Computer Vision II Building Rome in a Day

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1 Computer Vision II Building Rome in a Day

2 Recall Fundamental matrix song RANSAC song

3

4 How? Reading: the MVG bible (need ~2 years) 5-6 years Yes Coding PhD? No Crying: Not Working At All

5 + + =

6 Steps + = Images Points: Structure from Motion Points More points: Multiple View Stereo Points Meshes: Model Fitting Meshes Models: Texture Mapping Images Models: Image-based Modeling

7 Steps + = Images Points: Structure from Motion Points More points: Multiple View Stereo Points Meshes: Model Fitting Meshes Models: Texture Mapping Images Models: Image-based Modeling + + =

8 Steps + = Images Points: Structure from Motion Points More points: Multiple View Stereo Points Meshes: Model Fitting Meshes Models: Texture Mapping Images Models: Image-based Modeling + + =

9 Steps + = Images Points: Structure from Motion Points More points: Multiple View Stereo Points Meshes: Model Fitting Meshes Models: Texture Mapping Images Models: Image-based Modeling =

10 Steps + = Images Points: Structure from Motion Points More points: Multiple View Stereo Points Meshes: Model Fitting Meshes Models: Texture Mapping Images Models: Image-based Modeling

11 Steps + = Images Points: Structure from Motion Points More points: Multiple View Stereo Points Meshes: Model Fitting Meshes Models: Texture Mapping Images Models: Image-based Modeling

12 Steps + = Images Points: Structure from Motion Points More points: Multiple View Stereo Points Meshes: Model Fitting Meshes Models: Texture Mapping Images Models: Image-based Modeling

13 Image-based Modeling

14 Image-based Modeling

15 Steps + = Images Points: Structure from Motion Points More points: Multiple View Stereo Points Meshes: Model Fitting Meshes Models: Texture Mapping Images Models: Image-based Modeling + + =

16 Steps + = Images Points: Structure from Motion Points More points: Multiple View Stereo Points Meshes: Model Fitting Meshes Models: Texture Mapping Images Models: Image-based Modeling + + =

17 Steps + = Images Points: Structure from Motion Points More points: Multiple View Stereo Points Meshes: Model Fitting Meshes Models: Texture Mapping Images Models: Image-based Modeling + + =

18 Structure From Motion Structure = 3D Point Cloud of the Scene Motion = Camera Location and Orientation SFM = Get the Point Cloud from Moving Cameras Structure and Motion: Joint Problems to Solve + + =

19 Pipeline Structure from Motion (SFM) Multi-view Stereo (MVS)

20 Pipeline Structure from Motion (SFM) Multi-view Stereo (MVS)

21 Two-view Reconstruction

22 Two-view Reconstruction

23 Two-view Reconstruction keypoints keypoints match fundamental matrix essential matrix [R t] triangulation

24 Keypoints Detection keypoints keypoints match fundamental matrix essential matrix [R t] triangulation

25 Descriptor for each point SIFT descriptor SIFT descriptor keypoints keypoints match fundamental matrix essential matrix [R t] triangulation

26 Same for the other images SIFT descriptor SIFT descriptor SIFT descriptor SIFT descriptor keypoints keypoints match fundamental matrix essential matrix [R t] triangulation

27 Point Match for correspondences SIFT descriptor SIFT descriptor SIFT descriptor SIFT descriptor keypoints keypoints match fundamental matrix essential matrix [R t] triangulation

28 Point Match for correspondences SIFT descriptor SIFT descriptor SIFT descriptor SIFT descriptor keypoints keypoints match fundamental matrix essential matrix [R t] triangulation

29 Fundamental Matrix Image 1 R 1,t 1 Image 2 R 2,t 2

30 Exercise What is the difference between Fundamental Matrix and Homography? (Both of them are to explain 2D point to 2D point correspondences.)

31 Estimating Fundamental Matrix Given a correspondence The basic incidence relation is Need 8 points

32 Estimating Fundamental Matrix for 8 point correspondences: Direct Linear Transformation (DLT)

33 Algebraic Error vs. Geometric Error Algebraic Error Geometric Error (better) Unit: pixel Solved by (non-linear) least square solver (e.g. Ceres)

34 RANSAC to Estimate Fundamental Matrix For many times Pick 8 points Compute a solution for using these 8 points Count number of inliers that with close to 0 Pick the one with the largest number of inliers

35 Minimal problems in Computer Vision

36 Fundamental Matrix Essential Matrix Image 1 R 1,t 1 Image 2 R 2,t 2

37 Essential Matrix Image 1 R 1,t 1 Image 2 R 2,t 2

38 Essential Matrix Result For a given essential matrix and the first camera matrix, there are four possible choices for the second camera matrix : Page 259 of the bible (Multiple View Geometry, 2 nd Ed)

