Local features e.g. SIFT and its affine and learned variants provide region-to-region rather than point-to-point correspondences. This has recently been exploited to create new minimal solvers for classical problems such as homography, essential and fundamental matrix estimation. The main advantage of such solvers is that their sample size is smaller, e.g., only two instead of four matches are required to estimate a homography. Works proposing such solvers often claim a significant improvement in run-time thanks to fewer RANSAC iterations. We show that this argument is not valid in practice if the solvers are used naively. To overcome this, we propose guidelines for effective use of region-to-region matches in the course of a full model estimation pipeline. We propose a method for refining the local feature geometries by symmetric intensity-based matching, combine uncertainty propagation inside RANSAC with preemptive model verification, show a general scheme for computing uncertainty of minimal solvers results, and adapt the sample cheirality check for homography estimation. Our experiments show that affine solvers can achieve accuracy comparable to point-based solvers at faster run-times when following our guidelines. We make code available at https://github.com/danini/affine-correspondences-for-camera-geometry.
This paper presents a deep architecture for dense semantic correspondence, called pyramidal affine regression networks (PARN), that estimates locally-varying affine transformation fields across images. To deal with intra-class appearance and shape variations that commonly exist among different instances within the same object category, we leverage a pyramidal model where affine transformation fields are progressively estimated in a coarse-to-fine manner so that the smoothness constraint is naturally imposed within deep networks. PARN estimates residual affine transformations at each level and …
A minimal solution using two affine correspondences is presented to estimate the common focal length and the fundamental matrix between two semi-calibrated cameras - known intrinsic parameters except a common focal length. To the best of our knowledge, this problem is unsolved. The proposed approach extends point correspondence-based techniques with linear constraints derived from local affine transformations. The obtained multivariate polynomial system is efficiently solved by the hidden-variable technique. Observing the geometry of local affinities, we introduce novel conditions eliminating …
Light-weight camera localization in existing maps is essential for vision-based navigation. Currently, visual and visual-inertial odometry (VO\&VIO) techniques are well-developed for state estimation but with inevitable accumulated drifts and pose jumps upon loop closure. To overcome these problems, we propose an efficient monocular camera localization method in prior LiDAR maps using direct 2D-3D line correspondences. To handle the appearance differences and modality gaps between LiDAR point clouds and images, geometric 3D lines are extracted offline from LiDAR maps while robust 2D lines are …
Learning Affine Correspondences by Integrating Geometric Constraints
College of Aerospace Science and Engineering, National University of Defense Technology（国防科技大学航天科学与工程学院）；ETH Zurich（苏黎世联邦理工学院）；HUN-REN SZTAKI（匈牙利科学院核子研究所）
Eotvos Lorand University（厄特沃什·罗兰大学）；Czech Technical University in Prague（布拉格捷克理工大学）；MTA SZTAKI（匈牙利科学院计算机科学与控制研究所）
Two solvers are proposed for estimating the extrinsic camera parameters from a single affine correspondence assuming general planar motion. In this case, the camera movement is constrained to a plane and the image plane is orthogonal to the ground. The algorithms do not assume other constraints, e.g.\ the non-holonomic one, to hold. A new minimal solver is proposed for the semi-calibrated case, i.e. the camera parameters are known except a common focal length. Another method is proposed for the fully calibrated case. Due to requiring a single correspondence, robust estimation, e.g. histogram v…
University of Oulu（奥卢大学）；Czech Technical University in Prague（布拉格捷克理工大学）；ETH Zürich（苏黎世联邦理工学院）
In this paper we study the problem of estimating the semi-generalized pose of a partially calibrated camera, i.e., the pose of a perspective camera with unknown focal length w.r.t. a generalized camera, from a hybrid set of 2D-2D and 2D-3D point correspondences. We study all possible camera configurations within the generalized camera system. To derive practical solvers to previously unsolved challenging configurations, we test different parameterizations as well as different solving strategies based on the state-of-the-art methods for generating efficient polynomial solvers. We evaluate the t…
Max Planck Institute for Informatics（马克斯·普朗克信息学研究所）；Intel Visual Computing Institute（英特尔视觉计算研究所）；University of Bath（巴斯大学）
