Variational Methods in Image Segmentation

Variational Methods in Image Segmentation
Author: Jean-Michel Morel
Publisher: Springer Science & Business Media
Total Pages: 257
Release: 2012-12-06
Genre: Mathematics
ISBN: 1468405675

This book contains both a synthesis and mathematical analysis of a wide set of algorithms and theories whose aim is the automatic segmen tation of digital images as well as the understanding of visual perception. A common formalism for these theories and algorithms is obtained in a variational form. Thank to this formalization, mathematical questions about the soundness of algorithms can be raised and answered. Perception theory has to deal with the complex interaction between regions and "edges" (or boundaries) in an image: in the variational seg mentation energies, "edge" terms compete with "region" terms in a way which is supposed to impose regularity on both regions and boundaries. This fact was an experimental guess in perception phenomenology and computer vision until it was proposed as a mathematical conjecture by Mumford and Shah. The third part of the book presents a unified presentation of the evi dences in favour of the conjecture. It is proved that the competition of one-dimensional and two-dimensional energy terms in a variational for mulation cannot create fractal-like behaviour for the edges. The proof of regularity for the edges of a segmentation constantly involves con cepts from geometric measure theory, which proves to be central in im age processing theory. The second part of the book provides a fast and self-contained presentation of the classical theory of rectifiable sets (the "edges") and unrectifiable sets ("fractals").

Variational Methods in Image Processing

Variational Methods in Image Processing
Author: Luminita A. Vese
Publisher: CRC Press
Total Pages: 416
Release: 2015-11-18
Genre: Computers
ISBN: 1439849749

Variational Methods in Image Processing presents the principles, techniques, and applications of variational image processing. The text focuses on variational models, their corresponding Euler-Lagrange equations, and numerical implementations for image processing. It balances traditional computational models with more modern techniques that solve t

Image Processing and Analysis

Image Processing and Analysis
Author: Tony F. Chan
Publisher: SIAM
Total Pages: 414
Release: 2005-09-01
Genre: Computers
ISBN: 089871589X

This book develops the mathematical foundation of modern image processing and low-level computer vision, bridging contemporary mathematics with state-of-the-art methodologies in modern image processing, whilst organizing contemporary literature into a coherent and logical structure. The authors have integrated the diversity of modern image processing approaches by revealing the few common threads that connect them to Fourier and spectral analysis, the machinery that image processing has been traditionally built on. The text is systematic and well organized: the geometric, functional, and atomic structures of images are investigated, before moving to a rigorous development and analysis of several image processors. The book is comprehensive and integrative, covering the four most powerful classes of mathematical tools in contemporary image analysis and processing while exploring their intrinsic connections and integration. The material is balanced in theory and computation, following a solid theoretical analysis of model building and performance with computational implementation and numerical examples.

Variational Methods in Imaging

Variational Methods in Imaging
Author: Otmar Scherzer
Publisher: Springer Science & Business Media
Total Pages: 323
Release: 2008-09-26
Genre: Mathematics
ISBN: 0387692770

This book is devoted to the study of variational methods in imaging. The presentation is mathematically rigorous and covers a detailed treatment of the approach from an inverse problems point of view. Many numerical examples accompany the theory throughout the text. It is geared towards graduate students and researchers in applied mathematics. Researchers in the area of imaging science will also find this book appealing. It can serve as a main text in courses in image processing or as a supplemental text for courses on regularization and inverse problems at the graduate level.

Mathematical Image Processing

Mathematical Image Processing
Author: Kristian Bredies
Publisher: Springer
Total Pages: 481
Release: 2019-02-06
Genre: Mathematics
ISBN: 3030014584

This book addresses the mathematical aspects of modern image processing methods, with a special emphasis on the underlying ideas and concepts. It discusses a range of modern mathematical methods used to accomplish basic imaging tasks such as denoising, deblurring, enhancing, edge detection and inpainting. In addition to elementary methods like point operations, linear and morphological methods, and methods based on multiscale representations, the book also covers more recent methods based on partial differential equations and variational methods. Review of the German Edition: The overwhelming impression of the book is that of a very professional presentation of an appropriately developed and motivated textbook for a course like an introduction to fundamentals and modern theory of mathematical image processing. Additionally, it belongs to the bookcase of any office where someone is doing research/application in image processing. It has the virtues of a good and handy reference manual. (zbMATH, reviewer: Carl H. Rohwer, Stellenbosch)

Medical Image Computing and Computer-Assisted Intervention - MICCAI 2008

Medical Image Computing and Computer-Assisted Intervention - MICCAI 2008
Author: Dimitris Metaxas
Publisher: Springer
Total Pages: 1161
Release: 2008-10-30
Genre: Computers
ISBN: 354085990X

