Handbook of Mathematical Models in Computer Vision

By: Nikos Paragios (Editor), Yunmei Chen (Editor), Olivier D. Faugeras (Editor)

Write A Review

Hardcover | 31 October 2005

At a Glance

Hardcover
640 Pages

Dimensions(cm)
24.77 x 16.51 x 3.81

Hardcover

$169.00

or 4 interest-free payments of $42.25 with

Ships in 5 to 7 business days

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.

Industry Reviews

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)

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $79.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

You Can Find This Book In

Non-Fiction Computing & I.T.Computer Science Artificial Intelligence Computer Vision Graphical & Digital Media Applications 3D Graphics & Modelling Mathematics Applied Mathematics Mathematical Modelling Digital Lifestyle & Online World: Consumer & User Guides Internet Guides & Online Services

Other Editions and Formats

Paperback

Published: 29th October 2010

View Product

Preface	p. xix
List of Contributors	p. xxiii
Image Reconstruction	p. 1
Diffusion Filters and Wavelets: What Can They Learn from Each Other?	p. 3
Introduction	p. 3
Basic Methods	p. 4
Relations for Space-Discrete Diffusion	p. 6
Relations for Fully Discrete Diffusion	p. 9
Wavelets with Higher Vanishing Moments	p. 13
Summary	p. 16
Total Variation Image Restoration: Overview and Recent Developments	p. 17
Introduction	p. 17
Properties and Extensions	p. 19
Caveats	p. 21
Variants	p. 22
Further Applications to Image Reconstruction	p. 26
Numerical Methods	p. 29
PDE-Based Image and Surface Inpainting	p. 33
Introduction	p. 33
Inpainting by Propagation of Information	p. 36
Variational Models for Filling-In	p. 42
Surface Reconstruction: The Laplace and the Absolute Minimizing Lipschitz Extension Interpolation	p. 52
Dealing with texture	p. 55
Other Approaches	p. 58
Concluding Remarks	p. 60
Appendix	p. 60
Acknowledgments	p. 61
Boundary Extraction, Segmentation and Grouping	p. 63
Levelings: Theory and Practice	p. 65
Introduction	p. 65
Binary connected operators	p. 66
Flat grey-tone connected operators	p. 67
Extended connected operators	p. 68
Levelings for image simplification	p. 71
Conclusion	p. 77
Graph Cuts in Vision and Graphics: Theories and Applications	p. 79
Introduction	p. 79
Graph Cuts Basics	p. 80
Graph Cuts for Binary Optimization	p. 82
Graph Cuts as Hypersurfaces	p. 84
Generalizing Graph Cuts for Multi-Label Problems	p. 92
Minimal Paths and Fast Marching Methods for Image Analysis	p. 97
Introduction	p. 97
Minimal Paths	p. 98
Minimal paths from a set of endpoints p[subscript k]	p. 105
Multiple minimal paths between regions R[subscript k]	p. 107
Segmentation by Fast Marching	p. 108
Centered Minimal Paths and virtual endoscopy	p. 110
Conclusion	p. 111
Integrating Shape and Texture in Deformable Models: from Hybrid Methods to Metamorphs	p. 113
Introduction	p. 113
Hybrid Segmentation Method	p. 116
Metamorphs: Deformable Shape and Texture Models	p. 120
Conclusions	p. 128
Variational Segmentation with Shape Priors	p. 131
Introduction	p. 131
Shape Representation	p. 133
Learning Shape Statistics	p. 136
Variational Segmentation and Shape Priors	p. 139
Conclusion and Further Work	p. 142
Curve Propagation, Level Set Methods and Grouping	p. 145
Introduction	p. 145
On the Propagation of Curves	p. 146
Data-driven Segmentation	p. 151
Prior Knowledge	p. 154
Discussion	p. 159
On a Stochastic Model of Geometric Snakes	p. 161
Introduction	p. 161
Overview of Geodesic Snake Models	p. 163
Birth and Death Zero Range Particle Systems	p. 163
Poisson System Simulation	p. 164
Choosing a Random Event	p. 166
Similarity Invariant Flows	p. 168
Stochastic Snakes	p. 171
Experimental Results	p. 173
Conclusions and Future Research	p. 174
Shape Modeling & Registration	p. 175
Invariant Processing and Occlusion Resistant Recognition of Planar Shapes	p. 177
Introduction	p. 177
Invariant Point Locations and Displacements	p. 178
Invariant Boundary Signatures for Recognition under Partial Occlusions	p. 182
Invariant Processing of Planar Shapes	p. 184
Concluding Remarks	p. 188
Planar Shape Analysis and Its Applications in Image-Based Inferences	p. 189
Introduction	p. 189
A Framework for Planar Shape Analysis	p. 191
Clustering of Shapes	p. 194
Interpolation of Shapes in Echocardiographic Image-Sequences	p. 196
Study of Human Silhouettes in Infrared Images	p. 200
Summary & Discussion	p. 202
Diffeomorphic Point Matching	p. 205
Introduction	p. 205
Diffeomorphic Landmark Matching	p. 206
Diffeomorphic Point Shape Matching	p. 214
Discussion	p. 219
Uncertainty-Driven, Point-Based Image Registration	p. 221
Introduction	p. 221
Objective Function, ICP and Normal Distances	p. 223
Parameter Estimates and Covariance Matrices	p. 226
Stable Sampling of ICP Constraints	p. 228