We propose a new technique for computing dense scene flow from two handheld videos with wide camera baselines and different photometric properties due to different sensors or camera settings like exposure and white balance. Our technique innovates in two ways over existing methods: (1) it supports independently moving cameras, and (2) it computes dense scene flow for wide-baseline scenarios.We achieve this by combining state-of-the-art wide-baseline correspondence finding with a variational scene flow formulation. First, we compute dense, wide-baseline correspondences using DAISY descriptors f…
Inria（法国国家信息与自动化研究所）；Université de Lorraine（洛林大学）；LORIA（洛林计算机科学及其应用实验室）；CNRS（法国国家科学研究中心）
In this paper, we propose an object-based camera pose estimation from a single RGB image and a pre-built map of objects, represented with ellipsoidal models. We show that contrary to point correspondences, the definition of a cost function characterizing the projection of a 3D object onto a 2D object detection is not straightforward. We develop an ellipse-ellipse cost based on level sets sampling, demonstrate its nice properties for handling partially visible objects and compare its performance with other common metrics. Finally, we show that the use of a predictive uncertainty on the detected…
SZTAKI（匈牙利科学院计算机与自动化研究所）；University of Debrecen（德布勒森大学）；Czech Technical University in Prague（布拉格捷克理工大学）
We propose a new approach for combining deep-learned non-metric monocular depth with affine correspondences (ACs) to estimate the relative pose of two calibrated cameras from a single correspondence. Considering the depth information and affine features, two new constraints on the camera pose are derived. The proposed solver is usable within 1-point RANSAC approaches. Thus, the processing time of the robust estimation is linear in the number of correspondences and, therefore, orders of magnitude faster than by using traditional approaches. The proposed 1AC+D solver is tested both on synthetic …
Rutgers University（罗格斯大学）；Toyota Motor North America（丰田汽车北美公司）
In Smart City and Vehicle-to-Everything (V2X) systems, acquiring pedestrians' accurate locations is crucial to traffic safety. Current systems adopt cameras and wireless sensors to detect and estimate people's locations via sensor fusion. Standard fusion algorithms, however, become inapplicable when multi-modal data is not associated. For example, pedestrians are out of the camera field of view, or data from camera modality is missing. To address this challenge and produce more accurate location estimations for pedestrians, we propose a Generative Adversarial Network (GAN) architecture. During…
We examine 3D reconstruction of architectural scenes in unordered sets of uncalibrated images. We introduce a linear method to self-calibrate and find the metric reconstruction of a camera pair. We assume unknown and different focal lengths but otherwise known internal camera parameters and a known projective reconstruction of the camera pair. We recover two possible camera configurations in space and use the Cheirality condition, that all 3D scene points are in front of both cameras, to disambiguate the solution. We show in two Theorems, first that the two solutions are in mirror positions an…
National University of Defense Technology（国防科技大学）；Graz University of Technology（格拉茨工业大学）；German Aerospace Center（德国航空航天中心）
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 vertic…
Correspondence search is an essential step in rigid point cloud registration algorithms. Most methods maintain a single correspondence at each step and gradually remove wrong correspondances. However, building one-to-one correspondence with hard assignments is extremely difficult, especially when matching two point clouds with many locally similar features. This paper proposes an optimization method that retains all possible correspondences for each keypoint when matching a partial point cloud to a complete point cloud. These uncertain correspondences are then gradually updated with the estima…
The performance of existing robust homography estimation algorithms is highly dependent on the inlier rate of feature point correspondences. In this paper, we present a novel procedure for homography estimation that is particularly well suited for inlier-poor domains. By utilizing the scale and rotation byproducts created by affine aware feature detectors such as SIFT and SURF, we obtain an initial homography estimate from a single correspondence pair. This estimate allows us to filter the correspondences to an inlier-rich subset for use with a robust estimator. Especially at low inlier rates,…
We address the problem of estimating the 3D pose of a network of cameras for large-environment wide-baseline scenarios, e.g., cameras for construction sites, sports stadiums, and public spaces. This task is challenging since detecting and matching the same 3D keypoint observed from two very different camera views is difficult, making standard structure-from-motion (SfM) pipelines inapplicable. In such circumstances, treating people in the scene as "keypoints" and associating them across different camera views can be an alternative method for obtaining correspondences. Based on this intuition, …
Globally Optimal Solution to the Generalized Relative Pose Estimation Problem using Affine Correspondences
