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3D Reconstruction from a Pair of Images. Srikumar Ramalingam Department of Computer Science University of California, Santa Cruz [email protected] Overview. Problem Definition Previous Work Solution Experiments and Results Conclusion and Future work.

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3d reconstruction from a pair of images l.jpg
3D Reconstruction from a Pair of Images

Srikumar Ramalingam

Department of Computer Science

University of California, Santa Cruz

[email protected]

Overview l.jpg

  • Problem Definition

  • Previous Work

  • Solution

  • Experiments and Results

  • Conclusion and Future work

Problem definition l.jpg
Problem Definition

3D Texture-Mapped Model



Perspective View of the Model

Previous work l.jpg
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.

Previous work5 l.jpg
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.

Solution l.jpg

  • Feature Detection

  • Getting Initial Set of Matches

  • Medium Robust Correspondence

  • Strong Robust Correspondence

  • Camera Calibration

  • 3D Reconstruction

Robust 1 1 correspondence l.jpg
Robust 1-1 Correspondence

  • Medium Robust Matches

    • Relaxation Techniques

-Strong Robust Matches

-Epipolar Geometry

Relaxation strategies l.jpg
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

Strong robust estimation using epipolar geometry l.jpg
Strong Robust Estimation using Epipolar Geometry

  • Epipolar Geometry and Constraint

  • Least Median of Squares

Epipolar geometry l.jpg
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

Least median of squares removal of outliers l.jpg
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.

3d reconstruction problem is solved for conventional baseline stereo system l.jpg
3D Reconstruction Problem is solved for Conventional Baseline Stereo System

X = b (xl+xr) / (2d)

Y = b (yl+yr) / (2d)

Z = bf / d

Intrinsic and extrinsic parameters l.jpg
Intrinsic and Extrinsic Parameters Baseline Stereo System

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

3d reconstruction triangulation l.jpg
3D Reconstruction- Triangulation Baseline Stereo System

Robust Correspondence + Intrinsic Parameters  Extrinsic Parameters

Robust Correspondence + Camera Parameters - 3D Points

Camera Matrix

Extrinsic Parameters

Reconstructed 3d model l.jpg
Reconstructed 3D Model Baseline Stereo System

Implementaton pipeline l.jpg
Implementaton Pipeline Baseline Stereo System

  • 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)

Standard data sets corner marked l.jpg
Standard Data Sets- Corner marked Baseline Stereo System

Robust 1 1 correspondence shown l.jpg
Robust 1-1 Correspondence shown Baseline Stereo System

3d delaunay triangulation l.jpg
3D Delaunay Triangulation Baseline Stereo System

Real data sets and results l.jpg
Real Data Sets and Results Baseline Stereo System

Baskin Engineering Parking Scene – Two Images

Robust set of matches l.jpg
Robust Set of Matches Baseline Stereo System

Color coding for z coordinates after 3d reconstruction29 l.jpg
Color Coding for Z Coordinates after 3D Reconstruction Baseline Stereo System

Red-Max, Green – Intermediate, Blue – Min depths

3d delaunay triangulation30 l.jpg
3D Delaunay Triangulation Baseline Stereo System

Texture mapped 3d model of the scene l.jpg
Texture Mapped 3D Model of the Scene Baseline Stereo System

Perspective View of the Texture Mapped 3D Model

Camera calibration experiment l.jpg
Camera Calibration Experiment Baseline Stereo System

  • -Checker pattern

  • -3 images taken in different orientations

  • Corners are marked

  • Computation of camera parameters

Conclusion and future work l.jpg
Conclusion and Future Work Baseline Stereo System

  • Increasing the number of feature points

    • Multiple Images

    • Alternate Algorithms

  • 3D Reconstruction of Urban Scenes (Faugeras 1995)

  • - Registration within GIS Data

  • Questions l.jpg
    Questions? Baseline Stereo System