Laurent Kneip

Jiaxin Wei, Xibin Song, Weizhe Liu et al.

While showing promising results, recent RGB-D camera-based category-level object pose estimation methods have restricted applications due to the heavy reliance on depth sensors. RGB-only methods provide an alternative to this problem yet suffer from inherent scale ambiguity stemming from monocular observations. In this paper, we propose a novel pipeline that decouples the 6D pose and size estimation to mitigate the influence of imperfect scales on rigid transformations. Specifically, we leverage a pre-trained monocular estimator to extract local geometric information, mainly facilitating the search for inlier 2D-3D correspondence. Meanwhile, a separate branch is designed to directly recover the metric scale of the object based on category-level statistics. Finally, we advocate using the RANSAC-P$n$P algorithm to robustly solve for 6D object pose. Extensive experiments have been conducted on both synthetic and real datasets, demonstrating the superior performance of our method over previous state-of-the-art RGB-based approaches, especially in terms of rotation accuracy. Code: https://github.com/goldoak/DMSR.

Zibin Liu, Banglei Guan, Yang Shang et al.

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.

Ling Gao, Yuxuan Liang, Jiaqi Yang et al. · tsinghua

Event cameras have recently gained in popularity as they hold strong potential to complement regular cameras in situations of high dynamics or challenging illumination. An important problem that may benefit from the addition of an event camera is given by Simultaneous Localization And Mapping (SLAM). However, in order to ensure progress on event-inclusive multi-sensor SLAM, novel benchmark sequences are needed. Our contribution is the first complete set of benchmark datasets captured with a multi-sensor setup containing an event-based stereo camera, a regular stereo camera, multiple depth sensors, and an inertial measurement unit. The setup is fully hardware-synchronized and underwent accurate extrinsic calibration. All sequences come with ground truth data captured by highly accurate external reference devices such as a motion capture system. Individual sequences include both small and large-scale environments, and cover the specific challenges targeted by dynamic vision sensors.

Jiaben Chen, Yichen Zhu, Dongze Lian et al. · tsinghua

Dynamic vision sensors or event cameras provide rich complementary information for video frame interpolation. Existing state-of-the-art methods follow the paradigm of combining both synthesis-based and warping networks. However, few of those methods fully respect the intrinsic characteristics of events streams. Given that event cameras only encode intensity changes and polarity rather than color intensities, estimating optical flow from events is arguably more difficult than from RGB information. We therefore propose to incorporate RGB information in an event-guided optical flow refinement strategy. Moreover, in light of the quasi-continuous nature of the time signals provided by event cameras, we propose a divide-and-conquer strategy in which event-based intermediate frame synthesis happens incrementally in multiple simplified stages rather than in a single, long stage. Extensive experiments on both synthetic and real-world datasets show that these modifications lead to more reliable and realistic intermediate frame results than previous video frame interpolation methods. Our findings underline that a careful consideration of event characteristics such as high temporal density and elevated noise benefits interpolation accuracy.

Jiaxin Wei, Stefan Leutenegger, Laurent Kneip

Perspective-$n$-Point (P$n$P) stands as a fundamental algorithm for pose estimation in various applications. In this paper, we present a new approach to the P$n$P problem with relaxed constraints, eliminating the need for precise 3D coordinates, which is especially suitable for object pose estimation where corresponding object models may not be available in practice. Built upon the classical EP$n$P solver, we refer to it as AEP$n$P due to its ability to handle unknown anisotropic scaling factors in addition to the common 6D transformation. Through a few algebraic manipulations and a well-chosen frame of reference, this new problem can be boiled down to a simple linear null-space problem followed by point registration-based identification of a similarity transformation. Experimental results on both simulated and real datasets demonstrate the effectiveness of AEP$n$P as a flexible and practical solution to object pose estimation. Code: https://github.com/goldoak/AEPnP.

Ling Gao, Hang Su, Daniel Gehrig et al.

Event-based cameras are ideal for line-based motion estimation, since they predominantly respond to edges in the scene. However, accurately determining the camera displacement based on events continues to be an open problem. This is because line feature extraction and dynamics estimation are tightly coupled when using event cameras, and no precise model is currently available for describing the complex structures generated by lines in the space-time volume of events. We solve this problem by deriving the correct non-linear parametrization of such manifolds, which we term eventails, and demonstrate its application to event-based linear motion estimation, with known rotation from an Inertial Measurement Unit. Using this parametrization, we introduce a novel minimal 5-point solver that jointly estimates line parameters and linear camera velocity projections, which can be fused into a single, averaged linear velocity when considering multiple lines. We demonstrate on both synthetic and real data that our solver generates more stable relative motion estimates than other methods while capturing more inliers than clustering based on spatio-temporal planes. In particular, our method consistently achieves a 100% success rate in estimating linear velocity where existing closed-form solvers only achieve between 23% and 70%. The proposed eventails contribute to a better understanding of spatio-temporal event-generated geometries and we thus believe it will become a core building block of future event-based motion estimation algorithms.

Xin Peng, Ling Gao, Yifu Wang et al.

Event cameras are bio-inspired sensors that perform well in challenging illumination conditions and have high temporal resolution. However, their concept is fundamentally different from traditional frame-based cameras. The pixels of an event camera operate independently and asynchronously. They measure changes of the logarithmic brightness and return them in the highly discretised form of time-stamped events indicating a relative change of a certain quantity since the last event. New models and algorithms are needed to process this kind of measurements. The present work looks at several motion estimation problems with event cameras. The flow of the events is modelled by a general homographic warping in a space-time volume, and the objective is formulated as a maximisation of contrast within the image of warped events. Our core contribution consists of deriving globally optimal solutions to these generally non-convex problems, which removes the dependency on a good initial guess plaguing existing methods. Our methods rely on branch-and-bound optimisation and employ novel and efficient, recursive upper and lower bounds derived for six different contrast estimation functions. The practical validity of our approach is demonstrated by a successful application to three different event camera motion estimation problems.