College of Aerospace Science and Engineering, National University of Defense Technology（航空科学与工程学院，国防科技大学）；Global Navigation Satellite System Research Center, Wuhan University（导航卫星系统研究所，武汉大学）
Shanghai Jiao Tong University（上海交通大学）；Zhengzhou University（郑州大学）；Nanjing University（南京大学）；Microsoft Research Asia（微软亚洲研究院）
This paper addresses the problem of handling spatial misalignments due to camera-view changes or human-pose variations in person re-identification. We first introduce a boosting-based approach to learn a correspondence structure which indicates the patch-wise matching probabilities between images from a target camera pair. The learned correspondence structure can not only capture the spatial correspondence pattern between cameras but also handle the viewpoint or human-pose variation in individual images. We further introduce a global-based matching process. It integrates a global matching cons…
An approach is proposed for recovering affine correspondences (ACs) from orientation- and scale-invariant, e.g. SIFT, features. The method calculates the affine parameters consistent with a pre-estimated epipolar geometry from the point coordinates and the scales and rotations which the feature detector obtains. The closed-form solution is given as the roots of a quadratic polynomial equation, thus having two possible real candidates and fast procedure, i.e. <1 millisecond. It is shown, as a possible application, that using the proposed algorithm allows us to estimate a homography for every si…
Australian National University（澳大利亚国立大学）；University of Technology Sydney（悉尼科技大学）
This paper tackles the problem of Cross-view Video-based camera Localization (CVL). The task is to localize a query camera by leveraging information from its past observations, i.e., a continuous sequence of images observed at previous time stamps, and matching them to a large overhead-view satellite image. The critical challenge of this task is to learn a powerful global feature descriptor for the sequential ground-view images while considering its domain alignment with reference satellite images. For this purpose, we introduce CVLNet, which first projects the sequential ground-view images in…
A Minimal Solver for Relative Pose Estimation with Unknown Focal Length from Two Affine Correspondences
School of Aerospace Science and Engineering, National University of Defense Technology（航天科学与工程学院，国防科技大学）；Hunan Provincial Key Laboratory of Image Measurement and Vision Navigation（图像测量与视觉导航省级重点实验室）；Global Navigation Satellite System Research Center（全球导航卫星系统研究中心）；School of Geodesy and Geomatics, Wuhan University（测绘学院，武汉大学）；School of Remote Sensing Information Engineering, Wuhan University（遥感信息工程学院，武汉大学）；School of Software, Henan University（软件学院，河南大学）
MTA SZTAKI（匈牙利科学院计算机与自动化研究所）；Czech Technical University（捷克技术大学）
The technique requires the epipolar geometry to be pre-estimated between each image pair. It exploits the constraints which the camera movement implies, in order to apply a closed-form correction to the parameters of the input affinities. Also, it is shown that the rotations and scales obtained by partially affine-covariant detectors, e.g., AKAZE or SIFT, can be completed to be full affine frames by the proposed algorithm. It is validated both in synthetic experiments and on publicly available real-world datasets that the method always improves the output of the evaluated affine-covariant feat…
Vellore Institute of Technology, Chennai（金奈韦洛尔理工大学）；Birla Institute of Technology and Science, Hyderabad（海得拉巴比尔拉理工学院）；Veermata Jijabai Technological Institute, Mumbai（孟买韦尔马塔·吉贾拜技术学院）；International Institute of Information and Technology, Hyderabad（海得拉巴国际信息技术学院）
With the advent of autonomous vehicles, LiDAR and cameras have become an indispensable combination of sensors. They both provide rich and complementary data which can be used by various algorithms and machine learning to sense and make vital inferences about the surroundings. We propose a novel pipeline and experimental setup to find accurate rigid-body transformation for extrinsically calibrating a LiDAR and a camera. The pipeling uses 3D-3D point correspondences in LiDAR and camera frame and gives a closed form solution. We further show the accuracy of the estimate by fusing point clouds fro…
Fitting model parameters to a set of noisy data points is a common problem in computer vision. In this work, we fit the 6D camera pose to a set of noisy correspondences between the 2D input image and a known 3D environment. We estimate these correspondences from the image using a neural network. Since the correspondences often contain outliers, we utilize a robust estimator such as Random Sample Consensus (RANSAC) or Differentiable RANSAC (DSAC) to fit the pose parameters. When the problem domain, e.g. the space of all 2D-3D correspondences, is large or ambiguous, a single network does not cov…
Australian National University（澳大利亚国立大学）；Data61 – CSIRO（澳大利亚联邦科学与工业研究组织 Data61）
