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Tables of Contents for Computer Vision
Chapter/Section Title
Page #
Page Count
Preface
v
1
Symbols
vi
1 Introduction
1
42
1.1 Shape Reconstruction
2
9
1.1.1 Tasks and Tools
2
3
1.1.2 Formal Specification of the Basic Task
5
2
1.1.3 Three Straightforward Limitations for Shape Reconstruction
7
3
1.1.4 Utilization of Context Knowledge
10
1
1.2 Gray Value and Color Images
11
8
1.2.1 Image Parameters and Two Color Models
12
3
1.2.2 Conversion Between These Color Models
15
4
1.3 Edge Detection
19
10
1.3.1 Edges in Gray Value Images
20
4
1.3.2 Laplacian-of-Gaussian Edge Detector
24
5
1.4 An Introductory Example--Static Stereo Image Analysis
29
9
1.4.1 Coplanar Stereo Image Geometry
29
4
1.4.2 Shirai Algorithm
33
5
1.5 References
38
2
1.6 Exercises
40
3
2 Image Acquisition
43
38
2.1 Geometric Camera Model
43
25
2.1.1 Central and Parallel Projection
44
4
2.1.2 A Camera Model for Central Projection
48
5
2.1.3 Calibration by Direct Linear Transformation
53
4
2.1.4 A Camera Model with Radial Lens Distortion
57
5
2.1.5 Tsai's Calibration Method
62
6
2.2 Sensor Model
68
7
2.2.1 Camera Hardware for Color Image Acquisition
69
2
2.2.2 Photometric Sensor Model
71
2
2.2.3 Pre-kneeing, Clipping, and Blooming
73
2
2.3 Photometric Calibration
75
3
2.3.1 Gamma Re-Correction
75
2
2.3.2 Black Level and White Balance
77
1
2.4 References
78
1
2.5 Exercises
79
2
3 Geometry of Object Surfaces
81
48
3.1 Functional Representations
81
14
3.1.1 Facets or Differentiable Functions
81
5
3.1.2 Normals and Gradients
86
4
3.1.3 Taylor Expansion
90
1
3.1.4 Sphere and Solid Angles
91
4
3.2 Projection and Reconstruction
95
10
3.2.1 Range Image, Depth Map, Height Map, and Gradient Map
95
4
3.2.2 Backprojection
99
3
3.2.3 Visualization of Gradient Maps
102
3
3.3 Depth Maps from Gradient Maps
105
11
3.3.1 Local Propagation Methods
105
4
3.3.2 Frankot-Chellappa Algorithm
109
7
3.4 Gradient Space
116
8
3.4.1 Three Coordinate Systems
117
4
3.4.2 Properties of the Gradient Space
121
3
3.5 References
124
1
3.6 Exercises
125
4
4 Static Stereo Analysis
129
48
4.1 Geometry of Static Stereo
130
5
4.2 Assumptions and Constraints
135
10
4.2.1 Epipolar Line Constraint
136
2
4.2.2 Uniqueness, Compatibility, and Similarity
138
1
4.2.3 Continuity of Disparities
139
1
4.2.4 Compatibility of Features
140
2
4.2.5 Disparity Limit and Disparity Gradient Limit
142
2
4.2.6 Ordering of Projected Points in the Image Plane
144
1
4.3 Intensity-Based Correspondence Analysis
145
14
4.3.1 Block-Matching Method
146
5
4.3.2 Matching of Epipolar Lines using Dynamic Programming
151
4
4.3.3 Block-Matching Method for Color Image Stereo Analysis
155
4
4.4 Feature-Based Correspondence Analysis
159
9
4.4.1 Stereo Analysis based on Zero-crossing Vectors
160
5
4.4.2 Feature-Based Color Stereo Analysis
165
3
4.5 Stereo Analysis with Three Cameras
168
4
4.5.1 Assignment Strategies
169
1
4.5.2 A Geometric Method
170
2
4.6 References
172
2
4.7 Exercises
174
3
5 Dynamic Stereo Analysis
177
50
5.1 Displacement Vectors and Reconstruction
177
13
5.1.1 Local Displacement Vectors
178
3
5.1.2 Object Motion and Local Displacement
181
1
