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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

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


Problem Definition

3D Texture-Mapped Model

Image-1

Image-2

Perspective View of the Model


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 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

  • Feature Detection

  • Getting Initial Set of Matches

  • Medium Robust Correspondence

  • Strong Robust Correspondence

  • Camera Calibration

  • 3D Reconstruction


Feature Detection : Harris Corner Detection


Establishing Initial Set of Matches


Ambiguities in the Matches


Robust 1-1 Correspondence

  • Medium Robust Matches

    • Relaxation Techniques

-Strong Robust Matches

-Epipolar Geometry


Relaxation Techniques


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

  • Epipolar Geometry and Constraint

  • Least Median of Squares


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

  • - 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

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

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

Z = bf / d


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


3D Reconstruction- Triangulation

Robust Correspondence + Intrinsic Parameters  Extrinsic Parameters

Robust Correspondence + Camera Parameters - 3D Points

Camera Matrix

Extrinsic Parameters


Reconstructed 3D Model


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)


Standard Data Sets- Corner marked


Robust 1-1 Correspondence shown


Color Coding for Z Coordinates after 3D Reconstruction


3D Delaunay Triangulation


3D Texture Mapped Model – On Rotation


Real Data Sets and Results

Baskin Engineering Parking Scene – Two Images


Feature Points using Corner Detection process


Robust Set of Matches


Color Coding for Z Coordinates after 3D Reconstruction

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


3D Delaunay Triangulation


Texture Mapped 3D Model of the Scene

Perspective View of the Texture Mapped 3D Model


Camera Calibration Experiment

  • -Checker pattern

  • -3 images taken in different orientations

  • Corners are marked

  • Computation of camera parameters


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?


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