Xin Peng, Yifu Wang, Ling Gao et al.

Event cameras are bio-inspired sensors that perform well in HDR conditions and have high temporal resolution. However, different from traditional frame-based cameras, event cameras measure asynchronous pixel-level brightness changes and return them in a highly discretised format, hence new algorithms are needed. The present paper looks at fronto-parallel motion estimation of an event camera. The flow of the events is modeled by a general homographic warping in a space-time volume, and the objective is formulated as a maximisation of contrast within the image of unwarped events. However, in stark contrast to prior art, we derive a globally optimal solution to this generally non-convex problem, and thus remove the dependency on a good initial guess. Our algorithm relies on branch-and-bound optimisation for which we derive novel, recursive upper and lower bounds for six different contrast estimation functions. The practical validity of our approach is supported by a highly successful application to AGV motion estimation with a downward facing event camera, a challenging scenario in which the sensor experiences fronto-parallel motion in front of noisy, fast moving textures.

Xinyue Zhang, Liangzu Peng, Wanting Xu et al.

Branch-and-bound-based consensus maximization stands out due to its important ability of retrieving the globally optimal solution to outlier-affected geometric problems. However, while the discovery of such solutions caries high scientific value, its application in practical scenarios is often prohibited by its computational complexity growing exponentially as a function of the dimensionality of the problem at hand. In this work, we convey a novel, general technique that allows us to branch over an n-1 dimensional space for an n-dimensional problem. The remaining degree of freedom can be solved globally optimally within each bound calculation by applying the efficient interval stabbing technique. While each individual bound derivation is harder to compute owing to the additional need for solving a sorting problem, the reduced number of intervals and tighter bounds in practice lead to a significant reduction in the overall number of required iterations. Besides an abstract introduction of the approach, we present applications to four fundamental geometric computer vision problems: camera resectioning, relative camera pose estimation, point set registration, and rotation and focal length estimation. Through our exhaustive tests, we demonstrate significant speed-up factors at times exceeding two orders of magnitude, thereby increasing the viability of globally optimal consensus maximizers in online application scenarios.

Zhongyang Ren, Bangyan Liao, Delei Kong et al.

Recovering the camera motion and scene geometry from visual data is a fundamental problem in the field of computer vision. Its success in standard vision is attributed to the maturity of feature extraction, data association and multi-view geometry. The recent emergence of neuromorphic event-based cameras places great demands on approaches that use raw event data as input to solve this fundamental problem. Existing state-of-the-art solutions typically infer implicitly data association by iteratively reversing the event data generation process. However, the nonlinear nature of these methods limits their applicability in real-time tasks, and the constant-motion assumption leads to unstable results under agile motion. To this end, we rethink the problem formulation in a way that aligns better with the differential working principle of event cameras. We show that the event-based normal flow can be used, via the proposed geometric error term, as an alternative to the full flow in solving a family of geometric problems that involve instantaneous first-order kinematics and scene geometry. Furthermore, we develop a fast linear solver and a continuous-time nonlinear solver on top of the proposed geometric error term. Experiments on both synthetic and real data show the superiority of our linear solver in terms of accuracy and efficiency, and indicate its complementary feature as an initialization method for existing nonlinear solvers. Besides, our continuous-time non-linear solver exhibits exceptional capability in accommodating sudden variations in motion since it does not rely on the constant-motion assumption.

Ling Gao, Junyan Su, Jiadi Cui et al.

The motion of planar ground vehicles is often non-holonomic, and as a result may be modelled by the 2 DoF Ackermann steering model. We analyse the feasibility of estimating such motion with a downward facing camera that exerts fronto-parallel motion with respect to the ground plane. This turns the motion estimation into a simple image registration problem in which we only have to identify a 2-parameter planar homography. However, one difficulty that arises from this setup is that ground-plane features are indistinctive and thus hard to match between successive views. We encountered this difficulty by introducing the first globally-optimal, correspondence-less solution to plane-based Ackermann motion estimation. The solution relies on the branch-and-bound optimisation technique. Through the low-dimensional parametrisation, a derivation of tight bounds, and an efficient implementation, we demonstrate how this technique is eventually amenable to accurate real-time motion estimation. We prove its property of global optimality and analyse the impact of assuming a locally constant centre of rotation. Our results on real data finally demonstrate a significant advantage over the more traditional, correspondence-based hypothesise-and-test schemes.

Ling Gao, Laurent Kneip

We present a novel framework for floor plan-based, full six degree-of-freedom LiDAR localization. Our approach relies on robust ceiling and ground plane detection, which solves part of the pose and supports the segmentation of vertical structure elements such as walls and pillars. Our core contribution is a novel nearest neighbour data structure for an efficient look-up of nearest vertical structure elements from the floor plan. The registration is realized as a pair-wise regularized windowed pose graph optimization. Highly efficient, accurate and drift-free long-term localization is demonstrated on multiple scenes.

Jiaxin Wei, Lan Hu, Chenyu Wang et al.

We present a new solution to the fine-grained retrieval of clean CAD models from a large-scale database in order to recover detailed object shape geometries for RGBD scans. Unlike previous work simply indexing into a moderately small database using an object shape descriptor and accepting the top retrieval result, we argue that in the case of a large-scale database a more accurate model may be found within a neighborhood of the descriptor. More importantly, we propose that the distinctiveness deficiency of shape descriptors at the instance level can be compensated by a geometry-based re-ranking of its neighborhood. Our approach first leverages the discriminative power of learned representations to distinguish between different categories of models and then uses a novel robust point set distance metric to re-rank the CAD neighborhood, enabling fine-grained retrieval in a large shape database. Evaluation on a real-world dataset shows that our geometry-based re-ranking is a conceptually simple but highly effective method that can lead to a significant improvement in retrieval accuracy compared to the state-of-the-art.

Runze Yuan, Tao Liu, Zijia Dai et al.

