Beyond Gr\"obner Bases: Basis Selection for Minimal Solvers

Many computer vision applications require robust estimation of the underlying geometry, in terms of camera motion and 3D structure of the scene. These robust methods often rely on running minimal solvers in a RANSAC framework. In this paper we show how we can make polynomial solvers based on the action matrix method faster, by careful selection of the monomial bases. These monomial bases have traditionally been based on a Gr\"obner basis for the polynomial ideal. Here we describe how we can enumerate all such bases in an efficient way. We also show that going beyond Gr\"obner bases leads to more efficient solvers in many cases. We present a novel basis sampling scheme that we evaluate on a number of problems

A clever elimination strategy for efficient minimal solvers

We present a new insight into the systematic generation of minimal solvers in computer vision, which leads to smaller and faster solvers. Many minimal problem formulations are coupled sets of linear and polynomial equations where image measurements enter the linear equations only. We show that it is useful to solve such systems by first eliminating all the unknowns that do not appear in the linear equations and then extending solutions to the rest of unknowns. This can be generalized to fully non-linear systems by linearization via lifting. We demonstrate that this approach leads to more efficient solvers in three problems of partially calibrated relative camera pose computation with unknown focal length and/or radial distortion. Our approach also generates new interesting constraints on the fundamental matrices of partially calibrated cameras, which were not known before.Comment: 13 pages, 7 figure

Infrastructure-based Multi-Camera Calibration using Radial Projections

Multi-camera systems are an important sensor platform for intelligent systems such as self-driving cars. Pattern-based calibration techniques can be used to calibrate the intrinsics of the cameras individually. However, extrinsic calibration of systems with little to no visual overlap between the cameras is a challenge. Given the camera intrinsics, infrastucture-based calibration techniques are able to estimate the extrinsics using 3D maps pre-built via SLAM or Structure-from-Motion. In this paper, we propose to fully calibrate a multi-camera system from scratch using an infrastructure-based approach. Assuming that the distortion is mainly radial, we introduce a two-stage approach. We first estimate the camera-rig extrinsics up to a single unknown translation component per camera. Next, we solve for both the intrinsic parameters and the missing translation components. Extensive experiments on multiple indoor and outdoor scenes with multiple multi-camera systems show that our calibration method achieves high accuracy and robustness. In particular, our approach is more robust than the naive approach of first estimating intrinsic parameters and pose per camera before refining the extrinsic parameters of the system. The implementation is available at https://github.com/youkely/InfrasCal.Comment: ECCV 202

MLPnP - A Real-Time Maximum Likelihood Solution to the Perspective-n-Point Problem

In this paper, a statistically optimal solution to the Perspective-n-Point (PnP) problem is presented. Many solutions to the PnP problem are geometrically optimal, but do not consider the uncertainties of the observations. In addition, it would be desirable to have an internal estimation of the accuracy of the estimated rotation and translation parameters of the camera pose. Thus, we propose a novel maximum likelihood solution to the PnP problem, that incorporates image observation uncertainties and remains real-time capable at the same time. Further, the presented method is general, as is works with 3D direction vectors instead of 2D image points and is thus able to cope with arbitrary central camera models. This is achieved by projecting (and thus reducing) the covariance matrices of the observations to the corresponding vector tangent space.Comment: Submitted to the ISPRS congress (2016) in Prague. Oral Presentation. Published in ISPRS Ann. Photogramm. Remote Sens. Spatial Inf. Sci., III-3, 131-13

Trust Your IMU: Consequences of Ignoring the IMU Drift

In this paper, we argue that modern pre-integration methods for inertial measurement units (IMUs) are accurate enough to ignore the drift for short time intervals. This allows us to consider a simplified camera model, which in turn admits further intrinsic calibration. We develop the first-ever solver to jointly solve the relative pose problem with unknown and equal focal length and radial distortion profile while utilizing the IMU data. Furthermore, we show significant speed-up compared to state-of-the-art algorithms, with small or negligible loss in accuracy for partially calibrated setups. The proposed algorithms are tested on both synthetic and real data, where the latter is focused on navigation using unmanned aerial vehicles (UAVs). We evaluate the proposed solvers on different commercially available low-cost UAVs, and demonstrate that the novel assumption on IMU drift is feasible in real-life applications. The extended intrinsic auto-calibration enables us to use distorted input images, making tedious calibration processes obsolete, compared to current state-of-the-art methods

Calibrated and Partially Calibrated Semi-Generalized Homographies

In this paper, we propose the first minimal solutions for estimating the semi-generalized homography given a perspective and a generalized camera. The proposed solvers use five 2D-2D image point correspondences induced by a scene plane. One of them assumes the perspective camera to be fully calibrated, while the other solver estimates the unknown focal length together with the absolute pose parameters. This setup is particularly important in structure-from-motion and image-based localization pipelines, where a new camera is localized in each step with respect to a set of known cameras and 2D-3D correspondences might not be available. As a consequence of a clever parametrization and the elimination ideal method, our approach only needs to solve a univariate polynomial of degree five or three. The proposed solvers are stable and efficient as demonstrated by a number of synthetic and real-world experiments

Hybrid Focal Stereo Networks for Pattern Analysis in Homogeneous Scenes

In this paper we address the problem of multiple camera calibration in the presence of a homogeneous scene, and without the possibility of employing calibration object based methods. The proposed solution exploits salient features present in a larger field of view, but instead of employing active vision we replace the cameras with stereo rigs featuring a long focal analysis camera, as well as a short focal registration camera. Thus, we are able to propose an accurate solution which does not require intrinsic variation models as in the case of zooming cameras. Moreover, the availability of the two views simultaneously in each rig allows for pose re-estimation between rigs as often as necessary. The algorithm has been successfully validated in an indoor setting, as well as on a difficult scene featuring a highly dense pilgrim crowd in Makkah.Comment: 13 pages, 6 figures, submitted to Machine Vision and Application