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3D Reconstruction from a Pair of Images

3D Reconstruction from a Pair of Images. Srikumar Ramalingam Department of Computer Science University of California, Santa Cruz srikumar@cse.ucsc.edu. Overview. Problem Definition Previous Work Solution Experiments and Results Conclusion and Future work.

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3D Reconstruction from a Pair of Images

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  1. 3D Reconstruction from a Pair of Images Srikumar Ramalingam Department of Computer Science University of California, Santa Cruz srikumar@cse.ucsc.edu

  2. Overview • Problem Definition • Previous Work • Solution • Experiments and Results • Conclusion and Future work

  3. Problem Definition 3D Texture-Mapped Model Image-1 Image-2 Perspective View of the Model

  4. Previous Work • Zhao, Aggarwal, Mandal and Vemuri, “3D Shape Reconstruction from Multiple Views ”, Handbook of Image and Video Processing, pages 243-257, Al Bovik, 2000. • Gang Xu and Zhengyou Zhang, “Epipolar Geometry in Stereo, Motion and Object Recognition”, Kluwer Academic Publishers, 1996. • Zhang and Faugeras, “3D Dyanamic Scene Analysis-A Stereo Based Approach”, Springer-Verlag, 1992. • Zhang, Deriche, Faugeras and Luong, “A Robust Technique for Matching Two Uncalibrated Images through the Recovery of the Unknown Epipolar Geometry”, INRIA Research Report, 1994. • Zhang, “A New Multistage Approach to Motion and Structure Estimation: From Essential Parameters to Euclidean Motion Via Fundamental Matrix”, INRIA Research Report, 1996.

  5. Previous Work • Zhang, “Determining the Epipolar Geometry and its Uncertainity: A Review”, INRIA Research Report, July 1996. • Zhang, “A Flexible New Technique for Camera Calibration”, Technical Report, Microsoft Research, 1998. • Deriche and Giraudon, “A Computational Approach for Corner and Vertex Detection”, INRIA Research Report, 1992.

  6. Solution • Feature Detection • Getting Initial Set of Matches • Medium Robust Correspondence • Strong Robust Correspondence • Camera Calibration • 3D Reconstruction

  7. Feature Detection : Harris Corner Detection

  8. Establishing Initial Set of Matches

  9. Ambiguities in the Matches

  10. Robust 1-1 Correspondence • Medium Robust Matches • Relaxation Techniques -Strong Robust Matches -Epipolar Geometry

  11. Relaxation Techniques

  12. Relaxation Strategies - Winner-take-all - Loser-take-nothing - Some-winners-take-all - ( 1 – Max_Strength / Sec_Max_St) End Result : No Ambiguities but False Matches

  13. Strong Robust Estimation using Epipolar Geometry • Epipolar Geometry and Constraint • Least Median of Squares

  14. Epipolar Geometry Point corresponding to m lies on its epipolar line lm on the other image Fundamental Matrix (F) –3x3 matrix, which relates the corresponding points

  15. Least Median of Squares – Removal of Outliers • - 8 Matches required for estimating F matrix • Different combinations (m) of 8 matches selected • Least median of squares algorithm is applied If ri < Threshold, the match is discarded.

  16. 3D Reconstruction Problem is solved for Conventional Baseline Stereo System X = b (xl+xr) / (2d) Y = b (yl+yr) / (2d) Z = bf / d

  17. Intrinsic and Extrinsic Parameters Intrinsic Parameters (5) Extrinsic Parameters (6) f – focal length 3 rotational parameters, 3 translational parameters u0, v0 – Center Intrinsic Matrix(A) ku - unit length along x direction kv – unit length along y direction Angle between x and y direction mnew(u,v)= A mold(x,y) Need to conduct an experiment to calibrate the camera

  18. 3D Reconstruction- Triangulation Robust Correspondence + Intrinsic Parameters  Extrinsic Parameters Robust Correspondence + Camera Parameters - 3D Points Camera Matrix Extrinsic Parameters

  19. Reconstructed 3D Model

  20. Implementaton Pipeline • Matlab Implementations • Harris Corner Detection Algorithm (Deriche1992, Zhang1994) • Initial Set of Matches Establishment (Zhang1994, Xu1996) • Medium Set of Matches using Relaxation Techniques (Zhang1994, Xu1996) • Strong Set of Matches using Epipolar Geometry (Zhang1994, Xu1996) • -Camera Calibration Experiment (Zhang1998) • -3D Points Reconstruction from Robust Matches and Camera Parameters (Zhang1994, Zhang1996, Xu1996) • -3D Polygonal Model Reconstruction (Delaunay Triangulation) • - Texture Mapping (OpenGL/C)

  21. Standard Data Sets- Corner marked

  22. Robust 1-1 Correspondence shown

  23. Color Coding for Z Coordinates after 3D Reconstruction

  24. 3D Delaunay Triangulation

  25. 3D Texture Mapped Model – On Rotation

  26. Real Data Sets and Results Baskin Engineering Parking Scene – Two Images

  27. Feature Points using Corner Detection process

  28. Robust Set of Matches

  29. Color Coding for Z Coordinates after 3D Reconstruction Red-Max, Green – Intermediate, Blue – Min depths

  30. 3D Delaunay Triangulation

  31. Texture Mapped 3D Model of the Scene Perspective View of the Texture Mapped 3D Model

  32. Camera Calibration Experiment • -Checker pattern • -3 images taken in different orientations • Corners are marked • Computation of camera parameters

  33. Conclusion and Future Work • Increasing the number of feature points • Multiple Images • Alternate Algorithms • 3D Reconstruction of Urban Scenes (Faugeras 1995) • - Registration within GIS Data

  34. Questions?

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