Estimating the 6-DoF pose of a camera from a single image relative to a pre-computed 3D point-set is an important task for many computer vision applications. Perspective-n-Point (PnP) solvers are routinely used for camera pose estimation, provided that a good quality set of 2D-3D feature correspondences are known beforehand. However, finding optimal correspondences between 2D key-points and a 3D point-set is non-trivial, especially when only geometric (position) information is known. Existing approaches to the simultaneous pose and correspondence problem use local optimisation, and are therefo…
RFA Engineering（RFA工程公司）；University of North Dakota（北达科他大学）
In this work we present a unified method of relative camera pose estimation from points and lines correspondences. Given a set of 2D points and lines correspondences in three views, of which two are known, a method has been developed for estimating the camera pose of the third view. Novelty of this algorithm is to combine both points and lines correspondences in the camera pose estimation which enables us to compute relative camera pose with a small number of feature correspondences. Our central idea is to exploit the tri-linear relationship between three views and generate a set of linear equ…
National University of Defense Technology（国防科技大学）；ETH Zürich（苏黎世联邦理工学院）；Graz University of Technology（格拉茨技术大学）；German Aerospace Center（德国航空航天中心）
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 re…
We consider the problem of reconstructing a 3-D scene from a moving camera with high frame rate using the affine projection model. This problem is traditionally known as Affine Structure from Motion (Affine SfM), and can be solved using an elegant low-rank factorization formulation. In this paper, we assume that an accelerometer and gyro are rigidly mounted with the camera, so that synchronized linear acceleration and angular velocity measurements are available together with the image measurements. We extend the standard Affine SfM algorithm to integrate these measurements through the use of i…
A challenge in image based metrology and forensics is intrinsic camera calibration when the used camera is unavailable. The unavailability raises two questions. The first question is how to find the projection model that describes the camera, and the second is to detect incorrect models. In this work, we use off-the-shelf extended PnP-methods to find the model from 2D-3D correspondences, and propose a method for model validation. The most common strategy for evaluating a projection model is comparing different models' residual variances - however, this naive strategy cannot distinguish whether…
In this work, we present a novel and practical approach to address one of the longstanding problems in computer vision: 2D and 3D affine invariant feature matching. Our Grassmannian Graph (GrassGraph) framework employs a two stage procedure that is capable of robustly recovering correspondences between two unorganized, affinely related feature (point) sets. The first stage maps the feature sets to an affine invariant Grassmannian representation, where the features are mapped into the same subspace. It turns out that coordinate representations extracted from the Grassmannian differ by an arbitr…
Scene coordinate regression has become an essential part of current camera re-localization methods. Different versions, such as regression forests and deep learning methods, have been successfully applied to estimate the corresponding camera pose given a single input image. In this work, we propose to regress the scene coordinates pixel-wise for a given RGB image by using deep learning. Compared to the recent methods, which usually employ RANSAC to obtain a robust pose estimate from the established point correspondences, we propose to regress confidences of these correspondences, which allows …
Australian National University（澳大利亚国立大学）；Data61/CSIRO（Data61/联邦科学与工业研究组织）；ShanghaiTech（上海科技大学）
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…
Correspondences between 3D lines and their 2D images captured by a camera are often used to determine position and orientation of the camera in space. In this work, we propose a novel algebraic algorithm to estimate the camera pose. We parameterize 3D lines using Plücker coordinates that allow linear projection of the lines into the image. A line projection matrix is estimated using Linear Least Squares and the camera pose is then extracted from the matrix. An algebraic approach to handle mismatched line correspondences is also included. The proposed algorithm is an order of magnitude faster y…
Accurate registration of 2D imagery with point clouds is a key technology for image-LiDAR point cloud fusion, camera to laser scanner calibration and camera localization. Despite continuous improvements, automatic registration of 2D and 3D data without using additional textured information still faces great challenges. In this paper, we propose a new 2D-3D registration method to estimate 2D-3D line feature correspondences and the camera pose in untextured point clouds of structured environments. Specifically, we first use geometric constraints between vanishing points and 3D parallel lines to …
Australian National University（澳大利亚国立大学）；Australian Centre for Robotic Vision（澳大利亚机器人视觉中心）；Baidu Research（百度研究院）
