A comprehensive and up-to-date textbook and reference for computational imaging, which combines vision, graphics, signal processing, and optics. Computational imaging involves the joint design of imaging hardware and computer algorithms to create novel imaging systems with unprecedented capabilities. In recent years such capabilities include cameras that operate at a trillion frames per second, microscopes that can see small viruses long thought to be optically irresolvable, and telescopes that capture images of black holes. This text offers a comprehensive and up-to-date introduction to this rapidly growing field, a convergence of vision, graphics, signal processing, and optics. It can be used as an instructional resource for computer imaging courses and as a reference for professionals. It covers the fundamentals of the field, current research and applications, and light transport techniques. The text first presents an imaging toolkit, including optics, image sensors, and illumination, and a computational toolkit, introducing modeling, mathematical tools, model-based inversion, data-driven inversion techniques, and hybrid inversion techniques. It then examines different modalities of light, focusing on the plenoptic function, which describes degrees of freedom of a light ray. Finally, the text outlines light transport techniques, describing imaging systems that obtain micron-scale 3D shape or optimize for noise-free imaging, optical computing, and non-line-of-sight imaging. Throughout, it discusses the use of computational imaging methods in a range of application areas, including smart phone photography, autonomous driving, and medical imaging. End-of-chapter exercises help put the material in context.

Collecting a set of classical and emerging methods previously unavailable in a single resource, Foundations of Computational Imaging: A Model-Based Approach is the first book to define a common foundation for the mathematical and statistical methods used in computational imaging. The book brings together a blend of research with applications in a variety of disciplines, including applied math, physics, chemistry, optics, and signal processing, to address a collection of problems that can benefit from a common set of methods. Readers will find basic techniques of model-based image processing, a comprehensive treatment of Bayesian and regularized image reconstruction methods, and an integrated treatment of advanced reconstruction techniques, such as majorization, constrained optimization, alternating direction method of multipliers (ADMM), and Plug-and-Play methods for model integration. Foundations of Computational Imaging can be used in courses on model-based or computational imaging, advanced numerical analysis, data science, numerical optimization, and approximation theory. It will also prove useful to researchers or practitioners in medical, scientific, commercial, and industrial imaging.

Digital geometry emerged as an independent discipline in the second half of the last century. It deals with geometric properties of digital objects and is developed with the unambiguous goal to provide rigorous theoretical foundations for devising new advanced approaches and algorithms for various problems of visual computing. Different aspects of digital geometry have been addressed in the literature. This book is the first one that explicitly focuses on the presentation of the most important digital geometry algorithms. Each chapter provides a brief survey on a major research area related to the general volume theme, description and analysis of related fundamental algorithms, as well as new original contributions by the authors. Every chapter contains a section in which interesting open problems are addressed.

Computational photography refers broadly to imaging techniques that enhance or extend the capabilities of digital photography. This new and rapidly developing research field has evolved from computer vision, image processing, computer graphics and applied optics—and numerous commercial products capitalizing on its principles have already appeared in diverse market applications, due to the gradual migration of computational algorithms from computers to imaging devices and software. Computational Photography: Methods and Applications provides a strong, fundamental understanding of theory and methods, and a foundation upon which to build solutions for many of today's most interesting and challenging computational imaging problems. Elucidating cutting-edge advances and applications in digital imaging, camera image processing, and computational photography, with a focus on related research challenges, this book: Describes single capture image fusion technology for consumer digital cameras Discusses the steps in a camera image processing pipeline, such as visual data compression, color correction and enhancement, denoising, demosaicking, super-resolution reconstruction, deblurring, and high dynamic range imaging Covers shadow detection for surveillance applications, camera-driven document rectification, bilateral filtering and its applications, and painterly rendering of digital images Presents machine-learning methods for automatic image colorization and digital face beautification Explores light field acquisition and processing, space-time light field rendering, and dynamic view synthesis with an array of cameras Because of the urgent challenges associated with emerging digital camera applications, image processing methods for computational photography are of paramount importance to research and development in the imaging community. Presenting the work of leading experts, and edited by a renowned authority in digital color imaging and camera image processing, this book considers the rapid developments in this area and addresses very particular research and application problems. It is ideal as a stand-alone professional reference for design and implementation of digital image and video processing tasks, and it can also be used to support graduate courses in computer vision, digital imaging, visual data processing, and computer graphics, among others.

