Simultaneous Localization and Mapping using RGB-D cameras has been a fertile research topic in the latest decade, due to the suitability of such sensors for indoor robotics. In this paper we propose a direct RGB-D SLAM algorithm with state-of-the-art accuracy and robustness at a los cost. Our experiments in the RGB-D TUM dataset [34] effectively show a better accuracy and robustness in CPU real time than direct RGB-D SLAM systems that make use of the GPU. The key ingredients of our approach are mainly two. Firstly, the combination of a semi-dense photometric and dense geometric error for the pose tracking (see Figure 1), which we demonstrate to be the most accurate alternative. And secondly, a model of the multi-view constraints and their errors in the mapping and tracking threads, which adds extra information over other approaches. We release the open-source implementation of our approach 1 . The reader is referred to a video with our results 2 for a more illustrative visualization of its performance.
@cite_4 proposes to use the inverse depth in the minimization of the geometric reprojection error. We evaluate this parametrization in our system.
@cite_4
1639700302
The technique of "renormalization" for geometric estimation attracted much attention when it was proposed in early 1990s for having higher accuracy than any other then known methods. Later, it was replaced by minimization of the reprojection error. This paper points out that renormalization can be modified so that it outperforms reprojection error minimization. The key fact is that renormalization directly specifies equations to solve, just as the "estimation equation" approach in statistics, rather than minimizing some cost. Exploiting this fact, we modify the problem so that the solution has zero bias up to high order error terms; we call the resulting scheme hyper-renormalization. We apply it to ellipse fitting to demonstrate that it indeed surpasses reprojection error minimization. We conclude that it is the best method available today. This paper addresses the problem of image-based surface reconstruction. The main contribution is the computation of the exact derivative of the reprojection error functional. This allows its rigorous minimization via gradient descent surface evolution. The main difficulty has been to correctly take into account the visibility changes that occur when the surface moves. A geometric and analytical study of these changes is presented and used for the computation of derivative. Our analysis shows the strong influence that the movement of the contour generators has on the reprojection error. As a consequence, during the proper minimization of the reprojection error, the contour generators of the surface are automatically moved to their correct location in the images. Therefore, current methods adding additional silhouettes or apparent contour constraints to ensure this alignment can now be understood and justified by a single criterion: the reprojection error. In this paper we present a dense visual odometry system for RGB-D cameras performing both photometric and geometric error minimisation to estimate the camera motion between frames. Contrary to most works in the literature, we parametrise the geometric error by the inverse depth instead of the depth, which translates into a better fit of the distribution of the geometric error to the used robust cost functions. We also provide a unified evaluation under the same framework of different estimators and ways of computing the scale of the residuals which can be found spread along the related literature. For the comparison of our approach with state-of-the-art approaches we use the popular dataset from the TUM for RGB-D benchmarking. Our approach shows to be competitive with state-of-the-art methods in terms of drift in meters per second, even compared to methods performing loop closure too. When comparing to approaches performing pure odometry like ours, our method outperforms them in the majority of the tested datasets. Additionally we show that our approach is able to work in real time and we provide a qualitative evaluation on our own sequences showing a low drift in the 3D reconstructions. We introduce gvnn, a neural network library in Torch aimed towards bridging the gap between classic geometric computer vision and deep learning. Inspired by the recent success of Spatial Transformer Networks, we propose several new layers which are often used as parametric transformations on the data in geometric computer vision. These layers can be inserted within a neural network much in the spirit of the original spatial transformers and allow backpropagation to enable end-to-end learning of a network involving any domain knowledge in geometric computer vision. This opens up applications in learning invariance to 3D geometric transformation for place recognition, end-to-end visual odometry, depth estimation and unsupervised learning through warping with a parametric transformation for image reconstruction error. We present a new parametrization for point features within monocular simultaneous localization and mapping (SLAM) that permits efficient and accurate representation of uncertainty during undelayed initialization and beyond, all within the standard extended Kalman filter (EKF). The key concept is direct parametrization of the inverse depth of features relative to the camera locations from which they were first viewed, which produces measurement equations with a high degree of linearity. Importantly, our parametrization can cope with features over a huge range of depths, even those that are so far from the camera that they present little parallax during motion---maintaining sufficient representative uncertainty that these points retain the opportunity to "come in'' smoothly from infinity if the camera makes larger