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

Surface Constraint of a Rational Interpolation and the Application in Medical Image Processing

Abstract : A new weighted bivariate blending rational spline with parameters is constructed based on function values of a function only. The interpolation is C1 in the whole interpolating region under the condition which free parameters is not limited. This study deals with the bounded property of the interpolation. In order to meet the needs of practical design, an interpolation technique is employed to control the shape of surfaces. This rational interpolation with parameters is used in the medical image enhancement. The value of the interpolating function at any point in the interpolating region can be modified under the condition that the interpolating data are not changed by selecting the suitable parameters. Using the surface control, the local enhancement of the image is implemented. The experimentations show that this algorithm is efficient

Constructing new control points for Bézier interpolating polynomials using new geometrical approach

Interpolation is a mathematical technique employed for estimating the value of missing data between data points. This technique assures that the resulting polynomial passes through all data points. One of the most useful interpolating polynomials is the parametric interpolating polynomial. Bézier interpolating curves and surfaces are parametric interpolating polynomials for two-dimensional (2D) and three-dimensional (3D) datasets, respectively, that produce smooth, flexible, and accurate functions. According to the previous studies, the most crucial component in deriving Bézier interpolating polynomials is the construction of control points. However, most of the existing strategies constructed control points that produce partial smooth functions. As a result, the approximate values of the missing data are not accurate. In this study, nine new strategies of geometrical approach for constructing new 2D and 3D Bézier control points are proposed. The obtained control points from each new strategies are substituted in the relevant Bézier curve and surface equations to derive Bézier piecewise and non-piecewise interpolating polynomials which leads to the development of nine new methods. The proposed methods are proven to preserve the stability and smoothness of the generated Bézier interpolating curves and surfaces. In addition, the numerical results show that most of the resulting polynomials are able to approximate the missing values more accurately compared to those derived by the existing methods. The Bézier interpolating surfaces derived by the proposed method with highest accuracy for 3D datasets are then applied to upscale grey and colour images by the factors of two and three. Not only does the proposed method produces higher quality upscaled images, the numerical results also show that it outperforms the existing methods in terms of accuracy. Therefore, this study has successfully proposed new strategies for constructing new 2D and 3D control points for deriving Bézier interpolating polynomials that are capable of approximating the missing values accurately. In terms of application, the derived Bézier interpolating surfaces have a great potential to be employed in image upscaling

Vedel-objektiiv abil salvestatud kaugseire piltide analüüs kasutades super-resolutsiooni meetodeid