39 Four Possible Solutions Page 260 of the bible (Multiple View Geometry, 2 nd Ed)

40 Triangulation Image 1 R 1,t 1 Image 2 R 2,t 2

41 In front of the camera? Camera Extrinsic Camera Center View Direction Camera Coordinate System World Coordinate System

42 In front of the camera? A point Direction from camera center to point Angle Between Two Vectors Angle Between Just need to test and View Direction

43 Pick the Solution With maximal number of points in front of both cameras. Page 260 of the bible (Multiple View Geometry, 2 nd Ed)

44 Two-view Reconstruction keypoints keypoints match fundamental matrix essential matrix [R t] triangulation

45 Pipeline Structure from Motion (SFM) Multi-view Stereo (MVS)

46 Pipeline Taught Next

47 Merge Two Point Cloud

48 Merge Two Point Cloud There can be only one

49 Merge Two Point Cloud From the 1 st and 2 nd images, we have and From the 2 nd and 3 rd images, we have and Exercise: How to transform the coordinate system of the second point cloud to align with the first point cloud so that there is only one?

50 Merge Two Point Cloud

51 Oops See From a Different Angle

52 Bundle Adjustment

53 I am very very sexy Image 1 R 1,t 1 Image 3 R 3,t 3 Image 2 R 2,t 2

54 I am very very sexy Point 1 Point 2 Point 3 Image 1 Image 2 Image 3

55 Rethinking the SFM problem Input: Observed 2D image position Output: Unknown Camera Parameters (with some guess) Unknown Point 3D coordinate (with some guess)

56 Bundle Adjustment A valid solution must let and Re-projection = Observation

57 Bundle Adjustment A valid solution and must let the Re-projection close to the Observation, i.e. to minimize the reprojection error

58 Bundle Adjustment A valid solution and must let the Re-projection close to the Observation, i.e. to minimize the reprojection error Question: What is the unit of this objective function?

59 Camera Bundle Adjustment A valid solution and must let the Re-projection close to the Observation, i.e. to minimize the reprojection error Points

60 Camera Linking Linking SIFT Matching SIFT Matching Points

61 Solving This Optimization Problem Theory: The Levenberg Marquardt algorithm Practice: The Ceres-Solver from Google

62 Parameterizing Rotation Matrix 2D Rotation

63 3D Rotation Yaw, pitch and roll are Euler angles are

64 Axis-angle representation 3D Rotation Quaternions Avoid Gimbal Lock! Triplet Representation Recommendation! (3 dof) Not over-parameterized Rodrigues' rotation formula

65 Initialization Matters Input: Observed 2D image position Output: Unknown Camera Parameters (with some guess) Unknown Point 3D coordinate (with some guess)

66 Pipeline Taught Next

67 Multiple View Stereo State-of-the-art: PMVS: Accurate, Dense, and Robust Multi-View Stereopsis, Y Furukawa and J Ponce, Benchmark: A Comparison and Evaluation of Multi-View Stereo Reconstruction Algorithms. SM Seitz, B Curless, J Diebel, D Scharstein, R Szeliski Baseline: Multi-view stereo revisited. M Goesele, B Curless, SM Seitz

68 当前无法显示此图像 当前无法显示此图像 当前无法显示此图像 Key idea: Matching Propagation [1] Learning Two-view Stereo Matching, J Xiao, J Chen, DY Yeung, and L Quan, [2] Accurate, Dense, and Robust Multi-View Stereopsis, Y Furukawa and J Ponce, [3] Multi-view stereo revisited. M Goesele, B Curless, SM Seitz [4] Robust Dense Matching Using Local and Global Geometric Constraints, M Lhuillier & L Quan, In another context: [5] PatchMatch: A Randomized Correspondence Algorithm for Structural Image Editing, C Barnes, E Shechtman, A Finkelstein, and DB Goldman, 2009.

