3-D shape estimation and image restoration : exploiting defocus and motion blur / Paolo Favaro and Stefano Soatto.

Format:

Book

Author/Creator:

Favaro, Paolo.

Contributor:

Soatto, Stefano.

Language:

English

Subjects (All):

Image processing--Digital techniques--Mathematics.

Image processing.

Three-dimensional imaging.

Image reconstruction.

Image processing--Digital techniques.

Physical Description:

xiv, 249 pages : illustrations ; 25 cm

Place of Publication:

London : Springer, [2007]

Summary:

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.

Contents:

1.1 The sense of vision 1

1.1.1 Stereo 4

1.1.2 Structure from motion 5

1.1.3 Photometric stereo and other techniques based on controlled light 5

1.1.4 Shape from shading 6

1.1.5 Shape from texture 6

1.1.6 Shape from silhouettes 6

1.1.7 Shape from defocus 6

1.1.8 Motion blur 7

1.1.9 On the relative importance and integration of visual cues 7

1.1.10 Visual inference in applications 8

1.2 Preview of coming attractions 9

1.2.1 Estimating 3-D geometry and photometry with a finite aperture 9

1.2.2 Testing the power and limits of models for accommodation cues 10

1.2.3 Formulating the problem as optimal inference 11

1.2.4 Choice of optimization criteria, and the design of optimal algorithms 12

1.2.5 Variational approach to modeling and inference from accommodation cues 12

2 Basic models of image formation 14

2.1 The simplest imaging model 14

2.1.1 The thin lens 14

2.1.2 Equifocal imaging model 16

2.1.3 Sensor noise and modeling errors 18

2.1.4 Imaging models and linear operators 19

2.2 Imaging occlusion-free objects 20

2.2.1 Image formation nuisances and artifacts 22

2.3 Dealing with occlusions 23

2.4 Modeling defocus as a diffusion process 26

2.4.1 Equifocal imaging as isotropic diffusion 28

2.4.2 Nonequifocal imaging model 29

2.5 Modeling motion blur 30

2.5.1 Motion blur as temporal averaging 30

2.5.2 Modeling defocus and motion blur simultaneously 34

3 Some analysis: When can 3-D shape be reconstructed from blurred images? 37

3.1 The problem of shape from defocus 38

3.2 Observability of shape 39

3.3 The role of radiance 41

3.3.1 Harmonic components 42

3.3.2 Band-limited radiances and degree of resolution 42

3.4 Joint observability of shape and radiance 46

3.5 Regularization 46

3.6 On the choice of objective function in shape from defocus 47

4 Least-squares shape from defocus 50

4.1 Least-squares minimization 50

4.2 A solution based on orthogonal projectors 53

4.2.1 Regularization via truncation of singular values 53

4.2.2 Learning the orthogonal projectors from images 55

4.3 Depth-map estimation algorithm 58

4.4.1 Explicit kernel model 60

4.4.2 Learning the kernel model 61

5 Enforcing positivity: Shape from defocus and image restoration by minimizing I-divergence 69

5.1 Information-divergence 70

5.2 Alternating minimization 71

5.3 Implementation 76

5.4.1 Examples with synthetic images 76

5.4.2 Examples with real images 78

6 Defocus via diffusion: Modeling and reconstruction 87

6.1 Blurring via diffusion 88

6.2 Relative blur and diffusion 89

6.3 Extension to space-varying relative diffusion 90

6.4 Enforcing forward diffusion 91

6.5 Depth-map estimation algorithm 92

6.5.1 Minimization of the cost functional 94

6.6 On the extension to multiple images 95

6.7.1 Examples with synthetic images 97

6.7.2 Examples with real images 99

7 Dealing with motion: Unifying defocus and motion blur 106

7.1 Modeling motion blur and defocus in one go 107

7.2 Well-posedness of the diffusion model 109

7.3 Estimating Radiance, Depth, and Motion 110

7.3.1 Cost Functional Minimization 111

7.4.1 Synthetic Data 114

7.4.2 Real Images 117

8 Dealing with multiple moving objects 120

8.1 Handling multiple moving objects 121

8.2 A closer look at camera exposure 124

8.3 Relative motion blur 125

8.3.1 Minimization algorithm 126

8.4 Dealing with changes in motion 127

8.4.1 Matching motion blur along different directions 129

8.4.2 A look back at the original problem 131

8.4.3 Minimization algorithm 132

8.5 Image restoration 135

8.5.1 Minimization algorithm 137

8.6.1 Synthetic data 138

8.6.2 Real data 141

9 Dealing with occlusions 147

9.1 Inferring shape and radiance of occluded surfaces 148

9.2 Detecting occlusions 150

9.3 Implementation of the algorithm 151

9.4.1 Examples on a synthetic scene 152

9.4.2 Examples on real images 154

A Concepts of radiometry 161

A.1 Radiance, irradiance, and the pinhole model 161

A.1.1 Foreshortening and solid angle 161

A.1.2 Radiance and irradiance 162

A.1.3 Bidirectional reflectance distribution function 163

A.1.4 Lambertian surfaces 163

A.1.5 Image intensity for a Lambertian surface and a pinhole lens model 164

A.2 Derivation of the imaging model for a thin lens 164

B Basic primer on functional optimization 168

B.1 Basics of the calculus of variations 169

B.1.1 Functional derivative 170

B.1.2 Euler-Lagrange equations 171

B.2 Detailed computation of the gradients 172

B.2.1 Computation of the gradients in Chapter 6 172

B.2.2 Computation of the gradients in Chapter 7 174

B.2.3 Computation of the gradients in Chapter 8 176

B.2.4 Computation of the gradients in Chapter 9 185

C Proofs 190

C.1 Proof of Proposition 3.2 190

C.2 Proof of Proposition 3.5 191

C.3 Proof of Proposition 4.1 192

C.4 Proof of Proposition 5.1 194

C.5 Proof of Proposition 7.1 195

D Calibration of defocused images 197

D.1 Zooming and registration artifacts 197

D.2 Telecentric optics 200

E Matlab implementation of some algorithms 202

E.1 Least-squares solution (Chapter 4) 202

E.2 I-divergence solution (Chapter 5) 212

E.3 Shape from defocus via diffusion (Chapter 6) 221

E.4 Initialization: A fast approximate method 229

F Regularization 232

F.1 Inverse problems 232

F.2 Ill-posed problems 234

F.3 Regularization 235

F.3.1 Tikhonov regularization 237

F.3.2 Truncated SVD 238.

Notes:

Includes bibliographical references (pages [239]-246) and index.

ISBN:

1846281768

9781846281761

OCLC:

70987384