct the model. To this end, studies that aim at understanding projected flood intensities under varying rainfall conditions beyond the anomalies used in this study are recommended. This is important to determine the trajectory of flood safe havens or hotspots across an entire study area. The study also develops two important indices, The West Sudanian Community Vulnerability Index (WESCVI) and The West Sudanian Community Risk Index (WESCRI). The underlying factors constituting the two indices are the elements of risk and vulnerability profiles of communities in West Africa. The WESCVI and WESCRI should help planners and policy makers to analyse and finally reduce vulnerability and risk. To evaluate the results of the risk indices, this thesis introduces a novel technique to validate the results of complex aggregation methods. Based on up to date knowledge, the CIS concept is the first in the available literature of risk assessment. The thesis also provides a theoretical concept to upscale risk and vulnerability indicators from watershed to higher spatial scales. Further studies are however recommended to apply these theoretical concepts. A conclusion of the thesis is that while it has neither been optimal to completely neglect classical approaches nor to take as an absolute fact opinion from local experts, more emphasis should be paid to the later in risk assessment that is supposed to serve the very people on whose behalf the assessment is done. Attempts should therefore be made in finding mechanisms where the two approaches could interact fruitfully and complement each other.Mehrfach-Gefährdungen und Risikoprofile in West Afrika : Abschätzung, Validierung und Hochskalierung Naturgefahren, wie beispielsweise Überflutungen und Dürren, bedrohen die Existenz von Gemeinden und insbesondere schwächeren Haushalten in West Afrika. Durch die zunehmende Klimavariabilität und den geschwächten Zustand der sozial-ökologischen Systeme haben die Verluste während der letzten Dekade ein besonders hohes Ausmaß erreicht. Bisher haben nur wenige Studien versucht, die unterschiedliche Zusammensetzung des Risikos im Hinblick auf mehrere Naturgefahren in Westafrika zu verstehen und über verschiedene Skalen hinweg, von ländlichen Gemeinden hin zu Wassereinzugsgebieten, Distrikten und Regionen zu analysieren. Eine signifikante Anzahl von Studien prognostiziert die zu erwarteten Schäden durch Naturgefahren wie Überflutungen und Dürren. Dies geschieht jedoch oftmals auf einem sehr groben Maßstab, wohingegen wenig über die lokalen Auswirkungen bekannt ist. Trotz mannigfaltiger Anstrengungen in Bezug auf Vulnerabilitätsassessments gab es bisher wenig Erfolg bei der Berücksichtigung verschiedener Skalen und Hierarchien. Die Hochskalierung von Risikoindizes ist jedoch nötig, um die Effekte über verschiedene Skalen hinweg zu verstehen. Diese Forschungslücken werden in dieser Arbeit aufgegriffen und mit methodischen Verfahren über einen „Bottom-up“-Ansatz adressiert, der zunächst die gefährdete Bevölkerung involviert, um die Risiken gegenüber von mehrfachen Gefährdungen in einem sozio-ökologischen System (SES) zu untersuchen. Außerdem verwendet die Studie Methoden, die es ermöglichen, die räumliche Variabilität der Überflutungsintensität auf Gemeindeebene zu reflektieren. Aufbauend auf diesen Forschungsergebnissen stellt diese Arbeit eine neue Vorgehensweise vor, die es erlaubt Verwundbarkeits- und Risikoindizes über verschiedene Skalen hinweg hochzuskalieren. Der Methodenmix umfasst partizipative und statistische Ansätze sowie Methoden basierend auf Geographische Informationssystemen (GIS) und Fernerkundung. Des Weiteren schlägt die Arbeit ein innovatives Konzept zur Quantifizierung der Gefährdungsauswirkungen auf Gemeindeebene vor, den sogenannten „Community Impact Score“ (CIS). Die Ergebnisse zeigen, dass etwas mehr als die Hälfte der in dieser Arbeit abgeleiteten Indikatoren auf Gemeindeebene und über zwei Drittel der Indikatoren auf Makroebene selten in den gegenwärtigen Risikoassessments der Region verwendet werden. Zudem wurde den Indikatoren, selbst wenn sie für alle drei Länder abgeleitet wurden, oftmals eine unterschiedliche Wichtigkeit zugesprochen. Die empirische Validierung der Hochwassergefährdungskarten mittels einer statistischen Konfusionsmatrix basierend auf einem partizipativen GIS zeigt, dass die durch Hochwasser gefährdeten Gebiete mit einer Genauigkeit von 77-81% kartiert werden konnten. Trotz dieser hohen Genauigkeit ist es jedoch möglich, dass sich die Hochwassergefährdungskategorien bei Anomalitäten, die über die modellierten Bedingungen hinausreichen, verändern. Dementsprechend werden weiterführende Studien, die eben diese Bedingungen untersuchen empfohlen. Dies ist zur Bestimmung von sicheren Zufluchtsorten oder Hotspots von großer Bedeutung. In dieser Studie wurden außerdem zwei verschiedene Indizes entwickelt, der sogenannte „West Sudanian Community Vulnerability Index“ (WESCVI) und der „West Sudanian Community Risk Index“ (WESCRI). Die den Indizes zugrunde liegenden Faktoren bilden außerdem die Bestandteile der Risiko- und Vulnerabilitätsprofile für die Gemeinden Westafrikas. Sowohl der WESCVI als auch der WESCRI sollen Planern und politischen Entscheidungsträgern dabei helfen, die Vulnerabilität und das Risiko zu analysieren und zu reduzieren. Um die Ergebnisse der Risikoindizes zu evaluieren stellt diese Arbeit ein innovatives Konzept zur Validierung solch komplexer Aggregationsmethoden vor. Nach aktuellem Kenntnisstand ist das CIS Konzept das erste seiner Art in der erhältlichen Literatur zu Risikoassessments. Des Weiteren wurde ein theoretisches Konzept zur Hochskalierung von Risiko- und Vulnerabilitätsindizes von Wassereinzugsgebieten hin zu höheren Ebenen erarbeitet.Dieses theoretische Konzept bietet eine Basis für weiterführende Untersuchungen im Hinblick auf die Anwendung und Umsetzung. Insgesamt unterstreicht diese Studie, dass weder die klassischen Ansätze allein noch das Gleichsetzen von lokalem Expertenwissen mit der absoluten Wahrheit als optimal erachtet werden können. Die Studie zeigt, dass man dem lokalen Expertenwissen in Risikoassessments mehr Gewicht beimessen sollte. Dementsprechend sollten Ansätze gefunden werden, bei denen sich beide Herangehensweisen erfolgreich ergänzen