69 Simplest Matching Propagation We are going to learn a very simple algorithm

70 Descriptor: ZNCC (Zero-mean Normalized Cross-Correlation) Invariant to linear radiometric changes More conservative than others such as sum of absolute or square differences in uniform regions More tolerant in textured areas where noise might be important

71 Descriptor: ZNCC (Zero-mean Normalized Cross-Correlation) Invariant to linear radiometric changes More conservative than others such as sum of absolute or square differences in uniform regions More tolerant in textured areas where noise might be important

72 Seed for propagation

73 Matching Propagation Maintain a priority queue Q Initialize: Put all seeds into Q with their ZNCC values as scores For each iteration: Pop the match with best ZNCC score from Q Add new potential matches in their immediate spatial neighborhood into Q Safety: handle uniqueness, and propagate only on matchable area

74 Matchable Area the area with maximal gradience > threshold

75 Result

76 Another Example

77 Another Example

78 Another Example

79 Triangulation Image 1 R 1,t 1 Image 3 R 3,t 3 Image 2 R 2,t 2

80 Final Result

81 Colorize the Point Cloud

82 Complete Pipeline Structure from Motion (SFM) Multi-view Stereo (MVS)

83 Wait: How to get the focal length? Auto-calibration Self-Calibration and Metric Reconstruction in spite of Varying and Unknown Internal Camera Parameters, M Pollefeys, R Koch and L Van Gool, Grid Search to look for the solution with minimal reprojection error for f=min_f:max_f do everything, then obtain reprojection error after bundle adjustment Optimize for this value in bundle adjustment Camera Calibration (with checkerboard) EXIF of JPEG file recorded from digital camera Read the code of Bundler to understand how to convert EXIF into focal length value

84 Steps + = Images Points: Structure from Motion Points More points: Multiple View Stereo Points Meshes: Model Fitting Meshes Models: Texture Mapping Images Models: Image-based Modeling + + =

85 Steps + = Images Points: Structure from Motion Points More points: Multiple View Stereo Points Meshes: Model Fitting Meshes Models: Texture Mapping Images Models: Image-based Modeling =

86 Real World Applications Streetview Reconstruction and Recognition Photo Tourism Microsoft Photosynth 2d3, boujor (Matchmovers) and movies Robotics: SLAM Simultaneous Localization And Mapping

87 Steps + = Images Points: Structure from Motion Points More points: Multiple View Stereo Points Meshes: Model Fitting Meshes Models: Texture Mapping Images Models: Image-based Modeling

88 Point Cloud 3D Mesh Model Surface Reconstruction Marching Cubes: Poisson Surface Reconstruction Model Fitting RANSAC & J-linkage InverseCSG GlobFit Face Model Fitting

89 Maps 92

90 Photorealistic Maps 93

91 What about indoors? The Birth of Venus 94

92 Uffizi Museum 95

93 Cartography 2D Line Drawing 3D Realistic Maps Outdoor Indoor? 96 Reconstructing the World's Museums. Xiao and Furukawa, 2012.

94 Photorealistic Indoor Maps 97

95 Photorealistic Indoor Maps Where is The Birth of Venus? 98

96 Visualize & Explore Big Data 100

97 Data-driven Brute-force 2-step algorithm 102

98 Data-driven Brute-force 1. Remove ceiling. 2. Take pictures from aerial viewpoints. 103

99 What is Wrong? I don t own the museums. 104

100 Old Approach 1. Remove ceiling. 2. Take pictures from aerial viewpoints. 105

101 New Approach 0. Own the museums. 1. Remove ceiling. 2. Take pictures from aerial viewpoints. 106

102 New Approach 0. Reconstruct the museums. 1. Remove ceiling. 2. Take pictures from aerial viewpoints. 107

103 108

104 InverseCSG Algorithm Reconstructing the World's Museums, J. Xiao and Y. Furukawa, 2012.

105 InverseCSG Algorithm

106 Noisy Points top-down view of input points

107 InverseCSG Algorithm Constructive Solid Geometry (CSG)

108 InverseCSG Algorithm Constructive Solid Geometry (CSG) Cuboids as primitives Xiao et al. NIPS 2012 Xiao et al. Siggraph Asia 2012a

109 Bottom-up & Top-down Model 3D Cuboid 2D Rectangle 2D Line Point 115

110 InverseCSG Algorithm gravity side view 3D Point Cloud 2D CSG 3D CSG Wall Final 116

111 Cut into Slices side view point count 3D Point Cloud 2D CSG 3D CSG Wall Final 117

112 Cut into Slices side view 3D Point Cloud 2D CSG 3D CSG Wall Final 118

113 2D CSG Reconstruction 1. Generate primitives 2. Choose a subset 3D Point Cloud 2D CSG 3D CSG Wall Final top view 119

114 2D CSG Reconstruction 1. Generate primitives Point Line 3D Point Cloud 2D CSG 3D CSG Wall Final top view 120

115 2D CSG Reconstruction 1. Generate primitives From 4 line segments Point Line Line Rectangle 3D Point Cloud 2D CSG 3D CSG Wall Final 121

