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Projective 3D-reconstruction from Perspective Images with Occlusions and Outliers

Daniel Martinec

Why is the task important?

  • Perspective projection, occlusions and outliers are often present.
  • Many images are often available -> a technique treating all data uniformly is needed.

Our solution

  • It can be used on both wide base-line stereo and sequences.
  • It has automatical outlier detection.
  • It is based on a factorization method -> linear solution is computed fast; subsequent non-linear bundle adjustment is optional.
  • Outliers are rejected using a simplified RANSAC technique. Significant speed-up is achieved using reconstructions from partial data.
  • Notation: x_p^i … outlier,  \times … occlusion, \lambda_p^i … projective depth ( \lambda_p^i x_p^i = p^i X_p )

        \[ \begin{bmatrix} \lambda_1^1 x_1^1 & \lambda_2^1 x_2^1 & \cdots & \lambda_n^1 x_n^1 \\ \times & \lambda_2^2 x_2^2 &  & \times \\ \vdots  &   & \ddots & \vdots  \\ \lambda_1^m x_1^m & \times & \cdots & \lambda_n^m x_n^m \end{bmatrix} = \begin{bmatrix} p^1  \\ p^2  \\ \vdots \\ p^m \end{bmatrix} \begin{bmatrix} X_1  & X_2  & \dots  & X_n \end{bmatrix} \]

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Results

House Dinosaur (Oxford) Temple (Leuven) Castle (Leuven) Valbonne (Oxford)
10 images of
203 points
36 images of
4983 points
5 images of
696 points
22 images of
1822 points
14 images of
376 points
[2952×2003] [720×576] [867×591] [768×576] [768×512]
manual detection Harris’ operator Harris’ operator Harris’ operator extremal regions
47.83 % occlusions 90.84 % occlusions 46.32 % occlusions 74.99 % occlusions 73.27 % occlusions
Mean errors [pxl]
With outliers
       linear method 1.76 0.49 41.97
       lin. method + bundle adj. 0.64 0.23 11.97
Outliers detected and removed corresp. in > 2 images
       linear method 3.91 0.57 0.37 0.65 0.50
       lin. method + bundle adj. 1.44 0.39 0.27 0.22 0.45

References

Presentation given at the Pattern Recognition and Computer Vision Colloquium, Summer 2002 [pdf]

Structure from many perspective images with occlusions. Daniel Martinec and Tomáš Pajdla. In Proceedings of the European Conference on Computer Vision (ECCV), pp. 355-369, Springer-Verlag, May 2002. [pdf], [poster]

Outlier Detection for Factorization-Based Reconstruction from Perspective Images with Occlusions. Daniel Martinec and Tomáš Pajdla. In Proceedings of the Photogrammetric Computer Vision (PCV), pp. 161-164, Inst. f. Computer Graphics and Vision, TU-Graz, September 2002. [pdf], [poster]

Automatic Factorization-Based Reconstruction from Perspective Images with Occlusions and Outliers. Daniel Martinec and Tomáš Pajdla. In Proceedings of the 8th Computer Vision Winter Workshop (CVWW), pp. 147-152, Czech Pattern Recognition Society, Prague, February 2003. [pdf]

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