5.1.3 Object Motion and Gradients
182
2
5.1.4 Local Displacement and Gradients
184
5
5.1.5 Camera Rotation about the Projection Center
189
1
5.2 Optical Flow
190
17
5.2.1 Solution Strategy
190
3
5.2.2 Horn-Schunck Method
193
8
5.2.3 Discussion
201
6
5.3 Object Rotation and Reconstruction
207
15
5.3.1 World Coordinates from Point Correspondence
207
5
5.3.2 Constrained Search Space for Correspondence Analysis
212
4
5.3.3 Discussion
216
2
5.3.4 3D Models from Occluding Boundaries
218
4
5.4 References
222
1
5.5 Exercises
223
4
6 Reflection Models
227
36
6.1 Radiometric Quantities and Laws
228
4
6.1.1 Quantities Independent from Solid Angles
228
1
6.1.2 Quantities Dependent on Solid Angles
229
1
6.1.3 A Fundamental Relationship
230
1
6.1.4 Inverse Square Law
231
1
6.2 Reflectance-Distribution Function
232
5
6.2.1 Definition of BRDF
233
1
6.2.2 BRDF of a Perfectly Diffuse Surface
234
1
6.2.3 Lambert's Cosine Law
235
1
6.2.4 Albedo
236
1
6.2.5 BRDF Measurement
236
1
6.3 Reflectance Maps
237
11
6.3.1 Definition and Representation
238
1
6.3.2 Linear Reflectance Maps
238
2
6.3.3 Lambertian Reflectance Maps
240
4
6.3.4 Generation of Reflectance Maps
244
4
6.4 Reflection Components
248
9
6.4.1 Diffuse Reflection
248
1
6.4.2 Specular Reflection
249
3
6.4.3 Dichromatic Reflection Model
252
4
6.4.4 Interreflections
256
1
6.5 Image Irradiance Equation
257
2
6.5.1 Image Formation
257
1
6.5.2 General Equation
258
1
6.6 References
259
2
6.7 Exercises
261
2
7 Shape from Shading
263
38
7.1 Introduction
263
8
7.1.1 SFS Constraints
264
3
7.1.2 Classification of SFS Methods
267
1
7.1.3 Direct Interpretation of Image Irradiances
268
3
7.2 Propagation Methods
271
9
7.2.1 Linear Reflectance Maps
271
4
7.2.2 Rotationally Symmetric and General Reflectance Maps
275
2
7.2.3 More Robust Methods
277
3
7.3 Global Minimization Approaches
280
13
7.3.1 Formulation of Constraints
280
4
7.3.2 Combination of Constraints
284
1
7.3.3 SFS as a Variational Problem
285
8
7.4 Local Shape from Shading
293
5
7.4.1 Spherical Approximation and Calculation of Tilt
293
2
7.4.2 Calculation of Slant
295
3
7.5 References
298
2
7.6 Exercises
300
1
8 Photometric Stereo
301
46
8.1 Limitations of SFS
302
5
8.2 Analysis of Irradiance Pairs
307
24
8.2.1 Linear Reflectance Maps
308
2
8.2.2 Albedo Dependent Analysis
310
7
8.2.3 Uniqueness by Integrability
317
9
8.2.4 Albedo Independent Analysis
326
2
8.2.5 Uniqueness by Spherical Approximation
328
3
8.3 Analysis of Irradiance Triplets
331
10
8.3.1 Albedo Dependent Analysis
331
4
8.3.2 Albedo Independent Analysis
335
5
8.3.3 Calculation of the Illumination Direction
340
1
8.4 References
341
2
8.5 Exercises
343
4
9 Structured Lighting
347
30
9.1 Projection of Simple Geometric Patterns
349
14
9.1.1 Light Spot Projection
349
4
9.1.2 Light Spot Stereo Analysis
353
2
9.1.3 Light Stripe Projection
355
7
9.1.4 Static Light Pattern Projection
362
1
9.2 Projection of Encoded Patterns
363
10
9.2.1 Binary Encoded Light Stripes and Phase Shifting
363
4
9.2.2 Color Encoded Light Stripe Projection
367
2
9.2.3 Active Color Stereo Analysis
369
4
9.3 References
373
1
9.4 Exercises
374
3
Appendix: Color Images
377
4
List of Algorithms
381
2
Index
383