Event cameras are an interesting visual exteroceptive sensor that reacts to brightness changes rather than integrating absolute image intensities. Owing to this design, the sensor exhibits strong performance in situations of challenging dynamics and illumination conditions. While event-based simultaneous tracking and mapping remains a challenging problem, a number of recent works have pointed out the sensor's suitability for prior map-based tracking. By making use of cross-modal registration paradigms, the camera's ego-motion can be tracked across a large spectrum of illumination and dynamics conditions on top of accurate maps that have been created a priori by more traditional sensors. The present paper follows up on a recently introduced event-based geometric semi-dense tracking paradigm, and proposes the addition of inertial signals in order to robustify the estimation. More specifically, the added signals provide strong cues for pose initialization as well as regularization during windowed, multi-frame tracking. As a result, the proposed framework achieves increased performance under challenging illumination conditions as well as a reduction of the rate at which intermediate event representations need to be registered in order to maintain stable tracking across highly dynamic sequences. Our evaluation focuses on a diverse set of real world sequences and comprises a comparison of our proposed method against a purely event-based alternative running at different rates.

Jiaqi Yang, Yucong Chen, Xiangting Meng et al.

Recently there has been a growing interest in category-level object pose and size estimation, and prevailing methods commonly rely on single view RGB-D images. However, one disadvantage of such methods is that they require accurate depth maps which cannot be produced by consumer-grade sensors. Furthermore, many practical real-world situations involve a moving camera that continuously observes its surroundings, and the temporal information of the input video streams is simply overlooked by single-view methods. We propose a novel solution that makes use of RGB video streams. Our framework consists of three modules: a scale-aware monocular dense SLAM solution, a lightweight object pose predictor, and an object-level pose graph optimizer. The SLAM module utilizes a video stream and additional scale-sensitive readings to estimate camera poses and metric depth. The object pose predictor then generates canonical object representations from RGB images. The object pose is estimated through geometric registration of these canonical object representations with estimated object depth points. All per-view estimates finally undergo optimization within a pose graph, culminating in the output of robust and accurate canonical object poses. Our experimental results demonstrate that when utilizing public dataset sequences with high-quality depth information, the proposed method exhibits comparable performance to state-of-the-art RGB-D methods. We also collect and evaluate on new datasets containing depth maps of varying quality to further quantitatively benchmark the proposed method alongside previous RGB-D based methods. We demonstrate a significant advantage in scenarios where depth input is absent or the quality of depth sensing is limited.

Tao Liu, Runze Yuan, Yi'ang Ju et al.

Reliable self-localization is a foundational skill for many intelligent mobile platforms. This paper explores the use of event cameras for motion tracking thereby providing a solution with inherent robustness under difficult dynamics and illumination. In order to circumvent the challenge of event camera-based mapping, the solution is framed in a cross-modal way. It tracks a map representation that comes directly from frame-based cameras. Specifically, the proposed method operates on top of gaussian splatting, a state-of-the-art representation that permits highly efficient and realistic novel view synthesis. The key of our approach consists of a novel pose parametrization that uses a reference pose plus first order dynamics for local differential image rendering. The latter is then compared against images of integrated events in a staggered coarse-to-fine optimization scheme. As demonstrated by our results, the realistic view rendering ability of gaussian splatting leads to stable and accurate tracking across a variety of both publicly available and newly recorded data sequences.

Xiang Ji, Jiaxin Wei, Yifu Wang et al.

Visual place recognition is an important problem towards global localization in many robotics tasks. One of the biggest challenges is that it may suffer from illumination or appearance changes in surrounding environments. Event cameras are interesting alternatives to frame-based sensors as their high dynamic range enables robust perception in difficult illumination conditions. However, current event-based place recognition methods only rely on event information, which restricts downstream applications of VPR. In this paper, we present the first cross-modal visual place recognition framework that is capable of retrieving regular images from a database given an event query. Our method demonstrates promising results with respect to the state-of-the-art frame-based and event-based methods on the Brisbane-Event-VPR dataset under different scenarios. We also verify the effectiveness of the combination of retrieval and classification, which can boost performance by a large margin.

Xinyue Zhang, Jiaqi Yang, Xiangting Meng et al.

In the realm of computer vision, the perception and reconstruction of the 3D world through vision signals heavily rely on camera intrinsic parameters, which have long been a subject of intense research within the community. In practical applications, without a strong scene geometry prior like the Manhattan World assumption or special artificial calibration patterns, monocular focal length estimation becomes a challenging task. In this paper, we propose a method for monocular focal length estimation using category-level object priors. Based on two well-studied existing tasks: monocular depth estimation and category-level object canonical representation learning, our focal solver takes depth priors and object shape priors from images containing objects and estimates the focal length from triplets of correspondences in closed form. Our experiments on simulated and real world data demonstrate that the proposed method outperforms the current state-of-the-art, offering a promising solution to the long-standing monocular focal length estimation problem.

Jiaxin Wei, Lige Liu, Ran Cheng et al.

Recent years have witnessed the surge of learned representations that directly build upon point clouds. Though becoming increasingly expressive, most existing representations still struggle to generate ordered point sets. Inspired by spherical multi-view scanners, we propose a novel sampling model called Spotlights to represent a 3D shape as a compact 1D array of depth values. It simulates the configuration of cameras evenly distributed on a sphere, where each virtual camera casts light rays from its principal point through sample points on a small concentric spherical cap to probe for the possible intersections with the object surrounded by the sphere. The structured point cloud is hence given implicitly as a function of depths. We provide a detailed geometric analysis of this new sampling scheme and prove its effectiveness in the context of the point cloud completion task. Experimental results on both synthetic and real data demonstrate that our method achieves competitive accuracy and consistency while having a significantly reduced computational cost. Furthermore, we show superior performance on the downstream point cloud registration task over state-of-the-art completion methods.