Väitekirja elektrooniline versioon ei sisalda publikatsiooneKäesolevas doktoritöös uuriti nii riist- kui ka tarkvaralisi lahendusi piltide töötlemiseks. Riist¬varalise poole pealt pakuti lahenduseks uudset vedelläätse, milles on dielekt¬rilisest elastomeerist kihilise täituriga membraan otse optilisel teljel. Doktoritöö käigus arendati välja kaks prototüüpi kahe erineva dielektrilisest elastomeerist ki¬hilise täituriga, mille aktiivne ala oli ühel juhul 40 ja teisel 20 mm. Läätse töö vas¬tas elastomeeri deformatsiooni mehaanikale ja suhtelistele muutustele fookuskau¬guses. Muutuste demonstreerimiseks meniskis ja läätse fookuskauguse mõõtmiseks kasutati laserkiirt. Katseandmetest selgub, et muutuste tekitamiseks on vajalik pinge vahemikus 50 kuni 750 volti. Tarkvaralise poole pealt pakuti uut satelliitpiltide parandamise süsteemi. Paku¬tud süsteem jagas mürase sisendpildi DT-CWT laineteisenduse abil mitmeteks sagedusalamribadeks. Pärast müra eemaldamist LA-BSF funktsiooni abil suu¬rendati pildi resolutsiooni DWT-ga ja kõrgsagedusliku alamriba piltide interpo¬leerimisega. Interpoleerimise faktor algsele pildile oli pool sellest, mida kasutati kõrgsagedusliku alamriba piltide interpoleerimisel ning superresolutsiooniga pilt rekonst¬rueeriti IDWT abil. Käesolevas doktoritöös pakuti tarkvaraliseks lahenduseks uudset sõnastiku baasil töötavat super-resolutsiooni (SR) meetodit, milles luuakse paarid suure resolutsiooniga (HR) ja madala resolut-siooniga (LR) piltidest. Kõigepealt jagati vastava sõnastiku loomiseks HR ja LR paarid omakorda osadeks. Esialgse HR kujutise saamiseks LR sisendpildist kombineeriti HR osi. HR osad valiti sõnastikust nii, et neile vastavad LR osad oleksid võimalikult lähedased sisendiks olevale LR pil¬dile. Iga valitud HR osa heledust korrigeeriti, et vähendada kõrvuti asuvate osade heleduse erine¬vusi superresolutsiooniga pildil. Plokkide efekti vähendamiseks ar¬vutati saadud SR pildi keskmine ning bikuupinterpolatsiooni pilt. Lisaks pakuti käesolevas doktoritöös välja kernelid, mille tulemusel on võimalik saadud SR pilte teravamaks muuta. Pakutud kernelite tõhususe tõestamiseks kasutati [83] ja [50] poolt pakutud resolutsiooni parandamise meetodeid. Superreso¬lutsiooniga pilt saadi iga kerneli tehtud HR pildi kombineerimise teel alpha blen¬dingu meetodit kasutades. Pakutud meetodeid ja kerneleid võrreldi erinevate tavaliste ja kaasaegsete meetoditega. Kvantita-tiivsetest katseandmetest ja saadud piltide kvaliteedi visuaal¬sest hindamisest selgus, et pakutud meetodid on tavaliste kaasaegsete meetoditega võrreldes paremad.In this thesis, a study of both hardware and software solutions for image enhance¬ment has been done. On the hardware side, a new liquid lens design with a DESA membrane located directly in the optical path has been demonstrated. Two pro¬totypes with two different DESA, which have a 40 and 20 mm active area in diameter, were developed. The lens performance was consistent with the mechan¬ics of elastomer deformation and relative focal length changes. A laser beam was used to show the change in the meniscus and to measure the focal length of the lens. The experimental results demonstrate that voltage in the range of 50 to 750 V is required to create change in the meniscus. On the software side, a new satellite image enhancement system was proposed. The proposed technique decomposed the noisy input image into various frequency subbands by using DT-CWT. After removing the noise by applying the LA-BSF technique, its resolution was enhanced by employing DWT and interpolating the high-frequency subband images. An original image was interpolated with half of the interpolation factor used for interpolating the high-frequency subband images, and the super-resolved image was reconstructed by using IDWT. A novel single-image SR method based on a generating dictionary from pairs of HR and their corresponding LR images was proposed. Firstly, HR and LR pairs were divided into patches in order to make HR and LR dictionaries respectively. The initial HR representation of an input LR image was calculated by combining the HR patches. These HR patches are chosen from the HR dictionary corre-sponding to the LR patches that have the closest distance to the patches of the in¬put LR image. Each selected HR patch was processed further by passing through an illumination enhancement processing order to reduce the noticeable change of illumination between neighbor patches in the super-resolved image. In order to reduce the blocking effect, the average of the obtained SR image and the bicubic interpolated image was calculated. The new kernels for sampling have also been proposed. The kernels can improve the SR by resulting in a sharper image. In order to demonstrate the effectiveness of the proposed kernels, the techniques from [83] and [50] for resolution enhance¬ment were adopted. The super-resolved image was achieved by combining the HR images produced by each of the proposed kernels using the alpha blending tech-nique. The proposed techniques and kernels are compared with various conventional and state-of-the-art techniques, and the quantitative test results and visual results on the final image quality show the superiority of the proposed techniques and ker¬nels over conventional and state-of-art technique

A Chronology of Interpolation: From Ancient Astronomy to Modern Signal and Image Processing

This paper presents a chronological overview of the developments in interpolation theory, from the earliest times to the present date. It brings out the connections between the results obtained in different ages, thereby putting the techniques currently used in signal and image processing into historical perspective. A summary of the insights and recommendations that follow from relatively recent theoretical as well as experimental studies concludes the presentation

Tensor B-spline numerical method for PDEs : a high performance approach

Solutions of Partial Differential Equations (PDEs) form the basis of many mathematical models in physics and medicine. In this work, a novel Tensor B-spline methodology for numerical solutions of linear second-order PDEs is proposed. The methodology applies the B-spline signal processing framework and computational tensor algebra in order to construct high-performance numerical solvers for PDEs. The method allows high-order approximations, is mesh-free, matrix-free and computationally and memory efficient. The first chapter introduces the main ideas of the Tensor B-spline method, depicts the main contributions of the thesis and outlines the thesis structure. The second chapter provides an introduction to PDEs, reviews the numerical methods for solving PDEs, introduces splines and signal processing techniques with B-splines, and describes tensors and the computational tensor algebra. The third chapter describes the principles of the Tensor B-spline methodology. The main aspects are 1) discretization of the PDE variational formulation via B-spline representation of the solution, the coefficients, and the source term, 2) introduction to the tensor B-spline kernels, 3) application of tensors and computational tensor algebra to the discretized variational formulation of the PDE, 4) tensor-based analysis of the problem structure, 5) derivation of the efficient computational techniques, and 6) efficient boundary processing and numerical integration procedures. The fourth chapter describes 1) different computational strategies of the Tensor B-spline solver and an evaluation of their performance, 2) the application of the method to the forward problem of the Optical Diffusion Tomography and an extensive comparison with the state-of-the-art Finite Element Method on synthetic and real medical data, 3) high-performance multicore CPU- and GPU-based implementations, and 4) the solution of large-scale problems on hardware with limited memory resources

