Cover image for 3-D shape estimation and image restoration : exploiting defocus and motion blur
Title:
3-D shape estimation and image restoration : exploiting defocus and motion blur
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Publication Information:
London : Springer, 2007
Physical Description:
xiv, 249 p. : ill., digital ; 24 cm.
ISBN:
9781846281761
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Available online version
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30000010141976 TA1637 F38 2007 Open Access Book Book
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30000010150706 TA1637 F38 2007 Open Access Book Book
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Summary

Summary

In the areas of image processing and computer vision, there is a particular need for software that can, given an unfocused or motion-blurred image, infer the three-dimensional shape of a scene. This book describes the analytical processes that go into designing such software, delineates the options open to programmers, and presents original algorithms. 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.


Table of Contents

Prefacep. vii
1 Introductionp. 1
1.1 The sense of visionp. 1
1.1.1 Stereop. 4
1.1.2 Structure from motionp. 5
1.1.3 Photometric stereo and other techniques based on controlled lightp. 5
1.1.4 Shape from shadingp. 6
1.1.5 Shape from texturep. 6
1.1.6 Shape from silhouettesp. 6
1.1.7 Shape from defocusp. 6
1.1.8 Motion blurp. 7
1.1.9 On the relative importance and integration of visual cuesp. 7
1.1.10 Visual inference in applicationsp. 8
1.2 Preview of coming attractionsp. 9
1.2.1 Estimating 3-D geometry and photometry with a finite aperturep. 9
1.2.2 Testing the power and limits of models for accommodation cuesp. 10
1.2.3 Formulating the problem as optimal inferencep. 11
1.2.4 Choice of optimization criteria, and the design of optimal algorithmsp. 12
1.2.5 Variational approach to modeling and inference from accommodation cuesp. 12
2 Basic models of image formationp. 14
2.1 The simplest imaging modelp. 14
2.1.1 The thin lensp. 14
2.1.2 Equifocal imaging modelp. 16
2.1.3 Sensor noise and modeling errorsp. 18
2.1.4 Imaging models and linear operatorsp. 19
2.2 Imaging occlusion-free objectsp. 20
2.2.1 Image formation nuisances and artifactsp. 22
2.3 Dealing with occlusionsp. 23
2.4 Modeling defocus as a diffusion processp. 26
2.4.1 Equifocal imaging as isotropic diffusionp. 28
2.4.2 Nonequifocal imaging modelp. 29
2.5 Modeling motion blurp. 30
2.5.1 Motion blur as temporal averagingp. 30
2.5.2 Modeling defocus and motion blur simultaneouslyp. 34
2.6 Summaryp. 35
3 Some analysis: When can 3-D shape be reconstructed from blurred images? 37
3.1 The problem of shape from defocusp. 38
3.2 Observability of shapep. 39
3.3 The role of radiancep. 41
3.3.1 Harmonic componentsp. 42
3.3.2 Band-limited radiances and degree of resolutionp. 42
3.4 Joint observability of shape and radiancep. 46
3.5 Regularizationp. 46
3.6 On the choice of objective function in shape from defocusp. 47
3.7 Summaryp. 49
4 Least-squares shape from defocusp. 50
4.1 Least-squares minimizationp. 50
4.2 A solution based on orthogonal projectorsp. 53
4.2.1 Regularization via truncation of singular valuesp. 53
4.2.2 Learning the orthogonal projectors from imagesp. 55
4.3 Depth-map estimation algorithmp. 58
4.4 Examplesp. 60
4.4.1 Explicit kernel modelp. 60
4.4.2 Learning the kernel modelp. 61
4.5 Summaryp. 65