Foundations of Computation is a free textbook for a one-semester course in theoretical computer science. It has been used for several years in a course at Hobart and William Smith Colleges. The course has no prerequisites other than introductory computer programming. The first half of the course covers material on logic, sets, and functions that would often be taught in a course in discrete mathematics. The second part covers material on automata, formal languages and grammar that would ordinarily be encountered in an upper level course in theoretical computer science.

An essential reference for optical sensor system design This is the first text to present an integrated view of the optical and mathematical analysis tools necessary to understand computational optical system design. It presents the foundations of computational optical sensor design with a focus entirely on digital imaging and spectroscopy. It systematically covers: Coded aperture and tomographic imaging Sampling and transformations in optical systems, including wavelets and generalized sampling techniques essential to digital system analysis Geometric, wave, and statistical models of optical fields The basic function of modern optical detectors and focal plane arrays Practical strategies for coherence measurement in imaging system design The sampling theory of digital imaging and spectroscopy for both conventional and emerging compressive and generalized measurement strategies Measurement code design Linear and nonlinear signal estimation The book concludes with a review of numerous design strategies in spectroscopy and imaging and clearly outlines the benefits and limits of each approach, including coded aperture and imaging spectroscopy, resonant and filter-based systems, and integrated design strategies to improve image resolution, depth of field, and field of view. Optical Imaging and Spectroscopy is an indispensable textbook for advanced undergraduate and graduate courses in optical sensor design. In addition to its direct applicability to optical system design, unique perspectives on computational sensor design presented in the text will be of interest for sensor designers in radio and millimeter wave, X-ray, and acoustic systems.

This book introduces the fundamentals of computer vision (CV), with a focus on extracting useful information from digital images and videos. Including a wealth of methods used in detecting and classifying image objects and their shapes, it is the first book to apply a trio of tools (computational geometry, topology and algorithms) in solving CV problems, shape tracking in image object recognition and detecting the repetition of shapes in single images and video frames. Computational geometry provides a visualization of topological structures such as neighborhoods of points embedded in images, while image topology supplies us with structures useful in the analysis and classification of image regions. Algorithms provide a practical, step-by-step means of viewing image structures. The implementations of CV methods in Matlab and Mathematica, classification of chapter problems with the symbols (easily solved) and (challenging) and its extensive glossary of key words, examples and connections with the fabric of CV make the book an invaluable resource for advanced undergraduate and first year graduate students in Engineering, Computer Science or Applied Mathematics. It offers insights into the design of CV experiments, inclusion of image processing methods in CV projects, as well as the reconstruction and interpretation of recorded natural scenes.

Computational Retinal Image Analysis: Tools, Applications and Perspectives gives an overview of contemporary retinal image analysis (RIA) in the context of healthcare informatics and artificial intelligence. Specifically, it provides a history of the field, the clinical motivation for RIA, technical foundations (image acquisition modalities, instruments), computational techniques for essential operations, lesion detection (e.g. optic disc in glaucoma, microaneurysms in diabetes) and validation, as well as insights into current investigations drawing from artificial intelligence and big data. This comprehensive reference is ideal for researchers and graduate students in retinal image analysis, computational ophthalmology, artificial intelligence, biomedical engineering, health informatics, and more.

Collection of papers by leading researchers in computational mathematics, suitable for graduate students and researchers.

Computational Photography combines plentiful computing, digital sensors, modern optics, actuators, probes, and smart lights to escape the limitations of traditional film cameras and enables novel imaging applications. This book provides a practical guide to topics in image capture and manipulation methods for generating compelling pictures for graphics, special effects, scene comprehension, and art. The computational techniques discussed cover topics in exploiting new ideas in manipulating optics, illumination, and sensors at time of capture. In addition, the authors describe sophisticated reconstruction procedures from direct and indirect pixel measurements that go well beyond the traditional digital darkroom experience.