Min Li, Laurent Kneip

We present an algorithmic contribution to improve the efficiency of robust trim-fitting in outlier affected geometric regression problems. The method heavily relies on the quick sort algorithm, and we present two important insights. First, partial sorting is sufficient for the incremental calculation of the x-th percentile value. Second, the normal equations in linear fitting problems may be updated incrementally by logging swap operations across the x-th percentile boundary during sorting. Besides linear fitting problems, we demonstrate how the technique can be additionally applied to closed-form, non-linear energy minimization problems, thus enabling efficient trim fitting under geometrically optimal objectives. We apply our method to two distinct camera resectioning algorithms, and demonstrate highly efficient and reliable, geometric trim fitting.

Jiaxin Liu, Min Li, Wanting Xu et al.

Accurate state estimation for flexible robotic systems poses significant challenges, particularly for platforms with dynamically deforming structures that invalidate rigid-body assumptions. This paper addresses this problem and enables the extension of existing rigid-body pose estimation methods to non-rigid systems. Our approach integrates two core components: first, we capture elastic properties using a deformation-force model, efficiently learned via a Multi-Layer Perceptron; second, we resolve the platform's inherently smooth motion using continuous-time B-spline kinematic models. By continuously applying Newton's Second Law, our method formulates the relationship between visually-derived trajectory acceleration and predicted deformation-induced acceleration. We demonstrate that our approach not only enables robust and accurate pose estimation on non-rigid platforms, but also shows that the properly modeled platform physics allow for the recovery of inertial sensing properties. We validate this feasibility on a simple spring-camera system, showing how it robustly resolves the typically ill-posed problem of metric scale and gravity recovery in monocular visual odometry.

Tianyu Huang, Liangzu Peng, Xinyue Zhang et al.

To achieve outlier-robust geometric estimation, robust objective functions are generally employed to mitigate the influence of outliers. The widely used consensus maximization(CM) is highly robust when paired with global branch-and-bound(BnB) search. However, CM relies solely on inlier counts and is sensitive to the inlier threshold. Besides, the discrete nature of CM leads to loose bounds, necessitating extensive BnB iterations and computation cost. Truncated losses(TL), another continuous alternative, leverage residual information more effectively and could potentially overcome these issues. But to our knowledge, no prior work has systematically explored globally minimizing TL with BnB and its potential for enhanced threshold resilience or search efficiency. In this work, we propose GTM, the first unified BnB-based framework for globally-optimal TL loss minimization across diverse geometric problems. GTM involves a hybrid solving design: given an n-dimensional problem, it performs BnB search over an (n-1)-dimensional subspace while the remaining 1D variable is solved by bounding the objective function. Our hybrid design not only reduces the search space, but also enables us to derive Lipschitz-continuous bounding functions that are general, tight, and can be efficiently solved by a classic global Lipschitz solver named DIRECT, which brings further acceleration. We conduct a systematic evaluation on various BnB-based methods for CM and TL on the robust linear regression problem, showing that GTM enjoys remarkable threshold resilience and the highest efficiency compared to baseline methods. Furthermore, we apply GTM on different geometric estimation problems with diverse residual forms. Extensive experiments demonstrate that GTM achieves state-of-the-art outlier-robustness and threshold-resilience while maintaining high efficiency across these estimation tasks.

Ji Zhao, Banglei Guan, Zibin Liu et al.

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.

Wanting Xu, Si'ao Zhang, Li Cui et al.

Despite the promise of superior performance under challenging conditions, event-based motion estimation remains a hard problem owing to the difficulty of extracting and tracking stable features from event streams. In order to robustify the estimation, it is generally believed that fusion with other sensors is a requirement. In this work, we demonstrate reliable, purely event-based visual odometry on planar ground vehicles by employing the constrained non-holonomic motion model of Ackermann steering platforms. We extend single feature n-linearities for regular frame-based cameras to the case of quasi time-continuous event-tracks, and achieve a polynomial form via variable degree Taylor expansions. Robust averaging over multiple event tracks is simply achieved via histogram voting. As demonstrated on both simulated and real data, our algorithm achieves accurate and robust estimates of the vehicle's instantaneous rotational velocity, and thus results that are comparable to the delta rotations obtained by frame-based sensors under normal conditions. We furthermore significantly outperform the more traditional alternatives in challenging illumination scenarios. The code is available at \url{https://github.com/gowanting/NHEVO}.

Jinze Yu, Xin Peng, Zhengda Lu et al.

A spike camera is a specialized high-speed visual sensor that offers advantages such as high temporal resolution and high dynamic range compared to conventional frame cameras. These features provide the camera with significant advantages in many computer vision tasks. However, the tasks of novel view synthesis based on spike cameras remain underdeveloped. Although there are existing methods for learning neural radiance fields from spike stream, they either lack robustness in extremely noisy, low-quality lighting conditions or suffer from high computational complexity due to the deep fully connected neural networks and ray marching rendering strategies used in neural radiance fields, making it difficult to recover fine texture details. In contrast, the latest advancements in 3DGS have achieved high-quality real-time rendering by optimizing the point cloud representation into Gaussian ellipsoids. Building on this, we introduce SpikeGS, the method to learn 3D Gaussian fields solely from spike stream. We designed a differentiable spike stream rendering framework based on 3DGS, incorporating noise embedding and spiking neurons. By leveraging the multi-view consistency of 3DGS and the tile-based multi-threaded parallel rendering mechanism, we achieved high-quality real-time rendering results. Additionally, we introduced a spike rendering loss function that generalizes under varying illumination conditions. Our method can reconstruct view synthesis results with fine texture details from a continuous spike stream captured by a moving spike camera, while demonstrating high robustness in extremely noisy low-light scenarios. Experimental results on both real and synthetic datasets demonstrate that our method surpasses existing approaches in terms of rendering quality and speed.

Banglei Guan, Ji Zhao, Laurent Kneip

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. 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

Hang Su, Yunlong Feng, Daniel Gehrig et al.

