StereoVision_1 - Nanyang Technological University

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Quantifying Matching Localization For a particular image patch, we want to find out how accurately it can be localized 1. Consider image patch at the solution point (i.e. perfect matching location where SSD=0) 2. Estimate how much SSD increases when image patch is displaced by small amounts in different directions We can use partial derivatives to estimate the increase in SSD School of Computer Engineering Nanyang Technological University SC437 Computer Vision and Image Processing TJ Cham 2002-03 / S2
S( x 0 Quantifying Matching Localization + δx, y Express SSD as a function S(x,y) 2 nd order Taylor Series expansion: + δy) ≈ At solution point, School of Computer Engineering Nanyang Technological University 0 S 0 0 th order ⎡∂S + ⎢ ⎣ ∂x S 0 = 0, 0 ∂S ∂y ⎤⎡δx⎤ ⎥⎢ ⎥ + ⎦⎣δy⎦ SC437 Computer Vision and Image Processing 0 1 st order (gradient) ∂S ∂x 0 = ∂S ∂y 0 = 2 ⎡∂ S ⎢ ∂x 0 2 2 ∂ S ⎤ 0 ⎥ ∂x∂y ⎡δx⎤ [ δx δy] ⎢ ⎥ 2 2 ⎢ ⎥ ⎢∂ S0 ∂ S0 ⎥⎣δy⎦ 0 ⎢ ⎣∂y∂x ∂y 2 nd order (Hessian) 2 ⎥ ⎦ TJ Cham 2002-03 / S2
Page 1 and 2: School of Computer Engineering Nany
Page 3 and 4: Range Sensing Radars and Sonars Tim
Page 5 and 6: Representation of Raw Range Data Cl
Page 7 and 8: Fitting 3D Models to Range Data We
Page 9 and 10: Parallax Parallax refers to the obs
Page 11 and 12: Parallax from Z Translation Paralla
Page 13 and 14: No Parallax from Pure Rotation No p
Page 15 and 16: Simple 2D Triangulation Assume 1D c
Page 17 and 18: Simple 2D Triangulation Depth from
Page 19 and 20: Relation of Baseline to Accuracy Le
Page 21 and 22: Recap on Parallax and 1D Triangulat
Page 23 and 24: Matching Image Points Appearance-ba
Page 25 and 26: Appearance-based Matching Assumptio
Page 27 and 28: Minimize Sum-of-Squares Difference
Page 29 and 30: Appearance Matching Example Point G
Page 31: Matching Accuracy Examples SSD Imag
Page 35 and 36: Cornerness Cornerness is defined as
Page 37 and 38: Recap on Appearance-Based Matching
Page 39 and 40: Feature-based Matching Want to matc
Page 41 and 42: Feature-based Matching Example Exam
Page 43 and 44: Feature Matching Heuristics Example
Page 45 and 46: Geometric Search Constraint A very
Page 47 and 48: Stereo Rig for Epipolar Geometry Sc
Page 49 and 50: Epipoles and Epipolar Lines Example
Page 51 and 52: Epipolar Geometry Derivation P l,
Page 53 and 54: Epipolar Geometry Derivation Subst
Page 55 and 56: Fundamental Matrix Equation Affin
Page 57 and 58: Using Epipolar Geometry If we know
Page 59 and 60: Estimating Fundamental Matrix The F
Page 61 and 62: Estimating Fundamental Matrix We ca
Page 63 and 64: 3D Reconstruction from Perspective
Page 65 and 66: 3D Reconstruction from Perspective
Page 67 and 68: 3D Reconstruction from Weak- Perspe
Page 69 and 70: Recap on 3D Reconstruction 3D recon
Page 71 and 72: Example Application of 3D Reconstru
Page 73: Summary of 3D Stereo Vision Represe

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