We present a novel method to compute the relative pose of multi-camera systems using two affine correspondences (ACs). Existing solutions to the multi-camera relative pose estimation are either restricted to special cases of motion, have too high computational complexity, or require too many point correspondences (PCs). Thus, these solvers impede an efficient or accurate relative pose estimation when applying RANSAC as a robust estimator. This paper shows that the 6DOF relative pose estimation problem using ACs permits a feasible minimal solution, when exploiting the geometric constraints between ACs and multi-camera systems using a special parameterization. We present a problem formulation based on two ACs that encompass two common types of ACs across two views, i.e., inter-camera and intra-camera. Moreover, we exploit a unified and versatile framework for generating 6DOF solvers. Building upon this foundation, we use this framework to address two categories of practical scenarios. First, for the more challenging 7DOF relative pose estimation problem-where the scale transformation of multi-camera systems is unknown-we propose 7DOF solvers to compute the relative pose and scale using three ACs. Second, leveraging inertial measurement units (IMUs), we introduce several minimal solvers for constrained relative pose estimation problems. These include 5DOF solvers with known relative rotation angle, and 4DOF solver with known vertical direction. Experiments on both virtual and real multi-camera systems prove that the proposed solvers are more efficient than the state-of-the-art algorithms, while resulting in a better relative pose accuracy.

In recent years, affine correspondences (ACs) have emerged as widely adopted alternative to point correspondences (PCs) in geometric problems in computer vision. An AC is composed of a PC across two different views plus an affine transformation between the small patches around this PC. Prior studies have shown that a single affine correspondence (AC) generally yields three independent constraints for estimating relative pose. This work addresses relative pose estimation in multi-perspective camera systems, a relevant problem given their prevalence in modern technologies such as autonomous vehicles and augmented reality. More specifically, we introduce the first comprehensive suite of minimal solvers for 6DoF relative pose estimation across multiple cameras using only two ACs, which is notably valuable for robust model fitting scenarios. We analyze all possible configurations of two ACs in two views, and present minimal solvers covering all identified minimal cases. We make use of the hidden variable technique to eliminate the translation parameters, and represent rotation using either Cayley parameters or quaternions. We furthermore introduce novel constraints on the generalized relative pose problem that are beneficial in deriving more compact solvers with fewer solutions. Comprehensive experiments on synthetic and real-world data show that the proposed affine correspondence-based solvers are highly effective and computationally efficient.

Multi-camera systems offer rich observation capabilities for visual navigation and 3D scene reconstruction; however, the resulting feature redundancy often compromises computational efficiency. This challenge is particularly pronounced during bundle adjustment, where the non-linear optimization of both system poses and scene points incurs substantial computational overhead. To address this challenge, this paper introduces a pose-only geometric constraint for multi-camera systems and proposes a corresponding pose adjustment algorithm. Specifically, we use generalized camera model to establish a unified representation of the multi-camera system. Building upon this model, we formulate the multi-camera pose-only constraint, which implicitly represents a 3D scene point using two base observations and their associated poses, thereby achieving a pose-only representation of the projection geometry. Subsequently, we introduce a multi-camera pose adjustment algorithm that eliminates 3D points from the parameter space, thereby achieving efficient and focused pose optimization. Experimental results on both synthetic and real-world datasets demonstrate that the proposed algorithm outperforms baseline bundle adjustment methods in computational efficiency, while maintaining or even improving pose estimation accuracy.

Frame-based visual-inertial odometry (VIO) can be significantly enhanced by integrating event cameras, particularly in high-speed motion and high-dynamic-range (HDR) scenarios. However, existing VIO frameworks often process event and frame-based data simultaneously, introducing unnecessary computational overhead. Additionally, tracking handcrafted features on event streams typically requires extensive parameter tuning and lacks robustness against noise. To address these limitations, we propose Hybrid-EVIO, a method that effectively fuses event data, standard frames, and inertial measurement unit (IMU) measurements. Hybrid-EVIO consists of a hybrid visual front-end and a sliding-window-based back-end. The front-end combines traditional and learning-based techniques in a scene-adaptive manner: features are tracked using either conventional methods on frames or a learned sparse optical flow network on asynchronous events, depending on the imaging quality. IMU measurements are further utilized to construct epipolar constraints, prefiltering extreme outliers before Random Sample Consensus and thereby improving pose estimation accuracy. Finally, a tightly coupled, graph-based optimization framework integrates three sensor modalities for high-precision state estimation. We evaluate the proposed method on multiple representative and challenging public datasets. Our approach outperforms state-of-the-art methods, reducing trajectory errors by up to 34% in the best case. Our trajectories and evaluation code are publicly available at https://github.com/sssxxxkkkk/hybrid EVIO.

