Abstract
To reconstruct point geometry from multiple images, computation of the fundamental matrix is always necessary. With a new optimization criterion, i.e., the re-projective 3D metric geometric distance rather than projective space under RANSAC (Random Sample And Consensus) framework, our method can reveal the quality of the fundamental matrix visually through 3D reconstruction. The geometric distance is the projection error of 3D points to the corresponding image pixel coordinates in metric space. The reasonable visual figures of the reconstructed scenes are shown but only some numerical result were compared, as is standard practice. This criterion can lead to a better 3D reconstruction result especially in 3D metric space. Our experiments validate our new error criterion and the quality of fundamental matrix under the new criterion.
Highlights
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The initial F of the one images pair is computed by the eight-point method as described in Section 3.1 in the RANSAC framework based on the traditional distance from [u, u0 ] to epipolar line
In order to measure the precision of reconstruction in metric space, we add some noise into matching features’ position and reconstruct the scene Simu to compare the distance between the points with the ground-truth distance simulated out
Summary
F to reconstruct the two-view stereo, sometimes the reconstructed 3D scene was abnormal and occasionally kind of projective This means the average distance to epipolar lines is not the only, nor very robust, criteria to decide the fundamental matrix. A fundamental matrix with very small average distance to epipolar lines sometimes led to very poor 3D reconstruction results, such as two-view reconstruction based on F. This problem is critical in affine and projective reconstruction in which there is no meaningful metric information about the object space.
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