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Handbook of Mathematical Models in Computer VisionFrom Springer
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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^as a pioneering step tov^ards 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.
- Sales Rank: #2853398 in Books
- Published on: 2005-10-31
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x 1.44" w x 6.14" l, 2.16 pounds
- Binding: Hardcover
- 606 pages
From the Back Cover
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
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)
Most helpful customer reviews
14 of 14 people found the following review helpful.
Review from IARP (Arjan Kuijper)
By http://www.iapr.org/members/newsletter/Newsletter06-04/index_files/Page447.htm
When attending a general computer vision conference like xCCV, did you ever feel lost at certain sessions? Well, don't always blame the presenters! 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.
One can become a bit skeptical reading such a title. How complete can such a handbook be? However, going through the 33 chapters, indeed a wide breadth is treated. The focus of the book is on mathematical methods that both model and reproduce human visual abilities. This is the field of biological vision in which the editors have a strong background.
The editors chose three distinct categories of mathematical models, namely variational techniques (those attending Prof. Faugeras' talk at ICPR 2006 may remember his statement that they give the fundamental equations in computer vision!), statistical methods, and combinatorial approaches. The chapters are grouped in six sections that circle around these three categories. Although going through the book chapters by mentioning keyword may yield a rather boring list, it shows the wide variety of topics that are being dealt with.
The book starts with a section on low-level vision: Image Reconstruction. Here one can find information on diffusion filters and wavelets, total variation methods, and PDE based inpainting.
The second section is concerned with Boundary Extraction, Segmentation and Grouping. Here subjects like levelings, graph cuts, minimal paths and fast marching methods, deformable models, variational segmentation with shape priors, curve propagation, level set methods, and a stochastic model of geometric snakes are discussed.
Section three switches to high level vision. It deals with Shape Modeling & Registration, divided into topics concerning invariant processing and occlusion resistant recognition, image-based inferences, point matching and uncertainty-driven, point-based image registration.
In the fourth section, Motion Analysis, Optical Flow & Tracking, the concept of time is added and one encounters the topics of optical flow estimation, image warping, alignment and stitching, visual tracking, image and video segmentation, human motion capture, and dynamic textures.
Section five deals with 3D from Images, Projective Geometry & Stereo Reconstruction, treated by boundary detection, stereo, texture and color, shape from shading, calibration, motion and shape recovery, multi-view reconstruction, binocular stereo with occlusions, and modeling non-rigid dynamic scenes.
The last section may seem a bit odd: Applications: Medical Image Analysis. However, this is one of the most prominent areas in computer vision. Although here certain vision aspects do not occur, compared to natural images (just think of the influence of the sun), for many tasks the performance of the mathematical methods can be evaluated since a ground truth is often available - provided by humans whom the models are supposed to mimic. In this section, applications of interactive graph-based segmentation methods, 3D active shape and appearance models, characterization of diffusion anisotropy, segmentation, variational approaches, and statistical methods of registration are given.
The danger of publishing an edited volume is the difference in style and treatment of the topics among the various contributions. This is not the case here. 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 & computer vision community. As a bonus, the chapters can also be used in a seminar-based, advanced undergraduate course in mathematical based computer vision.
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