Structure and continuous motion estimation from point correspondences is a fundamental problem in computer vision that has been powered by well-known algorithms such as the familiar 5-point or 8-point algorithm. However, despite their acclaim, these algorithms are limited to processing point correspondences originating from a pair of views each one representing an instantaneous capture of the scene. Yet, in the case of rolling shutter cameras, or more recently, event cameras, this synchronization breaks down. In this work, we present a unified approach for structure and linear motion estimation from 2D point correspondences with arbitrary timestamps, from an arbitrary set of views. By formulating the problem in terms of first-order dynamics and leveraging a constant velocity motion model, we derive a novel, linear point incidence relation allowing for the efficient recovery of both linear velocity and 3D points with predictable degeneracies and solution multiplicities. Owing to its general formulation, it can handle correspondences from a wide range of sensing modalities such as global shutter, rolling shutter, and event cameras, and can even combine correspondences from different collocated sensors. We validate the effectiveness of our solver on both simulated and real-world data, where we show consistent improvement across all modalities when compared to recent approaches. We believe our work opens the door to efficient structure and motion estimation from asynchronous data. Code can be found at https://github.com/suhang99/AsyncTrack-Motion-Solver.

Wanting Xu, Xin Peng, Laurent Kneip

Traditional visual-inertial state estimation targets absolute camera poses and spatial landmark locations while first-order kinematics are typically resolved as an implicitly estimated sub-state. However, this poses a risk in velocity-based control scenarios, as the quality of the estimation of kinematics depends on the stability of absolute camera and landmark coordinates estimation. To address this issue, we propose a novel solution to tight visual-inertial fusion directly at the level of first-order kinematics by employing a dynamic vision sensor instead of a normal camera. More specifically, we leverage trifocal tensor geometry to establish an incidence relation that directly depends on events and camera velocity, and demonstrate how velocity estimates in highly dynamic situations can be obtained over short time intervals. Noise and outliers are dealt with using a nested two-layer RANSAC scheme. Additionally, smooth velocity signals are obtained from a tight fusion with pre-integrated inertial signals using a sliding window optimizer. Experiments on both simulated and real data demonstrate that the proposed tight event-inertial fusion leads to continuous and reliable velocity estimation in highly dynamic scenarios independently of absolute coordinates. Furthermore, in extreme cases, it achieves more stable and more accurate estimation of kinematics than traditional, point-position-based visual-inertial odometry.

Ling Gao, Daniel Gehrig, Hang Su et al.

Event cameras respond primarily to edges--formed by strong gradients--and are thus particularly well-suited for line-based motion estimation. Recent work has shown that events generated by a single line each satisfy a polynomial constraint which describes a manifold in the space-time volume. Multiple such constraints can be solved simultaneously to recover the partial linear velocity and line parameters. In this work, we show that, with a suitable line parametrization, this system of constraints is actually linear in the unknowns, which allows us to design a novel linear solver. Unlike existing solvers, our linear solver (i) is fast and numerically stable since it does not rely on expensive root finding, (ii) can solve both minimal and overdetermined systems with more than 5 events, and (iii) admits the characterization of all degenerate cases and multiple solutions. The found line parameters are singularity-free and have a fixed scale, which eliminates the need for auxiliary constraints typically encountered in previous work. To recover the full linear camera velocity we fuse observations from multiple lines with a novel velocity averaging scheme that relies on a geometrically-motivated residual, and thus solves the problem more efficiently than previous schemes which minimize an algebraic residual. Extensive experiments in synthetic and real-world settings demonstrate that our method surpasses the previous work in numerical stability, and operates over 600 times faster.

Hang Su, Ling Gao, Tao Liu et al.

As the ubiquity of smart mobile devices continues to rise, Optical Camera Communication systems have gained more attention as a solution for efficient and private data streaming. This system utilizes optical cameras to receive data from digital screens via visible light. Despite their promise, most of them are hindered by dynamic factors such as screen refreshing and rapid camera motion. CMOS cameras, often serving as the receivers, suffer from limited frame rates and motion-induced image blur, which degrade overall performance. To address these challenges, this paper unveils a novel system that utilizes event cameras. We introduce a dynamic visual marker and design event-based tracking algorithms to achieve fast localization and data streaming. Remarkably, the event camera's unique capabilities mitigate issues related to screen refresh rates and camera motion, enabling a high throughput of up to 114 Kbps in static conditions, and a 1 cm localization accuracy with 1% bit error rate under various camera motions.

Xiangting Meng, Jiaqi Yang, Mingshu Chen et al.

In the realm of object pose estimation, scenarios involving both dynamic objects and moving cameras are prevalent. However, the scarcity of corresponding real-world datasets significantly hinders the development and evaluation of robust pose estimation models. This is largely attributed to the inherent challenges in accurately annotating object poses in dynamic scenes captured by moving cameras. To bridge this gap, this paper presents a novel dataset DynOPETs and a dedicated data acquisition and annotation pipeline tailored for object pose estimation and tracking in such unconstrained environments. Our efficient annotation method innovatively integrates pose estimation and pose tracking techniques to generate pseudo-labels, which are subsequently refined through pose graph optimization. The resulting dataset offers accurate pose annotations for dynamic objects observed from moving cameras. To validate the effectiveness and value of our dataset, we perform comprehensive evaluations using 18 state-of-the-art methods, demonstrating its potential to accelerate research in this challenging domain. The dataset will be made publicly available to facilitate further exploration and advancement in the field.

Li Cui, Yang Ding, Richard Hartley et al.

We propose a novel, vision-only object-level SLAM framework for automotive applications representing 3D shapes by implicit signed distance functions. Our key innovation consists of augmenting the standard neural representation by a normalizing flow network. As a result, achieving strong representation power on the specific class of road vehicles is made possible by compact networks with only 16-dimensional latent codes. Furthermore, the newly proposed architecture exhibits a significant performance improvement in the presence of only sparse and noisy data, which is demonstrated through comparative experiments on synthetic data. The module is embedded into the back-end of a stereo-vision based framework for joint, incremental shape optimization. The loss function is given by a combination of a sparse 3D point-based SDF loss, a sparse rendering loss, and a semantic mask-based silhouette-consistency term. We furthermore leverage semantic information to determine keypoint extraction density in the front-end. Finally, experimental results on real-world data reveal accurate and reliable performance comparable to alternative frameworks that make use of direct depth readings. The proposed method performs well with only sparse 3D points obtained from bundle adjustment, and eventually continues to deliver stable results even under exclusive use of the mask-consistency term.

