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visu_uncertainty_ba.md

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Visualizing Spectral Bundle Adjustment Uncertainty

Author: Wilson

Year: 2022

Notes:

  • Study eigen vector of covariance matrices of a BA = tangent space perturbation of the model
  • Camera uncertainty computation in large 3D reconstruction seems interesting
  • Fast and accurate camera covariance computation for large 3D reconstructions. seems even better
  • Discussion about $\Sigma_m$ (covariance of measurement), they choose $\Sigma_m = Diag(r(x))$
  • Apply Schur Complement to get rid of 3D points parameters
  • Discuss about defining a norm in $\mathfrak{se}(3)$ that is not trivial, normalize the error in translation and in rotation using the average error in translation and rotation (important to have a good visualization, this is not an issue for us)
  • To avoid the inversion of the information matrix, they seek for the smallest eigenvectors of it (that should be the biggest of the cov)
  • Vibrate each node (I don't understand this)
  • This eigen value analysis doesn't allow to compare the accuracy of reconstructions