Wolfgang Förstner

Daniel Barath, Dmytro Mishkin, Michal Polic et al.

We present a large-scale dataset of Planes in 3D, Pi3D, of roughly 1000 planes observed in 10 000 images from the 1DSfM dataset, and HEB, a large-scale homography estimation benchmark leveraging Pi3D. The applications of the Pi3D dataset are diverse, e.g. training or evaluating monocular depth, surface normal estimation and image matching algorithms. The HEB dataset consists of 226 260 homographies and includes roughly 4M correspondences. The homographies link images that often undergo significant viewpoint and illumination changes. As applications of HEB, we perform a rigorous evaluation of a wide range of robust estimators and deep learning-based correspondence filtering methods, establishing the current state-of-the-art in robust homography estimation. We also evaluate the uncertainty of the SIFT orientations and scales w.r.t. the ground truth coming from the underlying homographies and provide codes for comparing uncertainty of custom detectors. The dataset is available at \url{https://github.com/danini/homography-benchmark}.

Daniel Barath, Michal Polic, Wolfgang Förstner et al.

Local features e.g. SIFT and its affine and learned variants provide region-to-region rather than point-to-point correspondences. This has recently been exploited to create new minimal solvers for classical problems such as homography, essential and fundamental matrix estimation. The main advantage of such solvers is that their sample size is smaller, e.g., only two instead of four matches are required to estimate a homography. Works proposing such solvers often claim a significant improvement in run-time thanks to fewer RANSAC iterations. We show that this argument is not valid in practice if the solvers are used naively. To overcome this, we propose guidelines for effective use of region-to-region matches in the course of a full model estimation pipeline. We propose a method for refining the local feature geometries by symmetric intensity-based matching, combine uncertainty propagation inside RANSAC with preemptive model verification, show a general scheme for computing uncertainty of minimal solvers results, and adapt the sample cheirality check for homography estimation. Our experiments show that affine solvers can achieve accuracy comparable to point-based solvers at faster run-times when following our guidelines. We make code available at https://github.com/danini/affine-correspondences-for-camera-geometry.

Michal Polic, Wolfgang Förstner, Tomas Pajdla

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 \wrt 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.