Accurate measurement of shock wave motion parameters with high spatiotemporal resolution is essential for applications such as power field testing and damage assessment. However, significant challenges are posed by the fast, uneven propagation of shock waves and unstable testing conditions. To address these challenges, a novel framework is proposed that utilizes multiple event cameras to estimate the asymmetry of shock waves, leveraging its high-speed and high-dynamic range capabilities. Initially, a polar coordinate system is established, which encodes events to reveal shock wave propagation patterns, with adaptive region-of-interest (ROI) extraction through event offset calculations. Subsequently, shock wave front events are extracted using iterative slope analysis, exploiting the continuity of velocity changes. Finally, the geometric model of events and shock wave motion parameters is derived according to event-based optical imaging model, along with the 3D reconstruction model. Through the above process, multi-angle shock wave measurement, motion field reconstruction, and explosive equivalence inversion are achieved. The results of the speed measurement are compared with those of the pressure sensors and the empirical formula, revealing a maximum error of 5.20% and a minimum error of 0.06%. The experimental results demonstrate that our method achieves high-precision measurement of the shock wave motion field with both high spatial and temporal resolution, representing significant progress.

Despite the rapid advancements in event-based motion estimation, current geometric methods primarily focus on velocity estimation. However, absolute pose estimation, which is equally crucial for key applications such as robotic navigation and augmented reality, remains relatively underexplored. Consequently, the simultaneous recovery of absolute pose and velocity from event streams remains an open and challenging problem. To address this gap, we propose a geometric framework for absolute pose and velocity estimation by leveraging 3D lines in the scene and the events they trigger. At the core of the framework lie two key geometric constraints: the orthogonality between a 3D line and the normal vector of its corresponding event plane, and the collinearity of an event with the 2D projection of its associated line. Based on these constraints, we present both linear and polynomial solvers for absolute pose estimation. The former enables efficient computation, while the latter provides a globally optimal solution for rotation. For velocity estimation, we develop an efficient linear solver and a more accurate optimization-based solver to recover both angular and linear velocities. Notably, our methods require a minimum of three event-line correspondences to determine the 6-DoF absolute pose or velocities independently. Extensive experiments in simulation and on real-world datasets demonstrate that our methods achieve state-of-the-art performance, with significant improvements in accuracy and computational efficiency compared to existing methods. The demo code is publicly available at https://github.com/Zibin6/EventPoseVelocity.

For event cameras, current sparse geometric solvers for egomotion estimation assume that the rotational displacements are known, such as those provided by an IMU. Thus, they can only recover the translational motion parameters. Recovering full-DoF motion parameters using a sparse geometric solver is a more challenging task, and has not yet been investigated. In this paper, we propose several solvers to estimate both rotational and translational velocities within a unified framework. Our method leverages event manifolds induced by line segments. The problem formulations are based on either an incidence relation for lines or a novel coplanarity relation for normal vectors. We demonstrate the possibility of recovering full-DoF egomotion parameters for both angular and linear velocities without requiring extra sensor measurements or motion priors. To achieve efficient optimization, we exploit the Adam framework with a first-order approximation of rotations for quick initialization. Experiments on both synthetic and real-world data demonstrate the effectiveness of our method. The code is available at https://github.com/jizhaox/relpose-event.

Affine correspondences have received significant attention due to their benefits in tasks like image matching and pose estimation. Existing methods for extracting affine correspondences still have many limitations in terms of performance; thus, exploring a new paradigm is crucial. In this paper, we present a new pipeline designed for extracting accurate affine correspondences by integrating dense matching and geometric constraints. Specifically, a novel extraction framework is introduced, with the aid of dense matching and a novel keypoint scale and orientation estimator. For this purpose, we propose loss functions based on geometric constraints, which can effectively improve accuracy by supervising neural networks to learn feature geometry. The experimental show that the accuracy and robustness of our method outperform the existing ones in image matching tasks. To further demonstrate the effectiveness of the proposed method, we applied it to relative pose estimation. Affine correspondences extracted by our method lead to more accurate poses than the baselines on a range of real-world datasets. The code is available at https://github.com/stilcrad/LearningACs.

