Accurate Visual Metrology from Single and Multiple Uncalibrated Images

1. Introduction.- 1.1 Accurate measurements from images.- 1.2 Why use vision.- 1.3 Why is visual metrology hard.- 1.4 Applications and examples.- 1.5 Summary.- 2.Related work.- 2.1 Using one view.- 2.2 Using two views.- 2.3 Using three or more views.- 2.4 Partial calibration.- 2.5 Parallax-based approaches.- 2.6 Investigation of accuracy.- 2.7 Projective geometry and history of art.- Background geometry and notation.- 3.1 Camera models and perspective mappings.- 3.2 Radial distortion correction.- 3.3 Vanishing points and vanishing lines.- 3.4 Uncertainty analysis.- Metrology on planes.- 4.1 Estimating the homography.- 4.2 Uncertainty analysis.- 4.3 Application — a plane measuring device.- 4.4 Duality and homologies.- 5. Single-view metrology.- 5.1 Geometry.- 5.2 Algebraic representation.- 5.3 Uncertainty analysis.- 5.4 Three-dimensional metrology from a single view.- 5.5 Applications.- 5.6 Missing base point.- 6. Metrology from planar parallax.- 6.1 Background.- 6.2 Geometry and duality.- 6.3 Scene reconstruction.- 6.4 Uncertainty analysis.- Gallery of examples.- 7.1 Reconstruction from photographs.- 7.2 Reconstruction from paintings.- 7.3 Discussion.- 8. Conclusion.- 8.1 Summary.- 8.2 Discussion.- 8.3 Future work.- A. Metrology on planes, computing uncertainty in the homography.- B. Maximum likelihood estimation of end points for isotropic uncertainties.- C. Single-view metrology, variance of distance between planes.- C.1 Covariance of maximum likelihood estimation (MLE) end points.- D. Single-view metrology, variance of the affine parameter ?.- E. Metrology from planar parallax, derivations.- E.1 Computing the motion constraints.- E.2 Computing distances of points from planes directly in the images.- F. Metrology from planar parallax, variance of distances.- F.1Definitions.- References.