Xinyue Zhang, Zijia Dai, Wanting Xu et al.

While automatically generated polynomial elimination templates have sparked great progress in the field of 3D computer vision, there remain many problems for which the degree of the constraints or the number of unknowns leads to intractability. In recent years, homotopy continuation has been introduced as a plausible alternative. However, the method currently depends on expensive parallel tracking of all possible solutions in the complex domain, or a classification network for starting problem-solution pairs trained over a limited set of real-world examples. Our innovation lies in a novel approach to finding solution-problem pairs, where we only need to predict a rough initial solution, with the corresponding problem generated by an online simulator. Subsequently, homotopy continuation is applied to track that single solution back to the original problem. We apply this elegant combination to generalized camera resectioning, and also introduce a new solution to the challenging generalized relative pose and scale problem. As demonstrated, the proposed method successfully compensates the raw error committed by the regressor alone, and leads to state-of-the-art efficiency and success rates.

Wanting Xu, Lan Hu, Manolis C. Tsakiris et al.

Over the past decade, the Gröbner basis theory and automatic solver generation have lead to a large number of solutions to geometric vision problems. In practically all cases, the derived solvers apply a fixed elimination template to calculate the Gröbner basis and thereby identify the zero-dimensional variety of the original polynomial constraints. However, it is clear that different variable or monomial orderings lead to different elimination templates, and we show that they may present a large variability in accuracy for a certain instance of a problem. The present paper has two contributions. We first show that for a common class of problems in geometric vision, variable reordering simply translates into a permutation of the columns of the initial coefficient matrix, and that -- as a result -- one and the same elimination template can be reused in different ways, each one leading to potentially different accuracy. We then prove that the original set of coefficients may contain sufficient information to train a classifier for online selection of a good solver, most notably at the cost of only a small computational overhead. We demonstrate wide applicability at the hand of generic dense polynomial problem solvers, as well as a concrete solver from geometric vision.

Min Li, Jiaqi Yang, Laurent Kneip

Multi-perspective cameras with potentially non-overlapping fields of view have become an important exteroceptive sensing modality in a number of applications such as intelligent vehicles, drones, and mixed reality headsets. In this work, we challenge one of the basic assumptions made in these scenarios, which is that the multi-camera rig is rigid. More specifically, we are considering the problem of estimating the relative pose between a static non-rigid rig in different spatial orientations while taking into account the effect of gravity onto the system. The deformable physical connections between each camera and the body center are approximated by a simple cantilever model, and inserted into the generalized epipolar constraint. Our results lead us to the important insight that the latent parameters of the deformation model, meaning the gravity vector in both views, become observable. We present a concise analysis of the observability of all variables based on noise, outliers, and rig rigidity for two different algorithms. The first one is a vision-only alternative, while the second one makes use of additional gravity measurements. To conclude, we demonstrate the ability to sense gravity in a real-world example, and discuss practical implications.

Yi-Fan Zuo, Wanting Xu, Xia Wang et al.

Vision-based localization is a cost-effective and thus attractive solution for many intelligent mobile platforms. However, its accuracy and especially robustness still suffer from low illumination conditions, illumination changes, and aggressive motion. Event-based cameras are bio-inspired visual sensors that perform well in HDR conditions and have high temporal resolution, and thus provide an interesting alternative in such challenging scenarios. While purely event-based solutions currently do not yet produce satisfying mapping results, the present work demonstrates the feasibility of purely event-based tracking if an alternative sensor is permitted for mapping. The method relies on geometric 3D-2D registration of semi-dense maps and events, and achieves highly reliable and accurate cross-modal tracking results. Practically relevant scenarios are given by depth camera-supported tracking or map-based localization with a semi-dense map prior created by a regular image-based visual SLAM or structure-from-motion system. Conventional edge-based 3D-2D alignment is extended by a novel polarity-aware registration that makes use of signed time-surface maps (STSM) obtained from event streams. We furthermore introduce a novel culling strategy for occluded points. Both modifications increase the speed of the tracker and its robustness against occlusions or large view-point variations. The approach is validated on many real datasets covering the above-mentioned challenging conditions, and compared against similar solutions realised with regular cameras.

Yi-Fan Zuo, Jiaqi Yang, Jiaben Chen et al.

We present a novel real-time visual odometry framework for a stereo setup of a depth and high-resolution event camera. Our framework balances accuracy and robustness against computational efficiency towards strong performance in challenging scenarios. We extend conventional edge-based semi-dense visual odometry towards time-surface maps obtained from event streams. Semi-dense depth maps are generated by warping the corresponding depth values of the extrinsically calibrated depth camera. The tracking module updates the camera pose through efficient, geometric semi-dense 3D-2D edge alignment. Our approach is validated on both public and self-collected datasets captured under various conditions. We show that the proposed method performs comparable to state-of-the-art RGB-D camera-based alternatives in regular conditions, and eventually outperforms in challenging conditions such as high dynamics or low illumination.

Yifu Wang, Wenqing Jiang, Kun Huang et al.

Multi-perspective cameras are quickly gaining importance in many applications such as smart vehicles and virtual or augmented reality. However, a large system size or absence of overlap in neighbouring fields-of-view often complicate their calibration. We present a novel solution which relies on the availability of an external motion capture system. Our core contribution consists of an extension to the hand-eye calibration problem which jointly solves multi-eye-to-base problems in closed form. We furthermore demonstrate its equivalence to the multi-eye-in-hand problem. The practical validity of our approach is supported by our experiments, indicating that the method is highly efficient and accurate, and outperforms existing closed-form alternatives.

