Depth from two cameras: stereopsis
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1 Depth from two cameras: stereopsis Epipolar Geometry Canonical Configuration Correspondence Matching School of Computer Science & Statistics Trinity College Dublin Dublin 2 Ireland Lecture Name Augmented Reality 1 1
2 Human Stereo Vision Faking Stereo Vision Stereoscope Random Dot Stereograms Stereo Glasses Head mounted VR display Emulating Stereo Vision Two cameras Active robot head Augmented Realty 2 2
3 Basics of depth extraction Single Camera calibrated intrinsics extrinsics inverse perspective transform Two Cameras Calibration extrinsics matching points correspondence problem intersection of rays (maybe) depth / disparity calculation Augmented Realty 3 3
4 Geometry of Stereo Baseline Connecting Camera Centers Epipolar constraint a point in one image must lie along a line in the other: l and l Image point and camera centers define a plane All planes pass through the epipoles Canonical configuration places epipoles at infinity Augmented Realty 4 4
5 Epipolar Constraint Augmented Realty 5 5
6 Essential Matrix Translation and Rotation between two cameras when we know the camera calibration Essential Matrix 9 coefficients Parameterised by 3 DoF of R and 2 DoF of t Relationship between points p[t (Rp )] p Ep =0where E =[t x ]R and [a x ]b = a b Augmented Realty 6 6
7 Fundamental Matrix Unknown camera calibration Fundamental Matrix Has 7 parameters Parameterised by 4 numbers (a,b,c,d) p = K p, p = K p p T Fp =0, where F = K T EK 1 e =(α, β) T and e =(α, β ) T Augmented Realty 7 7
8 Canonical configuration baseline parallel to image plane epipolar lines parallel image rectification to place images into canonical configuration search for correspondences along raster lines Andrea Fusiello, University of Verona (Reproduced with permission) Augmented Realty 8 8
9 Calculating Depth Point in 3D space P(x,y,z) Clear disparity in the views in both cameras: Pl and Pr simple geometry can be used to give depth Z Augmented Realty 9 9
10 Problem Solved? Stereo Assumptions see point in both images unique solution to correspondence problem Problems (Self) Occlusion Non-unique mappings Augmented Realty 10 10
11 Correspondence problem A key problem in computer vision one of these things looks a lot like the other Why should this be hard differences of view point specularities subtle scale changes Applying Constraints make this easier epipolar uniqueness pixel compatibility Augmented Realty
12 Other Constraints Disparity Smoothness Constraint with two scene points close to each other p & q Threshold = ( pl-pr - ql-qr ) Figural Disparity Constraint if an edge element: must be on one in both images Disparity limit constraint human visual system can only resolve stereo images if disparity is less than a threshold: sets a limit to the disparity search Augmented Realty
13 Paradigms to solve correspondence Correlation based - bottom up approaches Psychology > humans do not use monocular features to match Block Matching: 5X5, 7x7,... Matching Criteria: SSD, NCC, etc Other constraints must be used to produce good matching pyramidal approaches; use of edge info at finer resolutions Augmented Realty
14 Correlation based approaches Augmented Realty 14 14
15 Feature Based Approaches Augmented Realty 15 15
16 One Feature Based Approach PMF Stereo Algorithm Pollard, Mayhew and Frisby assumes features have been extracted correspondence pairs are generated 3 constraints used epipolar uniqueness disparity gradient limit Augmented Realty
17 Separation S(), disparity difference D() Augmented Realty 17 17
18 Definitions from PMF paper homepages.inf.ed.ac.uk/rbf/books/ MAYHEW/scan/ pdf Augmented Realty 18 18
19 PMF Algorithm from Sonka Augmented Realty 19 19
20 Disparity Map / Depth Image Augmented Realty 20 20
21 Disparity Map / Depth Image Augmented Realty 21 21
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