Dual-Bootstrap ICP	p. 230
Discussion and Conclusion	p. 234
Motion Analysis, Optical Flow & Tracking	p. 237
Optical Flow Estimation	p. 239
Introduction	p. 239
Basic Gradient-Based Estimation	p. 240
Iterative Optical Flow Estimation	p. 243
Robust Motion Estimation	p. 246
Motion Models	p. 247
Global Smoothing	p. 249
Conservation Assumptions	p. 250
Probabilistic Formulations	p. 252
Layered Motion	p. 253
Conclusions	p. 256
From Bayes to PDEs in Image Warping	p. 259
Motivation and problem statement	p. 259
Admissible warps	p. 260
Bayesian formulation of warp estimation	p. 262
Likelihood: Matching criteria	p. 264
Prior: Smoothness criteria	p. 266
Warp time and computing time	p. 269
From fluid registration to diffeomorphic minimizers	p. 270
Discussion and open problems	p. 271
Image Alignment and Stitching	p. 273
Introduction	p. 273
Motion models	p. 274
Direct and feature-based alignment	p. 277
Global registration	p. 283
Choosing a compositing surface	p. 286
Seam selection and pixel blending	p. 287
Extensions and open issues	p. 291
Visual Tracking: A Short Research Roadmap	p. 293
Introduction	p. 293
Simple appearance models	p. 294
Active contours	p. 296
Spatio-temporal filtering	p. 301
Further topics	p. 306
Shape Gradient for Image and Video Segmentation	p. 309
Introduction	p. 309
Problem Statement	p. 310
From shape derivation tools towards region-based active contours models	p. 312
Segmentation using Statistical Region-dependent descriptors	p. 317
Discussion	p. 322
Model-Based Human Motion Capture	p. 325
Introduction	p. 325
Methods	p. 327
Results	p. 334
Discussion	p. 338
Modeling Dynamic Scenes: An Overview of Dynamic Textures	p. 341
Introduction	p. 341
Representation of dynamic textures	p. 344
Learning dynamic textures	p. 344
Model validation	p. 347
Recognition	p. 349
Segmentation	p. 351
Discussion	p. 355
3D from Images, Projective Geometry & Stereo Reconstruction	p. 357
Differential Geometry from the Frenet Point of View: Boundary Detection, Stereo, Texture and Color	p. 359
Introduction	p. 359
Introduction to Frenet-Serret	p. 361
Co-Circularity in R[superscript 2] x S[superscript 1]	p. 363
Stereo: Inferring Frenet 3-Frames from 2-Frames	p. 365
Covariant Derivatives, Oriented Textures, and Color	p. 367
Discussion	p. 372
Shape From Shading	p. 375
Introduction	p. 375
Mathematical formulation of the SFS problem	p. 377
Mathematical study of the SFS problem	p. 379
Numerical solutions by "Propagation and PDEs methods"	p. 382
Examples of numerical results	p. 385
Conclusion	p. 388
3D from Image Sequences: Calibration, Motion and Shape Recovery	p. 389
Introduction	p. 389
Relating images	p. 392
Structure and motion recovery	p. 393
Dense surface estimation	p. 398
3D surface reconstruction	p. 400
Conclusion	p. 402
Multi-view Reconstruction of Static and Dynamic Scenes	p. 405
Introduction	p. 405
Reconstruction of Static Scenes	p. 406
Reconstruction of Dynamic Scenes	p. 416
Sensor Planning	p. 419
Conclusion	p. 421
Graph Cut Algorithms for Binocular Stereo with Occlusions	p. 423
Traditional stereo methods	p. 423
Stereo with occlusions	p. 426
Voxel labeling algorithm	p. 429
Pixel labeling algorithm	p. 430
Minimizing the energy	p. 431
Experimental results	p. 432
Conclusions	p. 434
Modelling Non-Rigid Dynamic Scenes from Multi-View Image Sequences	p. 439
Introduction	p. 439
Previous Work	p. 440
The Prediction Error as a New Metric for Stereovision and Scene Flow Estimation	p. 443
Experimental Results	p. 448
Conclusion and Future Work	p. 451
Applications: Medical Image Analysis	p. 453
Interactive Graph-Based Segmentation Methods in Cardiovascular Imaging	p. 455
Introduction	p. 455
Characteristic Behaviors of the Algorithms	p. 456
Applications on CT Cardiovascular data	p. 459
Conclusions	p. 469
3D Active Shape and Appearance Models in Cardiac Image Analysis	p. 471
Introduction	p. 471
Methods	p. 475
Discussion and Conclusion	p. 484
Characterization of Diffusion Anisotropy in DWI	p. 487
Introduction	p. 487
Estimation of PDF	p. 489
Estimation of ADC profiles	p. 493
Conclusion	p. 499
Segmentation of Diffusion Tensor Images	p. 503
Introduction	p. 503
K-means for DTI segmentation	p. 505
Boundary-based active contours for DTI segmentation	p. 505
Region-based active contour for DTI segmentation	p. 507
Conclusion	p. 514
Variational Approaches to the Estimation, Regularization and Segmentation of Diffusion Tensor Images	p. 517
Introduction	p. 517
Estimation of Diffusion Tensor Images	p. 518
Regularization of Diffusion Tensor Images	p. 520
Segmentation of Diffusion Tensor Images	p. 522
Conclusion	p. 530
An Introduction to Statistical Methods of Medical Image Registration	p. 531
Introduction	p. 531
The Similarity Measures	p. 532
Conclusion	p. 541
Bibliography	p. 543
Bibliography	p. 543
Table of Contents provided by Ingram. All Rights Reserved.

