Synopses & Reviews
Visual perception refers to the ability of understanding the visual information that is provided by the environment. Such a mechanism integrates several human abilities and was studied by many researchers with different scientific origins including philosophy, physiology, biology, neurobiology, mathematics and engineering. In particular in the recent years an effort to understand, formalize and finally reproduce mechanical visual perception systems able to see and understand the environment using computational theories was made by mathematicians, statisticians and engineers. Such a task connects visual tasks with optimization processes and the answer to the visual perception task corresponds to the lowest potential of a task-driven objective function. In this edited volume we present the most prominent mathematical models that are considered in computational vision. To this end, tasks of increasing complexity are considered and we present the state-of-the-art methods to cope with such tasks. The volume consists of six thematic areas that provide answers to the most dominant questions of computational vision: Image reconstruction, Segmentation and object extraction, Shape modeling and registration, Motion analysis and tracking, 3D from images, geometry and reconstruction Applications in medical image analysis
Review
The field covered by Computer Vision has become so broad that it is almost impossible to understand what is going on and to keep track of the latest developments. To (partially) overcome this problem, the editors of the Handbook of Mathematical Models in Computer Vision have done a great job. Each chapter gives a general introduction to the topic, introduces the mathematical model, discusses the underlying ideas globally, and shows some results. For the full details the readers are referred to the extensive bibliography with 929 entries. This book is a must-have for those interested in the full breadth of research done in the biological and computer vision community. As a bonus, the chapters can also be used in a seminar-based, advanced undergraduate course in mathematical based computer vision. Reviewed by Arjan Kuijper, IAPR Newsletter 28:4, October 2006
Review
From the reviews: "The focus of the book is on mathematical methods that both model and reproduce human visual abilities. ... This book is a must-have for those interested in the full breadth of research done in the biological & computer vision community. As a bonus, the chapters can also be used in a seminar-based, advanced undergraduate course in mathematical based computer vision. " (Arjan Kuijper, IAPR Newsletter, October, 2006) "Computational visual perception can be defined as the discipline of enabling computers to identify features in image data. ... I found this book to be detailed and comprehensive enough to be well worth the time spent on it. Citations linking the text to the relevant literature are profusely sprinkled throughout the text, and a very extensive bibliography is included ... . the production qualities are excellent. ... it should be a useful reference text for researchers or practitioners in this field." (R. M. Malyankar, Computing Reviews, January, 2006) "The editors of this important compendium view their task as a contribution to modeling and simulating human vision by machine. ... The editors should be congratulated for bringing together high-level researchers to contribute chapters on cutting-edge technologies based on mathematical modeling. This compendium is a solid contribution to the recent literature combining the theories and applications of mathematical modeling to the domain of computer vision." (R. Goldberg, Computing Reviews, June, 2006)
Review
From the reviews:
"The focus of the book is on mathematical methods that both model and reproduce human visual abilities. ... This book is a must-have for those interested in the full breadth of research done in the biological & computer vision community. As a bonus, the chapters can also be used in a seminar-based, advanced undergraduate course in mathematical based computer vision. " (Arjan Kuijper, IAPR Newsletter, October, 2006)
"Computational visual perception can be defined as the discipline of enabling computers to identify features in image data. ... I found this book to be detailed and comprehensive enough to be well worth the time spent on it. Citations linking the text to the relevant literature are profusely sprinkled throughout the text, and a very extensive bibliography is included ... . the production qualities are excellent. ... it should be a useful reference text for researchers or practitioners in this field." (R. M. Malyankar, Computing Reviews, January, 2006)
"The editors of this important compendium view their task as a contribution to modeling and simulating human vision by machine. ... The editors should be congratulated for bringing together high-level researchers to contribute chapters on cutting-edge technologies based on mathematical modeling. This compendium is a solid contribution to the recent literature combining the theories and applications of mathematical modeling to the domain of computer vision." (R. Goldberg, Computing Reviews, June, 2006)
Synopsis
This comprehensive volume is an essential reference tool for professional and academic researchers in the filed of computer vision, image processing, and applied mathematics. Continuing rapid advances in image processing have been enhanced by the theoretical efforts of mathematicians and engineers. This marriage of mathematics and computer vision - computational vision - has resulted in a discrete approach to image processing that is more reliable when leveraging in practical tasks. This comprehensive volume provides a detailed discourse on the mathematical models used in computational vision from leading educators and active research experts in this field. Topical areas include: image reconstruction, segmentation and object extraction, shape modeling and registration, motion analysis and tracking, and 3D from images, geometry and reconstruction. The book also includes a study of applications in medical image analysis. Handbook of Mathematical Models in Computer Vision provides a graduate-level treatment of this subject as well as serving as a complete reference work for professionals.
