Fast and Accurate Camera Covariance Computation for Large 3D Reconstruction

Abstract

Estimating uncertainty of camera parameters computed in Structure from Motion (SfM) is an important tool for evaluating the quality of the reconstruction and guiding the reconstruction process. Yet, the quality of the estimated parameters of large reconstructions has been rarely evaluated due to the computational challenges. We present a new algorithm which employs the sparsity of the uncertainty propagation and speeds the computation up about ten times w.r.t. previous approaches. Our computation is accurate and does not use any approximations. We can compute uncertainties of thousands of cameras in tens of seconds on a standard PC. We also demonstrate that our approach can be effectively used for reconstructions of any size by applying it to smaller sub-reconstructions.

Uncertainty Based Camera Model Selection

“…Let us denote the Moore-Penrose (MP) inversion by + . The largest eigenvalue λ max (Σ A is challenging [33]. Therefore, we use the relationship of Σ A to overcome this problem.…”

“…Run-time experiments were performed on a single computer with the AMD Ryzen 7 1700X processor. We used COLMAP [39] to compute the SfM models and USfM [33] for computing the Jacobians J…”

“…The model classifier dependence on the number of images is shown in Table 3. The accuracy is naturally growing with an increasing number of observations [33] and the differences between camera models become more obvious, see Fig. 5.…”

Uncertainty Analysis of 3D Line Reconstruction in a New Minimal Spatial Line Representation

“…Depth uncertainty of point reconstruction has been well-studied [25][26][27][28][29]. Recently, [30] proposed an efficient algorithm for uncertainty propagation which works with large scale 3D reconstruction. In comparison, the research on the uncertainty of line reconstruction is much less.…”

“…Firstly, the camera poses and sparse point reconstruction is computed by COLMAP [45,46], a general-purpose Structure-from-Motion (SfM) and Multi-View Stereo (MVS) pipeline with a graphical and command-line interface. Secondly, camera covariance matrixes are estimated by the method proposed in [30]. Then, a 3D line map is generated and the associated uncertainty is estimated by the proposed uncertainty fusion method.…”