Handbook of Mathematical Models in Computer Vision

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

More in Internet Guides & Online Services

The Bitcoin Standard

The Decentralized Alternative to Central Banking

This is For Everyone

Don't Stress, Just Invest

It's time to set up your investments and get on with your life

Lost in the Stream

How Algorithms Redefined the Way Movies Are Made and Watched (Gift for Movie Lovers, What to Watch)

The Tech-Media Hybrid

Google's News Ambition

In This Economy?

How Money and Markets Really Work

The Man Who Solved the Market

How Jim Simons Launched the Quant Revolution SHORTLISTED FOR THE FT & MCKINSEY BUSINESS BOOK OF THE YEAR AWARD 2019

The Devil Takes Bitcoin

cryptocurrency crimes and the Japanese connection

Syndicate

The breakneck new novel from the master of the racing thriller

Sensible Money

A guide on how to make better money choices for financial freedom, by the ABC's finance reporter, for readers of She's On the Money

The Intelligent Investor Third Edition

The Definitive Book on Value Investing

Mastering The Market Cycle

Getting the odds on your side

Digital Degrowth

Radically Rethinking our Digital Futures

The Wealth Ladder

Proven Strategies for Every Step of Your Financial Life

Become a YouTuber

Build Your Own YouTube Channel

This is Service Design Doing

Applying Service Design Thinking in the Real World

Laravel: Up & Running

3rd Edition - A Framework for Building Modern PHP Apps

Mind over Money

Why understanding your money behaviour will improve your financial freedom

Don't Make Me Think, Revisited

A Common Sense Approach to Web Usability

Web Scraping with Python

3rd Edition - Data Extraction from the Modern Web

The Art of SEO

Mastering Search Engine Optimization

Windows 11 for Seniors in Easy Steps

In Easy Steps

Customer Relationship Management

2nd edition

Responsive Web Design with HTML 5 & CSS

9th edition

This product is categorised by