5 Enforcing positivity: Shape from defocus and image restoration by minimizing I-divergencep. 69
5.1 Information-divergencep. 70
5.2 Alternating minimizationp. 71
5.3 Implementationp. 76
5.4 Examplesp. 76
5.4.1 Examples with synthetic imagesp. 76
5.4.2 Examples with real imagesp. 78
5.5 Summaryp. 79
6 Defocus via diffusion: Modeling and reconstructionp. 87
6.1 Blurring via diffusionp. 88
6.2 Relative blur and diffusionp. 89
6.3 Extension to space-varying relative diffusionp. 90
6.4 Enforcing forward diffusionp. 91
6.5 Depth-map estimation algorithmp. 92
6.5.1 Minimization of the cost functionalp. 94
6.6 On the extension to multiple imagesp. 95
6.7 Examplesp. 96
6.7.1 Examples with synthetic imagesp. 97
6.7.2 Examples with real imagesp. 99
6.8 Summaryp. 99
7 Dealing with motion: Unifying defocus and motion blurp. 106
7.1 Modeling motion blur and defocus in one gop. 107
7.2 Well-posedness of the diffusion modelp. 109
7.3 Estimating Radiance, Depth, and Motionp. 110
7.3.1 Cost Functional Minimizationp. 111
7.4 Examplesp. 113
7.4.1 Synthetic Datap. 114
7.4.2 Real Imagesp. 117
7.5 Summaryp. 118
8 Dealing with multiple moving objectsp. 120
8.1 Handling multiple moving objectsp. 121
8.2 A closer look at camera exposurep. 124
8.3 Relative motion blurp. 125
8.3.1 Minimization algorithmp. 126
8.4 Dealing with changes in motionp. 127
8.4.1 Matching motion blur along different directionsp. 129
8.4.2 A look back at the original problemp. 131
8.4.3 Minimization algorithmp. 132
8.5 Image restorationp. 135
8.5.1 Minimization algorithmp. 137
8.6 Examplesp. 138
8.6.1 Synthetic datap. 138
8.6.2 Real datap. 141
8.7 Summaryp. 146
9 Dealing with occlusionsp. 147
9.1 Inferring shape and radiance of occluded surfacesp. 148
9.2 Detecting occlusionsp. 150
9.3 Implementation of the algorithmp. 151
9.4 Examplesp. 152
9.4.1 Examples on a synthetic scenep. 152
9.4.2 Examples on real imagesp. 154
9.5 Summaryp. 157
10 Final remarksp. 159
A Concepts of radiometryp. 161
A.1 Radiance, irradiance, and the pinhole modelp. 161
A.1.1 Foreshortening and solid anglep. 161
A.1.2 Radiance and irradiancep. 162
A.1.3 Bidirectional reflectance distribution functionp. 163
A.1.4 Lambertian surfacesp. 163
A.1.5 Image intensity for a Lambertian surface and a pinhole lens modelp. 164
A.2 Derivation of the imaging model for a thin lensp. 164
B Basic primer on functional optimizationp. 168
B.1 Basics of the calculus of variationsp. 169
B.1.1 Functional derivativep. 170
B.1.2 Euler-Lagrange equationsp. 171
B.2 Detailed computation of the gradientsp. 172
B.2.1 Computation of the gradients in Chapter 6p. 172
B.2.2 Computation of the gradients in Chapter 7p. 174
B.2.3 Computation of the gradients in Chapter 8p. 176
B.2.4 Computation of the gradients in Chapter 9p. 185
C Proofsp. 190
C.1 Proof of Proposition 3.2p. 190
C.2 Proof of Proposition 3.5p. 191
C.3 Proof of Proposition 4.1p. 192
C.4 Proof of Proposition 5.1p. 194
C.5 Proof of Proposition 7.1p. 195
D Calibration of defocused imagesp. 197
D.1 Zooming and registration artifactsp. 197
D.2 Telecentric opticsp. 200
E Matlab implementation of some algorithmsp. 202
E.1 Least-squares solution (Chapter 4)p. 202
E.2 I-divergence solution (Chapter 5)p. 212
E.3 Shape from defocus via diffusion (Chapter 6)p. 221
E.4 Initialization: A fast approximate methodp. 229
F Regularizationp. 232
F.1 Inverse problemsp. 232
F.2 Ill-posed problemsp. 234
F.3 Regularizationp. 235
F.3.1 Tikhonov regularizationp. 237
F.3.2 Truncated SVDp. 238
Referencesp. 239
Indexp. 247