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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