6D pose confidence region estimation has emerged as a critical direction, aiming to perform uncertainty quantification for assessing the reliability of estimated poses. However, current sampling-based approach suffers from critical limitations that severely impede their practical deployment: 1) the sampling speed significantly decreases as the number of samples increases. 2) the derived confidence regions are often excessively large. To address these challenges, we propose a deterministic and efficient method for estimating pose confidence regions. Our approach uses inductive conformal prediction to calibrate the deterministically regressed Gaussian keypoint distributions into 2D keypoint confidence regions. We then leverage the implicit function theorem to propagate these keypoint confidence regions directly into 6D pose confidence regions. This method avoids the inefficiency and inflated region sizes associated with sampling and ensembling. It provides compact confidence regions that cover the ground-truth poses with a user-defined confidence level. Experimental results on the LineMOD Occlusion and SPEED datasets show that our method achieves higher pose estimation accuracy with reduced computational time. For the same coverage rate, our method yields significantly smaller confidence region volumes, reducing them by up to 99.9\% for rotations and 99.8\% for translations. The code will be available soon.

Relative pose estimation using point correspondences (PC) is a widely used technique. A minimal configuration of six PCs is required for two views of generalized cameras. In this paper, we present several minimal solvers that use six PCs to compute the 6DOF relative pose of multi-camera systems, including a minimal solver for the generalized camera and two minimal solvers for the practical configuration of two-camera rigs. The equation construction is based on the decoupling of rotation and translation. Rotation is represented by Cayley or quaternion parametrization, and translation can be eliminated by using the hidden variable technique. Ray bundle constraints are found and proven when a subset of PCs relate the same cameras across two views. This is the key to reducing the number of solutions and generating numerically stable solvers. Moreover, all configurations of six-point problems for multi-camera systems are enumerated by the Pólya enumeration theorem. Extensive experiments demonstrate the superior accuracy and efficiency of our solvers compared to state-of-the-art six-point methods. The code is available at https://github.com/jizhaox/relpose-6pt .

Pose tracking of uncooperative spacecraft is an essential technology for space exploration and on-orbit servicing, which remains an open problem. Event cameras possess numerous advantages, such as high dynamic range, high temporal resolution, and low power consumption. These attributes hold the promise of overcoming challenges encountered by conventional cameras, including motion blur and extreme illumination, among others. To address the standard on-orbit observation missions, we propose a line-based pose tracking method for uncooperative spacecraft utilizing a stereo event camera. To begin with, we estimate the wireframe model of uncooperative spacecraft, leveraging the spatiotemporal consistency of stereo event streams for line-based reconstruction. Then, we develop an effective strategy to establish correspondences between events and projected lines of uncooperative spacecraft. Using these correspondences, we formulate the pose tracking as a continuous optimization process over six-degree-of-freedom (6-DOF) motion parameters, achieved by minimizing event-line distances. Moreover, we construct a stereo event-based uncooperative spacecraft motion dataset, encompassing both simulated and real events. The proposed method is quantitatively evaluated through experiments conducted on our self-collected dataset, demonstrating an improvement in terms of effectiveness and accuracy over competing methods. The code will be open-sourced athttps://github.com/Zibin6/SE6PT.

Object pose tracking is one of the pivotal technologies in multimedia, attracting ever-growing attention in recent years. Existing methods employing traditional cameras encounter numerous challenges such as motion blur, sensor noise, partial occlusion, and changing lighting conditions. The emerging bio-inspired sensors, particularly event cameras, possess advantages such as high dynamic range and low latency, which hold the potential to address the aforementioned challenges. In this work, we present an optical flow-guided 6DoF object pose tracking method with an event camera. A 2D-3D hybrid feature extraction strategy is firstly utilized to detect corners and edges from events and object models, which characterizes object motion precisely. Then, we search for the optical flow of corners by maximizing the event-associated probability within a spatio-temporal window, and establish the correlation between corners and edges guided by optical flow. Furthermore, by minimizing the distances between corners and edges, the 6DoF object pose is iteratively optimized to achieve continuous pose tracking. Experimental results of both simulated and real events demonstrate that our methods outperform event-based state-of-the-art methods in terms of both accuracy and robustness.