Reactive Flows in Deformable, Complex Media

Many processes of highest actuality in the real life are described through systems of equations posed in complex domains. Of particular interest is the situation when the domain is variable, undergoing deformations that depend on the unknown quantities of the model. Such kind of problems are encountered as mathematical models in the subsurface, or biological systems. Such models include various processes at different scales, and the key issue is to integrate the domain deformation in the multi-scale context. Having this as the background theme, this workshop focused on novel techniques and ideas in the analysis, the numerical discretization and the upscaling of such problems, as well as on applications of major societal relevance today

Deep Learning for Single Image Super-Resolution: A Brief Review

Single image super-resolution (SISR) is a notoriously challenging ill-posed problem, which aims to obtain a high-resolution (HR) output from one of its low-resolution (LR) versions. To solve the SISR problem, recently powerful deep learning algorithms have been employed and achieved the state-of-the-art performance. In this survey, we review representative deep learning-based SISR methods, and group them into two categories according to their major contributions to two essential aspects of SISR: the exploration of efficient neural network architectures for SISR, and the development of effective optimization objectives for deep SISR learning. For each category, a baseline is firstly established and several critical limitations of the baseline are summarized. Then representative works on overcoming these limitations are presented based on their original contents as well as our critical understandings and analyses, and relevant comparisons are conducted from a variety of perspectives. Finally we conclude this review with some vital current challenges and future trends in SISR leveraging deep learning algorithms.Comment: Accepted by IEEE Transactions on Multimedia (TMM

Robustness properties of estimators in generalized Pareto Models

We study global and local robustness properties of several estimators for shape and scale in a generalized Pareto model. The estimators considered in this paper cover maximum likelihood estimators, skipped maximum likelihood estimators, moment-based estimators, Cramér-von-Mises Minimum Distance estimators, and, as a special case of quantile-based estimators, Pickands Estimator as well as variants of the latter tuned for higher finite sample breakdown point (FSBP), and lower variance. We further consider an estimator matching population median and median of absolute deviations to the empirical ones (MedMad); again, in order to improve its FSBP, we propose a variant using a suitable asymmetric Mad as constituent, and which may be tuned to achieve an expected FSBP of 34%. These estimators are compared to one-step estimators distinguished as optimal in the shrinking neighborhood setting, i.e., the most bias-robust estimator minimizing the maximal (asymptotic) bias and the estimator minimizing the maximal (asymptotic) MSE. For each of these estimators, we determine the FSBP, the influence function, as well as statistical accuracy measured by asymptotic bias, variance, and mean squared error—all evaluated uniformly on shrinking convex contamination neighborhoods. Finally, we check these asymptotic theoretical findings against finite sample behavior by an extensive simulation study

G-CSC Report 2010

The present report gives a short summary of the research of the Goethe Center for Scientific Computing (G-CSC) of the Goethe University Frankfurt. G-CSC aims at developing and applying methods and tools for modelling and numerical simulation of problems from empirical science and technology. In particular, fast solvers for partial differential equations (i.e. pde) such as robust, parallel, and adaptive multigrid methods and numerical methods for stochastic differential equations are developed. These methods are highly adanvced and allow to solve complex problems.. The G-CSC is organised in departments and interdisciplinary research groups. Departments are localised directly at the G-CSC, while the task of interdisciplinary research groups is to bridge disciplines and to bring scientists form different departments together. Currently, G-CSC consists of the department Simulation and Modelling and the interdisciplinary research group Computational Finance