We address the problem of estimating both translational and angular velocity of a camera from asynchronous point tracks, a formulation relevant to rolling shutter and event cameras. Since the original problem is non-polynomial, we propose a polynomial approximation, classify the resulting minimal problems, and determine their algebraic degrees. Furthermore, we develop minimal solvers for several problems with low degrees and evaluate them on synthetic and real datasets. The code is publicly available.

We propose a novel approach for estimating the relative pose between rolling shutter cameras using the intersections of line projections with a single scanline per image. This allows pose estimation without explicitly modeling camera motion. Alternatively, scanlines can be selected within a single image, enabling single-view relative pose estimation for scanlines of rolling shutter cameras. Our approach is designed as a foundational building block for rolling shutter structure-from-motion (SfM), where no motion model is required, and each scanline's pose can be computed independently. % We classify minimal solvers for this problem in both generic and specialized settings, including cases with parallel lines and known gravity direction, assuming known intrinsics and no lens distortion. Furthermore, we develop minimal solvers for the parallel-lines scenario, both with and without gravity priors, by leveraging connections between this problem and the estimation of 2D structure from 1D cameras. % Experiments on rolling shutter images from the Fastec dataset demonstrate the feasibility of our approach for initializing rolling shutter SfM, highlighting its potential for further development. % The code will be made publicly available.

We propose an approach for estimating the relative pose between calibrated image pairs by jointly exploiting points, lines, and their coincidences in a hybrid manner. We investigate all possible configurations where these data modalities can be used together and review the minimal solvers available in the literature. Our hybrid framework combines the advantages of all configurations, enabling robust and accurate estimation in challenging environments. In addition, we design a method for jointly estimating multiple vanishing point correspondences in two images, and a bundle adjustment that considers all relevant data modalities. Experiments on various indoor and outdoor datasets show that our approach outperforms point-based methods, improving AUC@ 10° by 1-7 points while running at comparable speeds. The source code of the solvers and hybrid framework will be made public.

We revisit certain problems of pose estimation based on 3D-2D correspondences between features which may be points or lines. Specifically, we address the two previously-studied minimal problems of estimating camera extrinsics from$p\in\{1,2\}$point-point correspondences and$l=3-p$line-line correspondences. To the best of our knowledge, all of the previously-known practical solutions to these problems required computing the roots of degree$\geq 4$(univariate) polynomials when$p=2$, or degree$\geq 8$polynomials when$p=1$. We describe and implement two elementary solutions which reduce the degrees of the needed polynomials from 4 to 2 and from 8 to 4, respectively. We show experimentally that the resulting solvers are numerically stable and fast: when compared to the previous state-of-the art, we may obtain nearly an order of magnitude speedup. The code is available at https://github.com/petrhruby97/efficient_absolute

We present novel solutions to previously unsolved prob-lems of relative pose estimation from images whose calibration parameters, namely focal lengths and radial distortion, are unknown. Our approach enables metric reconstruction without modeling these parameters. The minimal case for reconstruction requires 13 points in 4 views for both the calibrated and uncalibrated cameras. We describe and implement the first solution to these minimal problems. In the calibrated case, this may be modeled as a polynomial sys-tem of equations with 3584 solutions. Despite the apparent intractability, the problem decomposes spectacularly. Each solution falls into a Euclidean symmetry class of size 16, and we can estimate 224 class representatives by solving a sequence of three subproblems with 28, 2, and 4 solutions. We highlight the relationship between internal constraints on the radial quadrifocal tensor and the relations among the principal minors of a$4\times 4$matrix. We also address the case of 4 upright cameras, where 7 points are minimal. Finally, we evaluate our approach on simulated and real data and benchmark against previous calibration-free solutions, and show that our method provides an efficient startup for an SfM pipeline with radial cameras.

We tackle the problem of estimating a Manhattan frame, i.e. three orthogonal vanishing points, and the unknown focal length of the camera, leveraging a prior vertical direction. The direction can come from an Inertial Measurement Unit that is a standard component of recent consumer devices, e.g., smartphones. We provide an exhaustive analysis of minimal line configurations and derive two new 2-line solvers, one of which does not suffer from singularities affecting existing solvers. Additionally, we design a new non-minimal method, running on an arbitrary number of lines, to boost the performance in local optimization. Combining all solvers in a hybrid robust estimator, our method achieves increased accuracy even with a rough prior. Experiments on synthetic and real-world datasets demonstrate the superior accuracy of our method compared to the state of the art, while having comparable runtimes. We further demonstrate the applicability of our solvers for relative rotation estimation. The code is available at https://github.com/cvg/VP-Estimation-with-Prior-Gravity.

We present an approach to solving hard geometric optimization problems in the RANSAC framework. The hard minimal problems arise from relaxing the original geometric optimization problem into a minimal problem with many spurious solutions. Our approach avoids computing large numbers of spurious solutions. We design a learning strategy for selecting a starting problem-solution pair that can be numerically continued to the problem and the solution of interest. We demonstrate our approach by developing a RANSAC solver for the problem of computing the relative pose of three calibrated cameras, via a minimal relaxation using four points in each view. On average, we can solve a single problem in under 70$\mu s.$μs. We also benchmark and study our engineering choices on the very familiar problem of computing the relative pose of two calibrated cameras, via the minimal case of five points in two views.