Kun Huang, Yifu Wang, Laurent Kneip

Camera calibration is an important prerequisite towards the solution of 3D computer vision problems. Traditional methods rely on static images of a calibration pattern. This raises interesting challenges towards the practical usage of event cameras, which notably require image change to produce sufficient measurements. The current standard for event camera calibration therefore consists of using flashing patterns. They have the advantage of simultaneously triggering events in all reprojected pattern feature locations, but it is difficult to construct or use such patterns in the field. We present the first dynamic event camera calibration algorithm. It calibrates directly from events captured during relative motion between camera and calibration pattern. The method is propelled by a novel feature extraction mechanism for calibration patterns, and leverages existing calibration tools before optimizing all parameters through a multi-segment continuous-time formulation. As demonstrated through our results on real data, the obtained calibration method is highly convenient and reliably calibrates from data sequences spanning less than 10 seconds.

Yifu Wang, Jiaqi Yang, Xin Peng et al.

We present a new solution to tracking and mapping with an event camera. The motion of the camera contains both rotation and translation, and the displacements happen in an arbitrarily structured environment. As a result, the image matching may no longer be represented by a low-dimensional homographic warping, thus complicating an application of the commonly used Image of Warped Events (IWE). We introduce a new solution to this problem by performing contrast maximization in 3D. The 3D location of the rays cast for each event is smoothly varied as a function of a continuous-time motion parametrization, and the optimal parameters are found by maximizing the contrast in a volumetric ray density field. Our method thus performs joint optimization over motion and structure. The practical validity of our approach is supported by an application to AGV motion estimation and 3D reconstruction with a single vehicle-mounted event camera. The method approaches the performance obtained with regular cameras, and eventually outperforms in challenging visual conditions.

Yu Chen, Ji Zhao, Laurent Kneip

We address rotation averaging (RA) and its application to real-world 3D reconstruction. Local optimisation based approaches are the de facto choice, though they only guarantee a local optimum. Global optimisers ensure global optimality in low noise conditions, but they are inefficient and may easily deviate under the influence of outliers or elevated noise levels. We push the envelope of rotation averaging by leveraging the advantages of a global RA method and a local RA method. Combined with a fast view graph filtering as preprocessing, the proposed hybrid approach is robust to outliers. We further apply the proposed hybrid rotation averaging approach to incremental Structure from Motion (SfM), the accuracy and robustness of SfM are both improved by adding the resulting global rotations as regularisers to bundle adjustment. Overall, we demonstrate high practicality of the proposed method as bad camera poses are effectively corrected and drift is reduced.

Yi Zhou, Hongdong Li, Laurent Kneip

The present paper reviews the classical problem of free-form curve registration and applies it to an efficient RGBD visual odometry system called Canny-VO, as it efficiently tracks all Canny edge features extracted from the images. Two replacements for the distance transformation commonly used in edge registration are proposed: Approximate Nearest Neighbour Fields and Oriented Nearest Neighbour Fields. 3D2D edge alignment benefits from these alternative formulations in terms of both efficiency and accuracy. It removes the need for the more computationally demanding paradigms of datato-model registration, bilinear interpolation, and sub-gradient computation. To ensure robustness of the system in the presence of outliers and sensor noise, the registration is formulated as a maximum a posteriori problem, and the resulting weighted least squares objective is solved by the iteratively re-weighted least squares method. A variety of robust weight functions are investigated and the optimal choice is made based on the statistics of the residual errors. Efficiency is furthermore boosted by an adaptively sampled definition of the nearest neighbour fields. Extensive evaluations on public SLAM benchmark sequences demonstrate state-of-the-art performance and an advantage over classical Euclidean distance fields.

Lan Hu, Haomin Shi, Laurent Kneip

The present work proposes a solution to the challenging problem of registering two partial point sets of the same object with very limited overlap. We leverage the fact that most objects found in man-made environments contain a plane of symmetry. By reflecting the points of each set with respect to the plane of symmetry, we can largely increase the overlap between the sets and therefore boost the registration process. However, prior knowledge about the plane of symmetry is generally unavailable or at least very hard to find, especially with limited partial views, and finding this plane could strongly benefit from a prior alignment of the partial point sets. We solve this chicken-and-egg problem by jointly optimizing the relative pose and symmetry plane parameters, and notably do so under global optimality by employing the branch-and-bound (BnB) paradigm. Our results demonstrate a great improvement over the current state-of-the-art in globally optimal point set registration for common objects. We furthermore show an interesting application of our method to dense 3D reconstruction of scenes with repetitive objects.

Jianxiong Cai, Jiawei Hou, Yiren Lu et al.

In this paper, we focus on the question: how might mobile robots take advantage of affordable RGB-D sensors for object detection? Although current CNN-based object detectors have achieved impressive results, there are three main drawbacks for practical usage on mobile robots: 1) It is hard and time-consuming to collect and annotate large-scale training sets. 2) It usually needs a long training time. 3) CNN-based object detection shows significant weakness in predicting location. We propose an improved method for the detection of planar objects, which rectifies images with geometric information to compensate for the perspective distortion before feeding it to the CNN detector module, typically a CNN-based detector like YOLO or MASK RCNN. By dealing with the perspective distortion in advance, we eliminate the need for the CNN detector to learn that. Experiments show that this approach significantly boosts the detection performance. Besides, it effectively reduces the number of training images required. In addition to the novel detection framework proposed, we also release an RGBD dataset and source code for hazmat sign detection. To the best of our knowledge, this is the first work of image rectification for CNN-based object detection, and the dataset is the first public available hazmat sign detection dataset with RGB-D sensors.

Lan Hu, Wanting Xu, Kun Huang et al.