Conventional absolute camera pose via a Perspective-n-Point (PnP) solver often assumes that the correspondences between 2D image pixels and 3D points are given. When the correspondences between 2D and 3D points are not known a priori, the task becomes the much more challenging blind PnP problem. This paper proposes a deep CNN model which simultaneously solves for both the 6-DoF absolute camera pose and 2D--3D correspondences. Our model comprises three neural modules connected in sequence. First, a two-stream PointNet-inspired network is applied directly to both the 2D image keypoints and the 3…
College of Aerospace Science and Engineering, National University of Defense Technology（国防科技大学航天科学与工程学院）
The point correspondence (PC) and affine correspondence (AC) are widely used for relative pose estimation. An AC consists of a PC across two views and an affine transformation between the small patches around this PC. Previous work demonstrates that one AC generally provides three independent constraints for relative pose estimation. For multi-camera systems, there is still not any AC-based minimal solver for general relative pose estimation. To deal with this problem, we propose a complete solution to relative pose estimation from two ACs for multi-camera systems, consisting of a series of mi…
We provide criteria for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters. These criteria reduce the projection problem to a certain modification of the equivalence problem of planar curves under affine and projective transformations. The latter problem can be addressed using Cartan's moving frame method. This leads to a novel algorithmic solution of the projection problem for curves. The computational advantage of the algorithms presented here, in comparison to algorithms based on a straightforwar…
Eotvos Lorand University（厄特沃什·罗兰大学）；Czech Technical University in Prague（捷克理工大学）；MTA SZTAKI（匈牙利科学院计算机科学与控制研究所）
A new closed-form solver is proposed minimizing the algebraic error optimally, in the least-squares sense, to estimate the relative planar motion of two calibrated cameras. The main objective is to solve the over-determined case, i.e., when a larger-than-minimal sample of point correspondences is given - thus, estimating the motion from at least three correspondences. The algorithm requires the camera movement to be constrained to a plane, e.g. mounted to a vehicle, and the image plane to be orthogonal to the ground. The solver obtains the motion parameters as the roots of a 6-th degree polyno…
Australian Centre for Field Robotics（澳大利亚野外机器人学中心）；University of Sydney（悉尼大学）
This paper proposes an automated method to obtain the extrinsic calibration parameters between a camera and a 3D lidar with as low as 16 beams. We use a checkerboard as a reference to obtain features of interest in both sensor frames. The calibration board centre point and normal vector are automatically extracted from the lidar point cloud by exploiting the geometry of the board. The corresponding features in the camera image are obtained from the camera's extrinsic matrix. We explain the reasons behind selecting these features, and why they are more robust compared to other possibilities. To…
Practical solutions to the relative pose of three calibrated cameras
Visual Recognition Group, Faculty of Electrical Engineering, Czech Technical University in Prague（视觉识别组，电气工程系，布拉格捷克技术大学）；Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava（数学、物理和信息学系，布拉迪斯拉发康门尼乌斯大学）；ETH Zürich (Zurich), HUN-REN SZTAKI (Budapest)（苏黎世ETH，匈牙利-中国SZTAKI（布达佩斯））；Czech Institute of Informatics, Robotics and Cybernetics, Czech Technical University in Prague（捷克信息学、机器人学与自动控制研究所，布拉格捷克技术大学）
LIGM（LIGM实验室）；École des Ponts（巴黎路桥学院）；Univ Gustave Eiffel（Gustave Eiffel大学）；CNRS（法国国家科学研究中心）；IMS（IMS实验室）；University of Bordeaux（波尔多大学）；Bordeaux INP（波尔多国立综合理工学院）
Absolute camera pose estimation is usually addressed by sequentially solving two distinct subproblems: First a feature matching problem that seeks to establish putative 2D-3D correspondences, and then a Perspective-n-Point problem that minimizes, with respect to the camera pose, the sum of so-called Reprojection Errors (RE). We argue that generating putative 2D-3D correspondences 1) leads to an important loss of information that needs to be compensated as far as possible, within RE, through the choice of a robust loss and the tuning of its hyperparameters and 2) may lead to an RE that conveys …
University College London（伦敦大学学院）；Snap Inc.（色拉布公司）
We present To The Point (TTP), a method for reconstructing 3D objects from a single image using 2D to 3D correspondences learned from weak supervision. We recover a 3D shape from a 2D image by first regressing the 2D positions corresponding to the 3D template vertices and then jointly estimating a rigid camera transform and non-rigid template deformation that optimally explain the 2D positions through the 3D shape projection. By relying on 3D-2D correspondences we use a simple per-sample optimization problem to replace CNN-based regression of camera pose and non-rigid deformation and thereby o…
