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Self-Calibration and Metric Reconstruction from Single Images

Self-Calibration and Metric Reconstruction from Single Images. Ruisheng Wang Frank P. Ferrie Centre for Intelligent Machines, McGill University. Outline. Contributions Existing Methods The Idea Our Method Comparison Conclusion. Contributions.

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Self-Calibration and Metric Reconstruction from Single Images

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  1. Self-Calibration and Metric Reconstruction from Single Images Ruisheng Wang Frank P. Ferrie Centre for Intelligent Machines, McGill University

  2. Outline • Contributions • Existing Methods • The Idea • Our Method • Comparison • Conclusion

  3. Contributions • We developed a direct solution to 3D reconstruction from single images which is model based • No model-to-image projection and readjustment procedure • We made it possible to perform accurate 3D measurement using an uncalibrated* camera based on single images only • We quantitatively evaluated our model-based approach with vanishing point based method, and the results indicate our approach is better than vanishing point based method * Intrinsic parameters known/estimated

  4. Three vanishing points Vanishing Points (VPs) Based Method • Determine three orthogonal vanishing points • Manual detection • Search over Gaussian sphere • Hough transform • Projective geometry • Determine camera focal length and rotation • Determine camera translation and model dimensions

  5. Problems in VPs Based Method • Three orthogonal VPs may not be always available • One or two vanishing point only • Hard to accurately determine VPs • Need many lines • The accuracy of VPs affects the accuracy of the 3D reconstruction 1 Point Perspective 2 Points Perspective

  6. Methods with Ground Control Points/Lines • Point-based methods • Collinearity Equations • Line-based methods • Model-to-Image Fitting From Debevec et al.1996

  7. Z H 6 5 7 8 H Y 3 L W Z • X3, Y3 O 2 1 Y X X W 3 4 L The Idea • Use model to estimate camera exterior orientation • Need 6 parameters X3, Y3, L, W, H, • If an object-centered coordinate system selected • Need three parameters L, W, H • Divide camera parameters into two groups: rotation and translation • It’s possible to estimate relative camera exterior orientation without using GCPs and Vanishing Points

  8. Self-Calibration Recover camera rotation Initial estimate of camera rotation Refinement of camera rotation Determine camera translation and building dimensions Simultaneous estimates of camera translation and the first building dimensions Metric Reconstruction Roughly estimate the second building orientation Refine the second building orientation Determine the second building dimensions and location Overview of Our Approach

  9. Recover Camera Rotation • Initial estimate of camera rotation • Refinement of camera rotation Imaging Geometry Relationship

  10. Determine Camera Translation and the First Building Dimensions • Form objective function • Solve a constrained quadratic form minimization problem Imaging Geometry Relationship

  11. Y z x Camera Coordinate System Image edge 56{(x1, y1, -f), (x2, y2, -f)} C m (mx, my, mz ) 6 8 7 2 1 3 4 6 7 1 5 2 8 4 Building 1 Model edge67(v, u) 5 Building 2 Model edge 56 (v, u) 3( X3, Y3) Object Coordinate System Recover the Second Building Orientation • Assuming both buildings lie on the same ground plane • Initial estimate of the second building orientation • Refinement of the second building orientation t(X0,Y0,Z0) R 11 Imaging Geometry Relationship

  12. Y z x Camera Coordinate System Image edge 56{(x1, y1, -f), (x2, y2, -f)} C m (mx, my, mz ) 6 8 7 2 1 3 4 6 7 1 5 2 8 4 Building 1 Model edge67(v, u) 5 Building 2 Model edge 56 (v, u) 3( X3, Y3) Object Coordinate System Determine the Second Building Dimensions and Locations • Unknown parameters • Building dimensions L, W, H • Building locationX3, Y3 • Known parameters • Camera pose • Building orientation • Solution • Solve a set of linear equations t(X0,Y0,Z0) R 11 Imaging Geometry Relationship

  13. Using same error for two methods Additive random noise in endpoints of image segments Principle points offsets Impact on the outputs from two methods Camera pose Geometry of the reconstructed buildings Topology of the reconstructed buildings Comparison with VP based Methods Using Identical Simulation Data

  14. Random Errors in Image Segments

  15. Principle Point Offsets

  16. Digital Camera: Canon PowerShot SD750 Image size (3072x 2304 pixels) Comparison Using Identical Real Data Image 1: Two boxes Image 2: Burnside Hall, McGill university

  17. Results from the Image 1

  18. Results from the Image 2 Visualization of the recovered camera pose and building 3D model of Burnside Hall in Google Earth

  19. Interactive solution to metric reconstruction from single images Model-based approach but without model-to-image projection and readjustment procedure better than vanishing point based methods Using an off-the-shelf camera, taking a picture, one can get object dimensions Conclusions

  20. Thank You!

  21. Experimental Design • Camera Parameters • Building Parameters

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