movements. Feature initialization is undelayed in the sense that even distant features are immediately used to improve camera motion estimates, acting initially as bearing references but not permanently labeled as such. The inverse depth parametrization remains well behaved for features at all stages of SLAM processing, but has the drawback in computational terms that each point is represented by a 6-D state vector as opposed to the standard three of a Euclidean XYZ representation. We show that once the depth estimate of a feature is sufficiently accurate, its representation can safely be converted to the Euclidean XYZ form, and propose a linearity index that allows automatic detection and conversion to maintain maximum efficiency---only low parallax features need be maintained in inverse depth form for long periods. We present a real-time implementation at 30 Hz, where the parametrization is validated in a fully automatic 3-D SLAM system featuring a handheld single camera with no additional sensing. Experiments show robust operation in challenging indoor and outdoor environments with a very large ranges of scene depth, varied motion, and also real time 360deg loop closing. Accurate recovery of 3D geometrical surfaces from calibrated 2D multi-view images is a fundamental yet active research area in computer vision. Despite the steady progress in multi-view stereo (MVS) reconstruction, many existing methods are still limited in recovering fine-scale details and sharp features while suppressing noises, and may fail in reconstructing regions with less textures. To address these limitations, this paper presents a detail-preserving and content-aware variational (DCV) MVS method, which reconstructs the 3D surface by alternating between reprojection error minimization and mesh denoising. In reprojection error minimization, we propose a novel inter-image similarity measure, which is effective to preserve fine-scale details of the reconstructed surface and builds a connection between guided image filtering and image registration. In mesh denoising, we propose a content-aware @math -minimization algorithm by adaptively estimating the @math value and regularization parameters. Compared with conventional isotropic mesh smoothing approaches, the proposed method is much more promising in suppressing noise while preserving sharp features. Experimental results on benchmark data sets demonstrate that our DCV method is capable of recovering more surface details, and obtains cleaner and more accurate reconstructions than the state-of-the-art methods. In particular, our method achieves the best results among all published methods on the Middlebury dino ring and dino sparse data sets in terms of both completeness and accuracy. In this paper, we present a monocular visual-inertial odometry algorithm which, by directly using pixel intensity errors of image patches, achieves accurate tracking performance while exhibiting a very high level of robustness. After detection, the tracking of the multilevel patch features is closely coupled to the underlying extended Kalman filter (EKF) by directly using the intensity errors as innovation term during the update step. We follow a purely robocentric approach where the location of 3D landmarks are always estimated with respect to the current camera pose. Furthermore, we decompose landmark positions into a bearing vector and a distance parametrization whereby we employ a minimal representation of differences on a corresponding σ-Algebra in order to achieve better consistency and to improve the computational performance. Due to the robocentric, inverse-distance landmark parametrization, the framework does not require any initialization procedure, leading to a truly power-up-and-go state estimation system. The presented approach is successfully evaluated in a set of highly dynamic hand-held experiments as well as directly employed in the control loop of a multirotor unmanned aerial vehicle (UAV). Motivated by a Bayesian vision of the 3D multi-view reconstruction from images problem, we propose a dense 3D reconstruction technique that jointly refines the shape and the camera parameters of a scene by minimizing the photometric reprojection error between a generated model and the observed images, hence considering all pixels in the original images. The minimization is performed using a gradient descent scheme coherent with the shape representation (here a triangular mesh), where we derive evolution equations in order to optimize both the shape and the camera parameters. This can be used at a last refinement step in 3D reconstruction pipelines and helps improving the 3D reconstruction's quality by estimating the 3D shape and camera calibration more accurately. Examples are shown for multi-view stereo where the texture is also jointly optimized and improved, but could be used for any generative approaches dealing with multi-view reconstruction settings (ie depth map fusion, multi-view photometric stereo). We introduce a new approach for estimating a fine grained 3D shape and continuous pose of an object from a single image. Given a training set of view exemplars, we learn and select appearance-based discriminative parts which are mapped onto the 3D model through a facility location optimization. The training set of 3D models is summarized into a set of basis shapes from which we can generalize by linear combination. Given a test image, we detect hypotheses for each part. The main challenge is to select from these hypotheses and compute the 3D pose and shape coefficients at the same time. To achieve this, we optimize a function that considers simultaneously the appearance matching of the parts as well as the geometric reprojection error. We apply the alternating direction method of multipliers (ADMM) to minimize the resulting convex function. Our main and novel