Mobile devices equipped with a multi-camera system and an inertial measurement unit (IMU) are widely used nowadays, such as self-driving cars. The task of relative pose estimation using visual and inertial information has important applications in various fields. To improve the accuracy of relative pose estimation of multi-camera systems, we propose a globally optimal solver using affine correspondences to estimate the generalized relative pose with a known vertical direction. First, a cost function about the relative rotation angle is established after decoupling the rotation matrix and translation vector, which minimizes the algebraic error of geometric constraints from affine correspondences. Then, the global optimization problem is converted into two polynomials with two unknowns based on the characteristic equation and its first derivative is zero. Finally, the relative rotation angle can be solved using the polynomial eigenvalue solver, and the translation vector can be obtained from the eigenvector. Besides, a new linear solution is proposed when the relative rotation is small. The proposed solver is evaluated on synthetic data and real-world datasets. The experiment results demonstrate that our method outperforms comparable state-of-the-art methods in accuracy.

Pose estimation and tracking of objects is a fundamental application in 3D vision. Event cameras possess remarkable attributes such as high dynamic range, low latency, and resilience against motion blur, which enables them to address challenging high dynamic range scenes or high-speed motion. These features make event cameras an ideal complement over standard cameras for object pose estimation. In this work, we propose a line-based robust pose estimation and tracking method for planar or non-planar objects using an event camera. Firstly, we extract object lines directly from events, then provide an initial pose using a globally-optimal Branch-and-Bound approach, where 2D-3D line correspondences are not known in advance. Subsequently, we utilize event-line matching to establish correspondences between 2D events and 3D models. Furthermore, object poses are refined and continuously tracked by minimizing event-line distances. Events are assigned different weights based on these distances, employing robust estimation algorithms. To evaluate the precision of the proposed methods in object pose estimation and tracking, we have devised and established an event-based moving object dataset. Compared against state-of-the-art methods, the robustness and accuracy of our methods have been validated both on synthetic experiments and the proposed dataset. The source code is available at https://github.com/Zibin6/LOPET.

In this paper, we present a relative pose estimation algorithm based on lines knowing the vertical direction associated to each image. We demonstrate that a closed-form solution requiring only eight lines between three views is possible. As a linear solution, it is shown that our approach outperforms the standard trifocal estimation based on 13 triplets of lines and can be efficiently inserted into an hypothesize-and-test framework such as RANSAC. We also study our approach on different singular configurations of lines. The method is evaluated on both synthetic data and real-world sequences from KITTI and the Zürich Urban Micro Aerial Vehicle datasets. Our method is compared to 13 lines algorithm as well to points based methods such as 7-points, 5-points and 3-points.

The accuracy and robustness of visual odometry (VO) is significantly affected by the high dynamic range (HDR) environments, because traditional cameras have a limited dynamic range and inevitably miss information in both overexposed and underexposed areas. To overcome the above challenge, we use an spatially varying exposure (SVE) camera, which captures four images with different exposure levels simultaneously. Then, we propose a VO pipeline that leverages the advantages of the SVE camera. Specifically, we extract ORB features from four images in parallel firstly instead of fusing four images, then perform merging and filtering to provide more robust features. We demonstrate that the proposed system outperforms comparable state-of-the-art methods in terms of robustness and accuracy. The real-time performance of the proposed system is also guaranteed due to the elaborate design of the parallel algorithm.