The 11th International Conference on Medical Imaging and Computer Assisted Intervention, MICCAI 2008, was held at the Helen and Martin Kimmel Center of New York University, New York City, USA on September 6–10, 2008. MICCAI is the premier international conference in this domain, with - depth papers on the multidisciplinary ?elds of biomedical image computing and analysis, computer assisted intervention and medical robotics. The conference brings together biological scientists, clinicians, computer scientists, engineers, mathematicians, physicists and other interested researchers and o?ers them a forum to exchange ideas in these exciting and rapidly growing ?elds. The conference is both very selective and very attractive: this year we - ceived a record number of 700 submissions from 34 countries and 6 continents, fromwhich258papers were selectedfor publication,whichcorrespondsto a s- cess rate of approximately 36%. Some interesting facts about the distribution of submitted and accepted papers are shown graphically at the end of this preface. The paper selection process this year was based on the following procedure, which included the introduction of several novelties over previous years. 1. A ProgramCommittee (PC) of 49 members was recruited by the Program Chairs,to getthenecessarybody ofexpertiseandgeographicalcoverage.All PC members agreed in advance to participate in the ?nal paper selection process. 2. Key words grouped in 7 categories were used to describe the content of the submissions and the expertise of the reviewers.

Handbook of Mathematical Methods in Imaging

Handbook of Mathematical Methods in Imaging
Author: Otmar Scherzer
Publisher: Springer Science & Business Media
Total Pages: 1626
Release: 2010-11-23
Genre: Mathematics
ISBN: 0387929193

The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.

Advances in Image and Video Segmentation

Advances in Image and Video Segmentation
Author: Zhang, Yu-Jin
Publisher: IGI Global
Total Pages: 472
Release: 2006-05-31
Genre: Technology & Engineering
ISBN: 1591407559

"This book attempts to bring together a selection of the latest results of state-of-the art research in image and video segmentation, one of the most critical tasks of image and video analysis that has the objective of extracting information (represented by data) from an image or a sequence of images (video)"--Provided by publisher.

Hands-On Image Processing with Python

Hands-On Image Processing with Python
Author: Sandipan Dey
Publisher: Packt Publishing Ltd
Total Pages: 483
Release: 2018-11-30
Genre: Computers
ISBN: 178934185X

Explore the mathematical computations and algorithms for image processing using popular Python tools and frameworks. Key FeaturesPractical coverage of every image processing task with popular Python librariesIncludes topics such as pseudo-coloring, noise smoothing, computing image descriptorsCovers popular machine learning and deep learning techniques for complex image processing tasksBook Description Image processing plays an important role in our daily lives with various applications such as in social media (face detection), medical imaging (X-ray, CT-scan), security (fingerprint recognition) to robotics & space. This book will touch the core of image processing, from concepts to code using Python. The book will start from the classical image processing techniques and explore the evolution of image processing algorithms up to the recent advances in image processing or computer vision with deep learning. We will learn how to use image processing libraries such as PIL, scikit-mage, and scipy ndimage in Python. This book will enable us to write code snippets in Python 3 and quickly implement complex image processing algorithms such as image enhancement, filtering, segmentation, object detection, and classification. We will be able to use machine learning models using the scikit-learn library and later explore deep CNN, such as VGG-19 with Keras, and we will also use an end-to-end deep learning model called YOLO for object detection. We will also cover a few advanced problems, such as image inpainting, gradient blending, variational denoising, seam carving, quilting, and morphing. By the end of this book, we will have learned to implement various algorithms for efficient image processing. What you will learnPerform basic data pre-processing tasks such as image denoising and spatial filtering in PythonImplement Fast Fourier Transform (FFT) and Frequency domain filters (e.g., Weiner) in PythonDo morphological image processing and segment images with different algorithmsLearn techniques to extract features from images and match imagesWrite Python code to implement supervised / unsupervised machine learning algorithms for image processingUse deep learning models for image classification, segmentation, object detection and style transferWho this book is for This book is for Computer Vision Engineers, and machine learning developers who are good with Python programming and want to explore details and complexities of image processing. No prior knowledge of the image processing techniques is expected.

High-Order Models in Semantic Image Segmentation

High-Order Models in Semantic Image Segmentation
Author: Ismail Ben Ayed
Publisher: Academic Press
Total Pages: 184
Release: 2023-06-22
Genre: Technology & Engineering
ISBN: 0128092297

High-Order Models in Semantic Image Segmentation reviews recent developments in optimization-based methods for image segmentation, presenting several geometric and mathematical models that underlie a broad class of recent segmentation techniques. Focusing on impactful algorithms in the computer vision community in the last 10 years, the book includes sections on graph-theoretic and continuous relaxation techniques, which can compute globally optimal solutions for many problems. The book provides a practical and accessible introduction to these state-of -the-art segmentation techniques that is ideal for academics, industry researchers, and graduate students in computer vision, machine learning and medical imaging. - Gives an intuitive and conceptual understanding of this mathematically involved subject by using a large number of graphical illustrations - Provides the right amount of knowledge to apply sophisticated techniques for a wide range of new applications - Contains numerous tables that compare different algorithms, facilitating the appropriate choice of algorithm for the intended application - Presents an array of practical applications in computer vision and medical imaging - Includes code for many of the algorithms that is available on the book's companion website