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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

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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

Overview

  • Problem Definition

  • Previous Work

  • Solution

  • Experiments and Results

  • Conclusion and Future work


Problem definition l.jpg

Problem Definition

3D Texture-Mapped Model

Image-1

Image-2

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

Solution

  • Feature Detection

  • Getting Initial Set of Matches

  • Medium Robust Correspondence

  • Strong Robust Correspondence

  • Camera Calibration

  • 3D Reconstruction


Feature detection harris corner detection l.jpg

Feature Detection : Harris Corner Detection


Establishing initial set of matches l.jpg

Establishing Initial Set of Matches


Ambiguities in the matches l.jpg

Ambiguities in the Matches


Robust 1 1 correspondence l.jpg

Robust 1-1 Correspondence

  • Medium Robust Matches

    • Relaxation Techniques

-Strong Robust Matches

-Epipolar Geometry


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Relaxation Techniques


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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


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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


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Intrinsic and Extrinsic Parameters

Intrinsic Parameters(5)Extrinsic Parameters (6)

f – focal length3 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


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3D Reconstruction- Triangulation

Robust Correspondence + Intrinsic Parameters  Extrinsic Parameters

Robust Correspondence + Camera Parameters - 3D Points

Camera Matrix

Extrinsic Parameters


Reconstructed 3d model l.jpg

Reconstructed 3D Model


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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)


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Standard Data Sets- Corner marked


Robust 1 1 correspondence shown l.jpg

Robust 1-1 Correspondence shown


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Color Coding for Z Coordinates after 3D Reconstruction


3d delaunay triangulation l.jpg

3D Delaunay Triangulation


Slide25 l.jpg

3D Texture Mapped Model – On Rotation


Real data sets and results l.jpg

Real Data Sets and Results

Baskin Engineering Parking Scene – Two Images


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Feature Points using Corner Detection process


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Robust Set of Matches


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Color Coding for Z Coordinates after 3D Reconstruction

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


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3D Delaunay Triangulation


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Texture Mapped 3D Model of the Scene

Perspective View of the Texture Mapped 3D Model


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Camera Calibration Experiment

  • -Checker pattern

  • -3 images taken in different orientations

  • Corners are marked

  • Computation of camera parameters


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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


  • Questions l.jpg

    Questions?


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