The use of multi-camera systems is becoming more common in self-driving cars, micro aerial vehicles or augmented reality headsets. In order to perform 3D geometric tasks, the accuracy and efficiency of relative pose estimation algorithms are very important for the multi-camera systems, and is catching significant research attention these days. The point coordinates of point correspondences (PCs) obtained from feature matching strategies have been widely used for relative pose estimation. This paper exploits known scale ratios besides the point coordinates, which are also intrinsically provided by scale invariant feature detectors (e.g., SIFT). Two-view geometry of scale ratio associated with the extracted features is derived for multi-camera systems. Thanks to the constraints provided by the scale ratio across two views, the number of PCs needed for relative pose estimation is reduced from 6 to 3. Requiring fewer PCs makes RANSAC-like randomized robust estimation significantly faster. For different point correspondence layouts, four minimal solvers are proposed for typical two-camera rigs. Extensive experiments demonstrate that our solvers have better accuracy than the state-of-the-art ones and outperform them in terms of processing time.

In this article, we present four cases of minimal solutions for two-view relative pose estimation by exploiting the affine transformation between feature points, and we demonstrate efficient solvers for these cases. It is shown that under the planar motion assumption or with knowledge of a vertical direction, a single affine correspondence is sufficient to recover the relative camera pose. The four cases considered are two-view planar relative motion for calibrated cameras as a closed-form and least-squares solutions, a closed-form solution for unknown focal length, and the case of a known vertical direction. These algorithms can be used efficiently for outlier detection within a RANSAC loop and for initial motion estimation. All the methods are evaluated on both synthetic data and real-world datasets. The experimental results demonstrate that our methods outperform comparable state-of-the-art methods in accuracy with the benefit of a reduced number of needed RANSAC iterations. The source code is released at https://github.com/jizhaox/relative_pose_from_affine.

We propose three novel solvers for estimating the relative pose of a multi-camera system from affine correspondences (ACs). A new constraint is derived interpreting the relationship of ACs and the generalized camera model. Using the constraint, we demonstrate efficient solvers for two types of motions assumed. Considering that the cameras undergo planar motion, we propose a minimal solution using a single AC and a solver with two ACs to overcome the degenerate case. Also, we propose a minimal solution using two ACs with known vertical direction, e.g., from an IMU. Since the proposed methods require significantly fewer correspondences than state-of-the-art algorithms, they can be efficiently used within RANSAC for outlier removal and initial motion estimation. The solvers are tested both on synthetic data and on real-world scenes from the KITTI odometry benchmark. It is shown that the accuracy of the estimated poses is superior to the state-of-the-art techniques.

We propose an efficient method to estimate the relative pose of a multi-camera system from a minimum of two affine correspondences (ACs). Our solution is novel as it computes the 6DOF relative pose by utilizing a first-order rotation approximation. We directly derive a single polynomial based on the constraint between ACs and the generalized camera model. Then a closed-form solution is found analytically and it produces an accurate relative pose estimation efficiently. Benefiting from the low number of exploited correspondences and the speed of the solver, it speeds up robust estimators, e.g. RANSAC, significantly. The proposed method is evaluated both on synthetic data and real-world image sequences from the KITTI benchmark. It is shown that the proposed solver is superior to the state-of-the-art algorithms in terms of accuracy.

In this paper we present four cases of minimal solutions for two-view relative pose estimation by exploiting the affine transformation between feature points and we demonstrate efficient solvers for these cases. It is shown, that under the planar motion assumption or with knowledge of a vertical direction, a single affine correspondence is sufficient to recover the relative camera pose. The four cases considered are two-view planar relative motion for calibrated cameras as a closed-form and a least-squares solution, a closed-form solution for unknown focal length and the case of a known vertical direction. These algorithms can be used efficiently for outlier detection within a RANSAC loop and for initial motion estimation. All the methods are evaluated on both synthetic data and real-world datasets from the KITTI benchmark. The experimental results demonstrate that our methods outperform comparable state-of-the-art methods in accuracy with the benefit of a reduced number of needed RANSAC iterations.

In this paper we present minimal solutions for two-view relative motion estimation based on a homography formulation. By assuming a known vertical direction (e.g. from an IMU) and assuming a dominant ground plane we demonstrate that rotation and translation estimation can be decoupled. This result allows us to reduce the number of point matches needed to compute a motion hypothesis. We then derive different algorithms based on this decoupling that allow an efficient estimation. We also demonstrate how these algorithms can be used efficiently to compute an optimal inlier set using exhaustive search or histogram voting instead of a traditional RANSAC step. Our methods are evaluated on synthetic data and on the KITTI data set, demonstrating that our methods are well suited for visual odometry in road driving scenarios.