contribution is the simultaneous solution for part localization and detailed 3D geometry estimation by maximizing both appearance and geometric compatibility with convex relaxation. An emerging problem in computer vision is the reconstruction of 3D shape and pose of an object from a single image. Hitherto, the problem has been addressed through the application of canonical deep learning methods to regress from the image directly to the 3D shape and pose labels. These approaches, however, are problematic from two perspectives. First, they are minimizing the error between 3D shapes and pose labels - with little thought about the nature of this “label error” when reprojecting the shape back onto the image. Second, they rely on the onerous and ill-posed task of hand labeling natural images with respect to 3D shape and pose. In this paper we define the new task of pose-aware shape reconstruction from a single image, and we advocate that cheaper 2D annotations of objects silhouettes in natural images can be utilized. We design architectures of pose-aware shape reconstruction which reproject the predicted shape back on to the image using the predicted pose. Our evaluation on several object categories demonstrates the superiority of our method for predicting pose-aware 3D shapes from natural images. This article proposes a variational multi-view stereo vision method based on meshes for recovering 3D scenes (shape and radiance) from images. Our method is based on generative models and minimizes the reprojection error (difference between the observed images and the images synthesized from the reconstruction). Our contributions are twofold. 1) For the first time, we rigorously compute the gradient of the reprojection error for non smooth surfaces defined by discrete triangular meshes. The gradient correctly takes into account the visibility changes that occur when a surface moves; this forces the contours generated by the reconstructed surface to perfectly match with the apparent contours in the input images. 2) We propose an original modification of the Lambertian model to take into account deviations from the constant brightness assumption without explicitly modelling the reflectance properties of the scene or other photometric phenomena involved by the camera model. Our method is thus able to recover the shape and the diffuse radiance of non Lambertian scenes. We present a low-drift visual odometry algorithm that separately estimates rotational and translational motion from lines, planes, and points found in RGB-D images. Previous methods estimate drift-free rotational motion from structural regularities to reduce drift in the rotation estimate, which is the primary source of positioning inaccuracy in visual odometry. However, multiple orthogonal planes are required to be visible throughout the entire motion estimation process; otherwise, these VO approaches fail. We propose a new approach to estimate drift-free rotational motion jointly from both lines and planes by exploiting environmental regularities. We track the spatial regularities with an efficient SO(3)-manifold constrained mean shift algorithm. Once the drift-free rotation is found, we recover the translational motion from all tracked points with and without depth by minimizing the de-rotated reprojection error. We compare the proposed algorithm to other state-of-the-art visual odometry methods on a variety of RGB-D datasets (including especially challenging pure rotations) and demonstrate improved accuracy and lower drift error. Virtual immersive environments or telepresence setups often consist of multiple cameras that have to be calibrated, We present a convenient method for doing this. The minimum is three cameras, but there is no upper limit. The method is fully automatic and a freely moving bpdght spot is the only calibration object, A set of virtual 3D points is made by waving the bright spot through the working volume. Its projections are found with subpixel precision and verified by a robust RANSAC analysis. The cameras do not have to see all points; only reasonable overlap between camera subgroups is necessary. Projective structures are computed via rank-4 factorization and the Euclidean stratification is done by imposing geometric constraints. This linear estimate initializes a postprocessing computation of nonlinear distortion, which is also fully automatic. We suggest a trick on how to use a very ordinary laser pointer as the calibration object. We show that it is possible to calibrate an immersive virtual environment with 16 cameras in less than 60 minutes reaching about 1 5 pixel reprojection error, The method has been successfully tested on numerous multicamera environments using varying numbers of cameras of varying quality. In this paper, we revisit the classical perspective-n-point (PnP) problem, and propose the first non-iterative O(n) solution that is fast, generally applicable and globally optimal. Our basic idea is to formulate the PnP problem into a functional minimization problem and retrieve all its stationary points by using the Gr"obner basis technique. The novelty lies in a non-unit quaternion representation to parameterize the rotation and a simple but elegant formulation of the PnP problem into an unconstrained optimization problem. Interestingly, the polynomial system arising from its first-order optimality condition assumes two-fold symmetry, a nice property that can be utilized to improve speed and numerical stability of a Grobner basis solver. Experiment results have demonstrated that, in terms of accuracy, our proposed solution is definitely better than the state-of-the-art O(n) methods, and even comparable with the reprojection error minimization method. Dense semantic 3D reconstruction is typically formulated as a discrete or continuous problem over label assignments in a voxel