Camera Uncertainty Computation in Large 3D Reconstruction

Fast and Accurate Camera Covariance Computation for Large 3D Reconstruction

“…We present the first algorithm for uncertainty propagation from input feature points to camera parameters that works without any approximation of the natural form of the covariance matrix on thousands of cameras. It is about ten times faster than the state of the art algorithms [19], [26]. Our approach builds on top of Gauss-Markov estimation with constraints by Rao [29].…”

“…Our algorithm is faster, more accurate and more stable than any previous method [19], [26], [27]. The output of our work is publicly available as source code which can be used as an external library in nonlinear optimization pipelines, like Ceres Solver [2] and reconstruction pipelines like [23], [30], [32].…”

“…The uncertainty propagation is a well known process [9], [13], [18], [26]. Our goal is to propagate the uncertainties of input measurements, i.e.…”

“…However, it is not clear if the decomposition of Fisher information matrix holds for M-P inversion without fulfilling the rank additivity condition [33] and it was shown in [26] that approach [19] is not always accurate enough. Polic et al [26] evaluated the state of the art solutions against more accurate results computed in high precision arithmetics, i.e. using 100 digits instead of 15 significant digits of double precision.…”

“…Datasets 1 and 3 are synthetic, 2, 9 from COLMAP [30], and 4-8 from Bundler [31] # Dataset NP NX Nu Compared algorithms are listed in Table 2. The standard way of computing the covariance matrix ΣP is by using the M-P inversion of the information matrix using the Singular Value Decomposition (SVD) with the last seven singular values set to zeros and inverting the rest of them as in [26]. There are many implementations of this procedure that differ in numerical stability and speed.…”