In an effort to increase the capabilities of SLAM systems and produce object-level representations, the community increasingly investigates the imposition of higher-level priors into the estimation process. One such example is given by employing object detectors to load and register full CAD models. Our work extends this idea to environments with unknown objects and imposes object priors by employing modern class-specific neural networks to generate complete model geometry proposals. The difficulty of using such predictions in a real SLAM scenario is that the prediction performance depends on the view-point and measurement quality, with even small changes of the input data sometimes leading to a large variability in the network output. We propose a discrete selection strategy that finds the best among multiple proposals from different registered views by re-enforcing the agreement with the online depth measurements. The result is an effective object-level RGBD SLAM system that produces compact, high-fidelity, and dense 3D maps with semantic annotations. It outperforms traditional fusion strategies in terms of map completeness and resilience against degrading measurement quality.

Dylan Campbell, Lars Petersson, Laurent Kneip et al.

Determining the position and orientation of a calibrated camera from a single image with respect to a 3D model is an essential task for many applications. When 2D-3D correspondences can be obtained reliably, perspective-n-point solvers can be used to recover the camera pose. However, without the pose it is non-trivial to find cross-modality correspondences between 2D images and 3D models, particularly when the latter only contains geometric information. Consequently, the problem becomes one of estimating pose and correspondences jointly. Since outliers and local optima are so prevalent, robust objective functions and global search strategies are desirable. Hence, we cast the problem as a 2D-3D mixture model alignment task and propose the first globally-optimal solution to this formulation under the robust $L_2$ distance between mixture distributions. We search the 6D camera pose space using branch-and-bound, which requires novel bounds, to obviate the need for a pose estimate and guarantee global optimality. To accelerate convergence, we integrate local optimization, implement GPU bound computations, and provide an intuitive way to incorporate side information such as semantic labels. The algorithm is evaluated on challenging synthetic and real datasets, outperforming existing approaches and reliably converging to the global optimum.

Zhirui Wang, Laurent Kneip

While the common environment representation in structure from motion is given by a sparse point cloud, the community has also investigated the use of lines to better enforce the inherent regularities in man-made surroundings. Following the potential of this idea, the present paper introduces a more flexible higher-order extension of points that provides a general model for structural edges in the environment, no matter if straight or curved. Our model relies on linked Bézier curves, the geometric intuition of which proves great benefits during parameter initialization and regularization. We present the first fully automatic pipeline that is able to generate spline-based representations without any human supervision. Besides a full graphical formulation of the problem, we introduce both geometric and photometric cues as well as higher-level concepts such overall curve visibility and viewing angle restrictions to automatically manage the correspondences in the graph. Results prove that curve-based structure from motion with splines is able to outperform state-of-the-art sparse feature-based methods, as well as to model curved edges in the environment.

Manolis C. Tsakiris, Liangzu Peng, Aldo Conca et al.

Linear regression without correspondences is the problem of performing a linear regression fit to a dataset for which the correspondences between the independent samples and the observations are unknown. Such a problem naturally arises in diverse domains such as computer vision, data mining, communications and biology. In its simplest form, it is tantamount to solving a linear system of equations, for which the entries of the right hand side vector have been permuted. This type of data corruption renders the linear regression task considerably harder, even in the absence of other corruptions, such as noise, outliers or missing entries. Existing methods are either applicable only to noiseless data or they are very sensitive to initialization or they work only for partially shuffled data. In this paper we address these issues via an algebraic geometric approach, which uses symmetric polynomials to extract permutation-invariant constraints that the parameters $ξ^* \in \Re^n$ of the linear regression model must satisfy. This naturally leads to a polynomial system of $n$ equations in $n$ unknowns, which contains $ξ^*$ in its root locus. Using the machinery of algebraic geometry we prove that as long as the independent samples are generic, this polynomial system is always consistent with at most $n!$ complex roots, regardless of any type of corruption inflicted on the observations. The algorithmic implication of this fact is that one can always solve this polynomial system and use its most suitable root as initialization to the Expectation Maximization algorithm. To the best of our knowledge, the resulting method is the first working solution for small values of $n$ able to handle thousands of fully shuffled noisy observations in milliseconds.

Lan Hu, Yuchen Cao, Peng Wu et al.

Most problems involving simultaneous localization and mapping can nowadays be solved using one of two fundamentally different approaches. The traditional approach is given by a least-squares objective, which minimizes many local photometric or geometric residuals over explicitly parametrized structure and camera parameters. Unmodeled effects violating the lambertian surface assumption or geometric invariances of individual residuals are encountered through statistical averaging or the addition of robust kernels and smoothness terms. Aiming at more accurate measurement models and the inclusion of higher-order shape priors, the community more recently shifted its attention to deep end-to-end models for solving geometric localization and mapping problems. However, at test-time, these feed-forward models ignore the more traditional geometric or photometric consistency terms, thus leading to a low ability to recover fine details and potentially complete failure in corner case scenarios. With an application to dense object modeling from RGBD images, our work aims at taking the best of both worlds by embedding modern higher-order object shape priors into classical iterative residual minimization objectives. We demonstrate a general ability to improve mapping accuracy with respect to each modality alone, and present a successful application to real data.

Yi Zhou, Guillermo Gallego, Henri Rebecq et al.

Event cameras are bio-inspired sensors that offer several advantages, such as low latency, high-speed and high dynamic range, to tackle challenging scenarios in computer vision. This paper presents a solution to the problem of 3D reconstruction from data captured by a stereo event-camera rig moving in a static scene, such as in the context of stereo Simultaneous Localization and Mapping. The proposed method consists of the optimization of an energy function designed to exploit small-baseline spatio-temporal consistency of events triggered across both stereo image planes. To improve the density of the reconstruction and to reduce the uncertainty of the estimation, a probabilistic depth-fusion strategy is also developed. The resulting method has no special requirements on either the motion of the stereo event-camera rig or on prior knowledge about the scene. Experiments demonstrate our method can deal with both texture-rich scenes as well as sparse scenes, outperforming state-of-the-art stereo methods based on event data image representations.