grid, combining semantic and depth likelihoods in a Markov Random Field framework. The depth and semantic information is incorporated as a unary potential, smoothed by a pairwise regularizer. However, modelling likelihoods as a unary potential does not model the problem correctly leading to various undesirable visibility artifacts. We propose to formulate an optimization problem that directly optimizes the reprojection error of the 3D model with respect to the image estimates, which corresponds to the optimization over rays, where the cost function depends on the semantic class and depth of the first occupied voxel along the ray. The 2-label formulation is made feasible by transforming it into a graph-representable form under QPBO relaxation, solvable using graph cut. The multi-label problem is solved by applying α-expansion using the same relaxation in each expansion move. Our method was indeed shown to be feasible in practice, running comparably fast to the competing methods, while not suffering from ray potential approximation artifacts. This book introduces state-of-the-art verification techniques for real time embedded systems, based on the inverse method for parametric timed automata. It reviews popular formalisms for the specification and the verification of timed concurrent systems, and in particular timed automata and several extensions such as timed automata equipped with stopwatches, linear hybrid automata and affine hybrid automata. The inverse method is introduced, and its interest for guaranteeing robustness in real time systems is shown. Then it is shown how an iteration of the inverse method can solve the good parameters problem for parametric timed automata, by computing a behavioral cartography of the system. Different extensions are proposed, in particular for hybrid systems, and for applications to scheduling problems using timed automata with stopwatches. Various examples, both from the literature and from the industry, illustrate the techniques throughout the book. In particular, we perform parametric verification of abstractions of a memory circuit sold by the chipset manufacturer ST-Microelectronics, as well as of the prospective flight control system of the next generation of spacecrafts designed by ASTRIUM Space Transportation. We present a novel method for recovering the 3D structure and scene flow from calibrated multi-view sequences. We propose a 3D point cloud parametrization of the 3D structure and scene flow that allows us to directly estimate the desired unknowns. A unified global energy functional is proposed to incorporate the information from the available sequences and simultaneously recover both depth and scene flow. The functional enforces multi-view geometric consistency and imposes brightness constancy and piece-wise smoothness assumptions directly on the 3D unknowns. It inherently handles the challenges of discontinuities, occlusions, and large displacements. The main contribution of this work is the fusion of a 3D representation and an advanced variational framework that directly uses the available multi-view information. The minimization of the functional is successfully obtained despite the non-convex optimization problem. The proposed method was tested on real and synthetic data. This paper proposes an adaptive color-guided autoregressive (AR) model for high quality depth recovery from low quality measurements captured by depth cameras. We observe and verify that the AR model tightly fits depth maps of generic scenes. The depth recovery task is formulated into a minimization of AR prediction errors subject to measurement consistency. The AR predictor for each pixel is constructed according to both the local correlation in the initial depth map and the nonlocal similarity in the accompanied high quality color image. We analyze the stability of our method from a linear system point of view, and design a parameter adaptation scheme to achieve stable and accurate depth recovery. Quantitative and qualitative evaluation compared with ten state-of-the-art schemes show the effectiveness and superiority of our method. Being able to handle various types of depth degradations, the proposed method is versatile for mainstream depth sensors, time-of-flight camera, and Kinect, as demonstrated by experiments on real systems. This paper presents a spline-based solution method for the inverse kinematics of hyper-redundant manipulators. The reference or backbone curve, that describes the macroscopic geometric shape of the manipulator is modelled by cubic and quintic piecewise parametric spline segments. A procedure for the coordinate frame distribution is proposed that allows any desirable rotation to be deployed about the backbone curve. Moreover, control points are used to determine the optimum shape and to change the length of the manipulator. The proposed solution method is general and applicable to non-extensible as well as extensible planar or spatial hyper-redundant manipulators with different morphologies. The concept of depth from focus involves calculating distances to points in an observed scene by modeling the effect that the camera's focal parameters have on images acquired with a small depth of field. This technique is passive and requires only a single camera. The most difficult segment of calculating depth from focus is deconvolving the defocus operator from the scene and modeling it. Most current methods for determining the defocus operator employ inverse filtering. The authors reveal some fundamental problems with inverse filtering: inaccuracies in finding the frequency domain representation, windowing effects, and border effects. A general, matrix-based method using regularization is presented, which eliminates these problems. The new method is confirmed experimentally, with the results showing an RMS error of 1.3 .