Author: Clipp
Year: 2008
- pose estimation with scale with non overlapping FoV setups
- assumption: 5 temporal correspondences in cam + 1 corespondence in any additional camera
- Derive the expression of the scale using a single point correspondence
$x \leftrightarrow x'$ : $$ \lambda = -\frac{x'^TAx}{x'^TBx} $$ - Geometrical explanation: the view of a 3D point seen from the first camera crosses a plane made by the different
$C_2(\lambda)$ and the ray of$x'$ noted$v'$ . The$v'$ that points to this intersection point fixes the scale - Critical configurations:
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$v$ ,$v'$ and$C_2'(\lambda)$ can't be coplanar - Far away points (
$\pi$ and$v$ are parrallel) - The axis of rotation is perpendicular to the plane made by
$C_2, C_1'$ and$C_1$
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- Check for critical configurations: double the scale and check if there is still a big fraction of inliers
- 5pt algorithm + RANSAC + Chirality check to estimate motion up to scale
- One point RANSAC + pbM estimator to recover scale
- Inlier correspondences on the second camera are determined using the distance to epipolar lines
- then a linear least square calculation of the scale factor is made with inlier correspondences
- Then a bundle adjustement of the full multi camera system is performed
- simulations experiments with randomly generated points in a cube
- real experiments using 8 cameras
- Only the scale degrades when the motion becomes ambiguous