Surface modelling for 2D imagery

Vector graphics provides powerful tools for drawing scalable 2D imagery. With the rise of mobile computers, of different types of displays and image resolutions, vector graphics is receiving an increasing amount of attention. However, vector graphics is not the leading framework for creating and manipulating 2D imagery. The reason for this reluctance of employing vector graphical frameworks is that it is difficult to handle complex behaviour of colour across the 2D domain. A challenging problem within vector graphics is to define smooth colour functions across the image. In previous work, two approaches exist. The first approach, known as diffusion curves, diffuses colours from a set of input curves and points. The second approach, known as gradient meshes, defines smooth colour functions from control meshes. These two approaches are incompatible: diffusion curves do not support the local behaviour provided by gradient meshes and gradient meshes do not support freeform curves as input. My research aims to narrow the gap between diffusion curves and gradient meshes. With this aim in mind, I propose solutions to create control meshes from freeform curves. I demonstrate that these control meshes can be used to render a vector primitive similar to diffusion curves using subdivision surfaces. With the use of subdivision surfaces, instead of a diffusion process, colour gradients can be locally controlled using colour-gradient curves associated with the input curves. The advantage of local control is further explored in the setting of vector-centric image processing. I demonstrate that a certain contrast enhancement profile, known as the Cornsweet profile, can be modelled via surfaces in images. This approach does not produce saturation artefacts related with previous filter-based methods. Additionally, I demonstrate various approaches to artistic filtering, where the artist locally models given artistic effects. Gradient meshes are restricted to rectangular topology of the control meshes. I argue that this restriction hinders the applicability of the approach and its potential to be used with control meshes extracted from freeform curves. To this end, I propose a mesh-based vector primitive that supports arbitrary manifold topology of the mesh