116 2D CSG Reconstruction 1. Generate primitives 2. Choose a subset 3D Point Cloud 2D CSG 3D CSG Wall Final top view 122

117 2D CSG Reconstruction 1. Generate primitives 2. Choose a subset Repeat in each slice 3D Point Cloud 2D CSG 3D CSG Wall Final top view 123

118 Objective Function Likelihood Points Free space Prior Simple Points Free space Prior top view 3D Point Cloud 2D CSG 3D CSG Wall Final 124

119 Objective Function Likelihood Points Free space Prior Simple Points Free space Prior top view 3D Point Cloud 2D CSG 3D CSG Wall Final 125

120 Objective Function Likelihood Points Free space Prior Simple Points Free space Prior top view 3D Point Cloud 2D CSG 3D CSG Wall Final 126

121 Objective Function Likelihood Points Free space Prior Simple Points Free space Prior top view 3D Point Cloud 2D CSG 3D CSG Wall Final 127

122 Objective Function Likelihood Points Free space Prior Simple Points Free space Prior top view 3D Point Cloud 2D CSG 3D CSG Wall Final 128

123 Objective Function Likelihood Points Free space Prior Simple Points Free space Prior top view 3D Point Cloud 2D CSG 3D CSG Wall Final 129

124 3D CSG Reconstruction 1. Generate primitives (cuboids) 2. Choose a subset (of primitive candidates) 3D Point Cloud 2D CSG 3D CSG Wall Final 130

125 3D CSG Reconstruction 1. Generate primitives (cuboids) side view gravity 3D Point Cloud 2D CSG 3D CSG Wall Final 131

126 3D CSG Reconstruction 1. Generate primitives (cuboids) 2D CSG side view 3D Point Cloud 2D CSG 3D CSG Wall Final 132

127 oblique view top view 2D CSG side view 3D Point Cloud 2D CSG 3D CSG Wall Final 133

128 3D CSG Reconstruction 1. Generate primitives (cuboids) Rectangle Primitive 2D CSG side view 3D Point Cloud 2D CSG 3D CSG Wall Final 134

129 3D CSG Reconstruction 1. Generate primitives (cuboids) Rectangle Primitive 2D CSG side view 3D Point Cloud 2D CSG 3D CSG Wall Final 135

130 3D CSG Reconstruction 1. Generate primitives (cuboids) 2. Choose a subset side view 3D Point Cloud 2D CSG 3D CSG Wall Final 136

131 Algorithm on Run

132 Result

133 Steps + = Images Points: Structure from Motion Points More points: Multiple View Stereo Points Meshes: Model Fitting Meshes Models: Texture Mapping Images Models: Image-based Modeling

134 Texture Mapping Texture Stitching View-based Texture Mapping View Interpolation and Warping Interactive Visualization

135 Image Warping: Forward Warping Source Image Target Image Matlab interp2 example:

136 Image Warping: Backward Warping Source Image Target Image Matlab interp2 example:

137 Texture Stitching The process of assembling projected images to form a composite rendering Image from Paul Debevec s Thesis

138 Texture Stitching Image-based Street-side City Modeling. Xiao et al, 2009.

139 Texture Stitching Image 1 R 1,t 1 Image 3 R 3,t 3 Image 2 R 2,t 2

140 Texture Stitching Image-based Street-side City Modeling. Xiao et al, 2009.

141

142

143 View-Dependent Texture Mapping Modeling and Rendering Architecture from Photographs, Paul Debevec, PhD Thesis, UC Berkeley, 1996

144 View Interpolation Match Propagation from Image-based Modeling and Rendering M Lhuillier and L Quan, 2012

145 View Interpolation

146 View Interpolation Match Propagation from Image-based Modeling and Rendering, M Lhuillier and L Quan, 2012

147 Interactive Visualization Reconstructing Building Interiors from Images, Y Furukawa, B Curless, SM Seitz, R Szeliski, 2009 Download the Viewer from:

148 Aerial+Ground Visualization Reconstructing the World's Museums. J. Xiao and Y. Furukawa,

149 Ground vs. Aerial Ground + Aerial Ground Aerial Ground+Aerial Outdoor Google Streetview Google/Bing/NASA Google MapsGL Indoor Furukawa et al. Xiao et al. Xiao et al.

150 Finish our Journey! + = Images Points: Structure from Motion Points More points: Multiple View Stereo Points Meshes: Model Fitting Meshes Models: Texture Mapping Images Models: Image-based Modeling + + =

151 History of 3D Reconstruction

152 Longer Summary of the History Research Landmarks for 3D Reconstruction Steve Seitz "History of 3D Computer Vision NSF Frontiers in Computer Vision,

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