3-D Shape Estimation and Image Restoration: Exploiting Defocus and Motion-Blur / Edition 1

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Images contain information about the spatial properties of the scene they depict. When coupled with suitable assumptions, images can be used to infer three-dimensional information. This useful volume concentrates on motion blur and defocus, which can be exploited to infer the 3-D structure of a scene - as well as its radiance properties - and which in turn can be used to generate novel images with better quality.

3-D Shape Estimation and Image Restoration presents a coherent framework for the analysis and design of algorithms to estimate 3-D shape from defocused and motion-blurred images, and to eliminate defocus and motion blur to yield "restored" images. It provides a collection of algorithms that are optimal with respect to the chosen model and estimation criterion.

Written for readers with interests in image processing and computer vision and with backgrounds in engineering, science or mathematics, this highly practical text/reference is accessible to advanced students or those with a degree that includes basic linear algebra and calculus courses. It can also be seen as a resource for practitioners looking to expand their knowledge in the subject.

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Editorial Reviews

From the Publisher

"This book presents a framework for estimating three-dimensional (3D) shapes from defocused and motion-blurred images. The book systematically describes various problems involved in estimating 3D shapes, and provides solutions to these problems… The book is well-written, and is equipped with Matlab code that implements the estimators presented in the chapters… I recommend this book to engineers in image processing and computer vision. Readers will learn state-of-the-art methods for shape restoration." (Hsun-Hsien Chang, ACM Computing Reviews, Vol. 49 (9), September 2008)

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Product Details

  • ISBN-13: 9781846281761
  • Publisher: Springer-Verlag New York, LLC
  • Publication date: 12/18/2006
  • Edition description: 1st Edition.
  • Edition number: 1
  • Pages: 263
  • Product dimensions: 5.90 (w) x 9.30 (h) x 0.60 (d)

Table of Contents

Preface     vii
Introduction     1
The sense of vision     1
Stereo     4
Structure from motion     5
Photometric stereo and other techniques based on controlled light     5
Shape from shading     6
Shape from texture     6
Shape from silhouettes     6
Shape from defocus     6
Motion blur     7
On the relative importance and integration of visual cues     7
Visual inference in applications     8
Preview of coming attractions     9
Estimating 3-D geometry and photometry with a finite aperture     9
Testing the power and limits of models for accommodation cues     10
Formulating the problem as optimal inference     11
Choice of optimization criteria, and the design of optimal algorithms     12
Variational approach to modeling and inference from accommodation cues     12
Basic models of image formation     14
The simplest imaging model     14
The thin lens     14
Equifocal imaging model     16
Sensor noise and modeling errors     18
Imaging models and linear operators     19
Imaging occlusion-freeobjects     20
Image formation nuisances and artifacts     22
Dealing with occlusions     23
Modeling defocus as a diffusion process     26
Equifocal imaging as isotropic diffusion     28
Nonequifocal imaging model     29
Modeling motion blur     30
Motion blur as temporal averaging     30
Modeling defocus and motion blur simultaneously     34
Summary     35
Some analysis: When can 3-D shape be reconstructed from blurred images? 37
The problem of shape from defocus     38
Observability of shape     39
The role of radiance     41
Harmonic components     42
Band-limited radiances and degree of resolution     42
Joint observability of shape and radiance     46
Regularization     46
On the choice of objective function in shape from defocus     47
Summary     49
Least-squares shape from defocus     50
Least-squares minimization     50
A solution based on orthogonal projectors     53
Regularization via truncation of singular values     53
Learning the orthogonal projectors from images     55
Depth-map estimation algorithm      58
Examples     60
Explicit kernel model     60
Learning the kernel model     61
Summary     65
Enforcing positivity: Shape from defocus and image restoration by minimizing I-divergence     69
Information-divergence     70
Alternating minimization     71
Implementation     76
Examples     76
Examples with synthetic images     76
Examples with real images     78
Summary     79
Defocus via diffusion: Modeling and reconstruction     87
Blurring via diffusion     88
Relative blur and diffusion     89
Extension to space-varying relative diffusion     90
Enforcing forward diffusion     91
Depth-map estimation algorithm     92
Minimization of the cost functional     94
On the extension to multiple images     95
Examples     96
Examples with synthetic images     97
Examples with real images     99
Summary     99
Dealing with motion: Unifying defocus and motion blur     106
Modeling motion blur and defocus in one go     107
Well-posedness of the diffusion model      109
Estimating Radiance, Depth, and Motion     110
Cost Functional Minimization     111
Examples     113
Synthetic Data     114
Real Images     117
Summary     118
Dealing with multiple moving objects     120
Handling multiple moving objects     121
A closer look at camera exposure     124
Relative motion blur     125
Minimization algorithm     126
Dealing with changes in motion     127
Matching motion blur along different directions     129
A look back at the original problem     131
Minimization algorithm     132
Image restoration     135
Minimization algorithm     137
Examples     138
Synthetic data     138
Real data     141
Summary     146
Dealing with occlusions     147
Inferring shape and radiance of occluded surfaces     148
Detecting occlusions     150
Implementation of the algorithm     151
Examples     152
Examples on a synthetic scene     152
Examples on real images     154
Summary      157
Final remarks     159
Concepts of radiometry     161
Radiance, irradiance, and the pinhole model     161
Foreshortening and solid angle     161
Radiance and irradiance     162
Bidirectional reflectance distribution function     163
Lambertian surfaces     163
Image intensity for a Lambertian surface and a pinhole lens model     164
Derivation of the imaging model for a thin lens     164
Basic primer on functional optimization     168
Basics of the calculus of variations     169
Functional derivative     170
Euler-Lagrange equations     171
Detailed computation of the gradients     172
Computation of the gradients in Chapter 6     172
Computation of the gradients in Chapter 7     174
Computation of the gradients in Chapter 8     176
Computation of the gradients in Chapter 9     185
Proofs     190
Proof of Proposition 3.2     190
Proof of Proposition 3.5     191
Proof of Proposition 4.1     192
Proof of Proposition 5.1     194
Proof of Proposition 7.1     195
Calibration of defocused images      197
Zooming and registration artifacts     197
Telecentric optics     200
Matlab implementation of some algorithms     202
Least-squares solution (Chapter 4)     202
I-divergence solution (Chapter 5)     212
Shape from defocus via diffusion (Chapter 6)     221
Initialization: A fast approximate method     229
Regularization     232
Inverse problems     232
Ill-posed problems     234
Regularization     235
Tikhonov regularization     237
Truncated SVD     238
References     239
Index     247
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