Synopsis
Abstract Biological vision is a rather fascinating domain of research. Scientists of various origins like biology, medicine, neurophysiology, engineering, math- ematics, etc. aim to understand the processes leading to visual perception process and at reproducing such systems. Understanding the environment is most of the time done through visual perception which appears to be one of the most fundamental sensory abilities in humans and therefore a significant amount of research effort has been dedicated towards modelling and repro- ducing human visual abilities. Mathematical methods play a central role in this endeavour. Introduction David Marr's theory v DEGREESas a pioneering step tov DEGREESards understanding visual percep- tion. In his view human vision was based on a complete surface reconstruction of the environment that was then used to address visual subtasks. This approach was proven to be insufficient by neuro-biologists and complementary ideas from statistical pattern recognition and artificial intelligence were introduced to bet- ter address the visual perception problem. In this framework visual perception is represented by a set of actions and rules connecting these actions. The emerg- ing concept of active vision consists of a selective visual perception paradigm that is basically equivalent to recovering from the environment the minimal piece information required to address a particular task of interest.
Synopsis
A marriage of mathematics and computer vision - computational vision - has resulted in an innovative approach to image processing that is reliable across an expanding range of practical tasks. This volume provides a detailed discourse on the mathematical models used in computational vision, from leading educators and active research experts in this field. Topics include: image reconstruction, segmentation and object extraction, shape modeling and registration, motion analysis and tracking, and 3D from images, geometry and reconstruction. The book also includes a detailed study of applications in medical image analysis.
Table of Contents
Image Reconstruction.- Diffusion Filters and Wavelets.- Total Variation Image Restoration.- PDE-Based Image and Surface Inpainting.- Boundary Extraction, Segmentation and Grouping.- Theories and Applications of Graph Cuts in Vision and Graphics.- Minimal Paths and Fast Marching Methods for Image Analysis.- Integrating Shape and Texture in Deformable Models.- Variational Segmentation with Shape Priors.- Curve Propogation, Level Set Methods and Grouping.- Shape Modeling and Registration.- Invariant Processing and Occlusion Resistant Recognition of Planar Shapes.- Planar Shape Analysis and Its Applications in Image-Based Inferences.- Diffeomorphic Point Matching.- Uncertainty-Driven, Point-Based Image Registration.- Motion Analysis, Optical Flow and Tracking.- Optical Flow Estimation.- Image Alignment and Stitching.- Visual Tracking.- Shape Gradient for Image and Video Segmentation.- Model-Based Human Motion Capture.- Modeling Dynamic Scenes.- 3D from Images, Projective Geometry and Stereo Reconstruction.- Differential Geometry from the Frenet Point of View.- Shape from Shading.- Calibration, Motion and Shape Recovery from 3D Image Sequences.- Multi-view Recontruction of Static and Dynamic Scenes.- Medical Image Analysis.- Interactive Graph-Based Segmentation Methods in Cardiovascular Imaging.- Segmentation of Diffusion Tensor Images.- Statistical Methods of Medical Image Registration.