Mathematical Approaches for Image Enhancement Problems

This thesis develops novel techniques that can solve some image enhancement problems using theoretically and technically proven and very useful mathematical tools to image processing such as wavelet transforms, partial differential equations, and variational models. Three subtopics are mainly covered. First, color image denoising framework is introduced to achieve high quality denoising results by considering correlations between color components while existing denoising approaches can be plugged in flexibly. Second, a new and efficient framework for image contrast and color enhancement in the compressed wavelet domain is proposed. The proposed approach is capable of enhancing both global and local contrast and brightness as well as preserving color consistency. The framework does not require inverse transform for image enhancement since linear scale factors are directly applied to both scaling and wavelet coefficients in the compressed domain, which results in high computational efficiency. Also contaminated noise in the image can be efficiently reduced by introducing wavelet shrinkage terms adaptively in different scales. The proposed method is able to enhance a wavelet-coded image computationally efficiently with high image quality and less noise or other artifact. The experimental results show that the proposed method produces encouraging results both visually and numerically compared to some existing approaches. Finally, image inpainting problem is discussed. Literature review, psychological analysis, and challenges on image inpainting problem and related topics are described. An inpainting algorithm using energy minimization and texture mapping is proposed. Mumford-Shah energy minimization model detects and preserves edges in the inpainting domain by detecting both the main structure and the detailed edges. This approach utilizes faster hierarchical level set method and guarantees convergence independent of initial conditions. The estimated segmentation results in the inpainting domain are stored in segmentation map, which is referred by a texture mapping algorithm for filling textured regions. We also propose an inpainting algorithm using wavelet transform that can expect better global structure estimation of the unknown region in addition to shape and texture properties since wavelet transforms have been used for various image analysis problems due to its nice multi-resolution properties and decoupling characteristics

Echocardiography

The book "Echocardiography - New Techniques" brings worldwide contributions from highly acclaimed clinical and imaging science investigators, and representatives from academic medical centers. Each chapter is designed and written to be accessible to those with a basic knowledge of echocardiography. Additionally, the chapters are meant to be stimulating and educational to the experts and investigators in the field of echocardiography. This book is aimed primarily at cardiology fellows on their basic echocardiography rotation, fellows in general internal medicine, radiology and emergency medicine, and experts in the arena of echocardiography. Over the last few decades, the rate of technological advancements has developed dramatically, resulting in new techniques and improved echocardiographic imaging. The authors of this book focused on presenting the most advanced techniques useful in today's research and in daily clinical practice. These advanced techniques are utilized in the detection of different cardiac pathologies in patients, in contributing to their clinical decision, as well as follow-up and outcome predictions. In addition to the advanced techniques covered, this book expounds upon several special pathologies with respect to the functions of echocardiography

Mapping and Deep Analysis of Image Dehazing: Coherent Taxonomy, Datasets, Open Challenges, Motivations, and Recommendations

Our study aims to review and analyze the most relevant studies in the image dehazing field. Many aspects have been deemed necessary to provide a broad understanding of various studies that have been examined through surveying the existing literature. These aspects are as follows: datasets that have been used in the literature, challenges that other researchers have faced, motivations, and recommendations for diminishing the obstacles in the reported literature. A systematic protocol is employed to search all relevant articles on image dehazing, with variations in keywords, in addition to searching for evaluation and benchmark studies. The search process is established on three online databases, namely, IEEE Xplore, Web of Science (WOS), and ScienceDirect (SD), from 2008 to 2021. These indices are selected because they are sufficient in terms of coverage. Along with definition of the inclusion and exclusion criteria, we include 152 articles to the final set. A total of 55 out of 152 articles focused on various studies that conducted image dehazing, and 13 out 152 studies covered most of the review papers based on scenarios and general overviews. Finally, most of the included articles centered on the development of image dehazing algorithms based on real-time scenario (84/152) articles. Image dehazing removes unwanted visual effects and is often considered an image enhancement technique, which requires a fully automated algorithm to work under real-time outdoor applications, a reliable evaluation method, and datasets based on different weather conditions. Many relevant studies have been conducted to meet these critical requirements. We conducted objective image quality assessment experimental comparison of various image dehazing algorithms. In conclusions unlike other review papers, our study distinctly reflects different observations on image dehazing areas. We believe that the result of this study can serve as a useful guideline for practitioners who are looking for a comprehensive view on image dehazing

Advanced Image Acquisition, Processing Techniques and Applications

"Advanced Image Acquisition, Processing Techniques and Applications" is the first book of a series that provides image processing principles and practical software implementation on a broad range of applications. The book integrates material from leading researchers on Applied Digital Image Acquisition and Processing. An important feature of the book is its emphasis on software tools and scientific computing in order to enhance results and arrive at problem solution

Curvilinear Structure Enhancement in Biomedical Images

Curvilinear structures can appear in many different areas and at a variety of scales. They can be axons and dendrites in the brain, blood vessels in the fundus, streets, rivers or fractures in buildings, and others. So, it is essential to study curvilinear structures in many fields such as neuroscience, biology, and cartography regarding image processing. Image processing is an important field for the help to aid in biomedical imaging especially the diagnosing the disease. Image enhancement is the early step of image analysis. In this thesis, I focus on the research, development, implementation, and validation of 2D and 3D curvilinear structure enhancement methods, recently established. The proposed methods are based on phase congruency, mathematical morphology, and tensor representation concepts. First, I have introduced a 3D contrast independent phase congruency-based enhancement approach. The obtained results demonstrate the proposed approach is robust against the contrast variations in 3D biomedical images. Second, I have proposed a new mathematical morphology-based approach called the bowler-hat transform. In this approach, I have combined the mathematical morphology with a local tensor representation of curvilinear structures in images. The bowler-hat transform is shown to give better results than comparison methods on challenging data such as retinal/fundus images. The bowler-hat transform is shown to give better results than comparison methods on challenging data such as retinal/fundus images. Especially the proposed method is quite successful while enhancing of curvilinear structures at junctions. Finally, I have extended the bowler-hat approach to the 3D version to prove the applicability, reliability, and ability of it in 3D