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Contents

I IMAGE FORMATION 1

1 Geometric Camera Models 3
1.1 Image Formation . . . . . . . .. .. .. ... .. ... .. .. ... . 4
1.1.1 Pinhole Perspective . .. .. .. ... .. ... .. .. ... . 4
1.1.2 Weak Perspective . . . .. .. .. ... .. ... .. .. ... . 6
1.1.3 Cameras with Lenses . .. .. .. ... .. ... .. .. ... . 8
1.1.4 The Human Eye .. ... .. .. ... .. ... .. .. ... . 12
1.2 Intrinsic and Extrinsic Parameters . .. ... .. ... .. .. ... . 14
1.2.1 Rigid Transformations and Homogeneous Coordinates . . . . 14
1.2.2 Intrinsic Parameters . .. .. .. ... .. ... .. .. ... . 16
1.2.3 Extrinsic Parameters ... .. .. ... .. ... .. .. ... . 18
1.2.4 Perspective Projection Matrices . . .. .. ... .. .. ... . 19
1.2.5 Weak-Perspective Projection Matrices .. ... .. .. ... . 20
1.3 Geometric Camera Calibration . .. .. ... .. ... .. .. ... . 22
1.3.1 A Linear Approach to Camera Calibration . . . . . . . . . . . 23
1.3.2 A Nonlinear Approach to Camera Calibration . . . . . . . . . 27
1.4 Notes . . . . . . .. .. .. ... .. .. ... .. ... .. .. ... . 29
2 Light and Shading 32
2.1 Modelling Pixel Brightness . . . . . . . . . . . . . . . . . . . . . . . 32
2.1.1 Reflection at Surfaces .. .. .. ... .. ... .. .. ... . 33
2.1.2 Sources and Their Effects . . . . ... .. ... .. .. ... . 34
2.1.3 The Lambertian+Specular Model ... .. ... .. .. ... . 36
2.1.4 Area Sources .. .. ... .. .. ... .. ... .. .. ... . 36
2.2 Inference from Shading . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.2.1 Radiometric Calibration and High Dynamic Range Images . . 38
2.2.2 The Shape of Specularities . . . ... .. ... .. .. ... . 40
2.2.3 Inferring Lightness and Illumination . . . . . . . . . . . . . . 43
2.2.4 Photometric Stereo: Shape from Multiple Shaded Images . . 46
2.3 Modelling Interreflection . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.3.1 The Illumination at a Patch Due to an Area Source . . . . . 52
2.3.2 Radiosity and Exitance . .. .. ... .. ... .. .. ... . 54
2.3.3 An Interreflection Model . . . . . . .. .. ... .. .. ... . 55
2.3.4 Qualitative Properties of Interreflections . . . . . . . . . . . . 56
2.4 Shape from One Shaded Image . . . . . ... .. ... .. .. ... . 59

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