Exploratory search in time-oriented primary data

In a variety of research fields, primary data that describes scientific phenomena in an original condition is obtained. Time-oriented primary data, in particular, is an indispensable data type, derived from complex measurements depending on time. Today, time-oriented primary data is collected at rates that exceed the domain experts’ abilities to seek valuable information undiscovered in the data. It is widely accepted that the magnitudes of uninvestigated data will disclose tremendous knowledge in data-driven research, provided that domain experts are able to gain insight into the data. Domain experts involved in data-driven research urgently require analytical capabilities. In scientific practice, predominant activities are the generation and validation of hypotheses. In analytical terms, these activities are often expressed in confirmatory and exploratory data analysis. Ideally, analytical support would combine the strengths of both types of activities. Exploratory search (ES) is a concept that seamlessly includes information-seeking behaviors ranging from search to exploration. ES supports domain experts in both gaining an understanding of huge and potentially unknown data collections and the drill-down to relevant subsets, e.g., to validate hypotheses. As such, ES combines predominant tasks of domain experts applied to data-driven research. For the design of useful and usable ES systems (ESS), data scientists have to incorporate different sources of knowledge and technology. Of particular importance is the state-of-the-art in interactive data visualization and data analysis. Research in these factors is at heart of Information Visualization (IV) and Visual Analytics (VA). Approaches in IV and VA provide meaningful visualization and interaction designs, allowing domain experts to perform the information-seeking process in an effective and efficient way. Today, bestpractice ESS almost exclusively exist for textual data content, e.g., put into practice in digital libraries to facilitate the reuse of digital documents. For time-oriented primary data, ES mainly remains at a theoretical state. Motivation and Problem Statement. This thesis is motivated by two main assumptions. First, we expect that ES will have a tremendous impact on data-driven research for many research fields. In this thesis, we focus on time-oriented primary data, as a complex and important data type for data-driven research. Second, we assume that research conducted to IV and VA will particularly facilitate ES. For time-oriented primary data, however, novel concepts and techniques are required that enhance the design and the application of ESS. In particular, we observe a lack of methodological research in ESS for time-oriented primary data. In addition, the size, the complexity, and the quality of time-oriented primary data hampers the content-based access, as well as the design of visual interfaces for gaining an overview of the data content. Furthermore, the question arises how ESS can incorporate techniques for seeking relations between data content and metadata to foster data-driven research. Overarching challenges for data scientists are to create usable and useful designs, urgently requiring the involvement of the targeted user group and support techniques for choosing meaningful algorithmic models and model parameters. Throughout this thesis, we will resolve these challenges from conceptual, technical, and systemic perspectives. In turn, domain experts can benefit from novel ESS as a powerful analytical support to conduct data-driven research. Concepts for Exploratory Search Systems (Chapter 3). We postulate concepts for the ES in time-oriented primary data. Based on a survey of analysis tasks supported in IV and VA research, we present a comprehensive selection of tasks and techniques relevant for search and exploration activities. The assembly guides data scientists in the choice of meaningful techniques presented in IV and VA. Furthermore, we present a reference workflow for the design and the application of ESS for time-oriented primary data. The workflow divides the data processing and transformation process into four steps, and thus divides the complexity of the design space into manageable parts. In addition, the reference workflow describes how users can be involved in the design. The reference workflow is the framework for the technical contributions of this thesis. Visual-Interactive Preprocessing of Time-Oriented Primary Data (Chapter 4). We present a visual-interactive system that enables users to construct workflows for preprocessing time-oriented primary data. In this way, we introduce a means of providing content-based access. Based on a rich set of preprocessing routines, users can create individual solutions for data cleansing, normalization, segmentation, and other preprocessing tasks. In addition, the system supports the definition of time series descriptors and time series distance measures. Guidance concepts support users in assessing the workflow generalizability, which is important for large data sets. The execution of the workflows transforms time-oriented primary data into feature vectors, which can subsequently be used for downstream search and exploration techniques. We demonstrate the applicability of the system in usage scenarios and case studies. Content-Based Overviews (Chapter 5). We introduce novel guidelines and techniques for the design of contentbased overviews. The three key factors are the creation of meaningful data aggregates, the visual mapping of these aggregates into the visual space, and the view transformation providing layouts of these aggregates in the display space. For each of these steps, we characterize important visualization and interaction design parameters allowing the involvement of users. We introduce guidelines supporting data scientists in choosing meaningful solutions. In addition, we present novel visual-interactive quality assessment techniques enhancing the choice of algorithmic model and model parameters. Finally, we present visual interfaces enabling users to formulate visual queries of the time-oriented data content. In this way, we provide means of combining content-based exploration with content-based search. Relation Seeking Between Data Content and Metadata (Chapter 6). We present novel visual interfaces enabling domain experts to seek relations between data content and metadata. These interfaces can be integrated into ESS to bridge analytical gaps between the data content and attached metadata. In three different approaches, we focus on different types of relations and define algorithmic support to guide users towards most interesting relations. Furthermore, each of the three approaches comprises individual visualization and interaction designs, enabling users to explore both the data and the relations in an efficient and effective way. We demonstrate the applicability of our interfaces with usage scenarios, each conducted together with domain experts. The results confirm that our techniques are beneficial for seeking relations between data content and metadata, particularly for data-centered research. Case Studies - Exploratory Search Systems (Chapter 7). In two case studies, we put our concepts and techniques into practice. We present two ESS constructed in design studies with real users, and real ES tasks, and real timeoriented primary data collections. The web-based VisInfo ESS is a digital library system facilitating the visual access to time-oriented primary data content. A content-based overview enables users to explore large collections of time series measurements and serves as a baseline for content-based queries by example. In addition, VisInfo provides a visual interface for querying time oriented data content by sketch. A result visualization combines different views of the data content and metadata with faceted search functionality. The MotionExplorer ESS supports domain experts in human motion analysis. Two content-based overviews enhance the exploration of large collections of human motion capture data from two perspectives. MotionExplorer provides a search interface, allowing domain experts to query human motion sequences by example. Retrieval results are depicted in a visual-interactive view enabling the exploration of variations of human motions. Field study evaluations performed for both ESS confirm the applicability of the systems in the environment of the involved user groups. The systems yield a significant improvement of both the effectiveness and the efficiency in the day-to-day work of the domain experts. As such, both ESS demonstrate how large collections of time-oriented primary data can be reused to enhance data-centered research. In essence, our contributions cover the entire time series analysis process starting from accessing raw time-oriented primary data, processing and transforming time series data, to visual-interactive analysis of time series. We present visual search interfaces providing content-based access to time-oriented primary data. In a series of novel explorationsupport techniques, we facilitate both gaining an overview of large and complex time-oriented primary data collections and seeking relations between data content and metadata. Throughout this thesis, we introduce VA as a means of designing effective and efficient visual-interactive systems. Our VA techniques empower data scientists to choose appropriate models and model parameters, as well as to involve users in the design. With both principles, we support the design of usable and useful interfaces which can be included into ESS. In this way, our contributions bridge the gap between search systems requiring exploration support and exploratory data analysis systems requiring visual querying capability. In the ESS presented in two case studies, we prove that our techniques and systems support data-driven research in an efficient and effective way