Computing camera focal length by zooming a single point

In this paper we present a novel simple procedure to compute the focal length of a camera. The method is based on zooming in and out only a single point. The same approach allows computing the principal point when only two points are available on a pair of images surveyed with a different focal length. Experimental results show that the method is as accurate as classical full calibration methods. Moreover, its application to augmented reality produces more accurate results than those obtained when the simple pin-hole model is considered.     

Solving camera parameters from the perspective projection of a parameterized curve

Given the two-dimensional perspective projection of a known conic or polygon of unknown size and position in three-dimensional space, we show how to determine the camera look angles relative to the plane where the curve lies. Separate cases are discussed for conic and polygons. We then show that this technique can be used to solve for any planar or nonplanar curves, as long as they can be represented in parametric forms.     

Two-layer dual gait generative models for human motion estimation from a single camera

This paper presents a two-layer gait representation framework for video-based human motion estimation that extends our recent dual gait generative models, visual gait generative model (VGGM) and kinematic gait generative model (KGGM), with a new capability of part-whole gait modeling. Specifically, the idea of gait manifold learning is revisited to capture the gait variability among different individuals at both whole and part levels. A key issue is the selection of an appropriate distance metric to evaluate the dissimilarity between two gaits (either at whole or part levels) that determines an optimal manifold topology. Several metrics are studied and compared in terms of their effectiveness for gait manifold learning at both whole and part levels. This work involves one whole-based and two part-level gait manifolds by which three pairs of KGGM and VGGM can be learned and integrated for part-whole gait modeling. Moreover, a two-stage Monte Carlo Markov Chain (MCMC) inference algorithm is developed for video-based part-whole motion estimation. The proposed algorithm is tested on the HumanEva data and reaches state-of-art results.     

A minimal solution for relative pose with unknown focal length

Assume that we have two perspective images with known intrinsic parameters except for an unknown common focal length. It is a minimally constrained problem to find the relative orientation between the two images given six corresponding points. To this problem which to the best of our knowledge was unsolved we present an efficient solver. Through numerical experiments we demonstrate that the algorithm is correct, numerically stable and useful. The solutions are found through eigen-decomposition of a 15×15 matrix. The matrix itself is generated in closed form.     

一种基于单视图的可变焦相机标定方法

提出了一种新的可变焦相机的标定方法。它采用至少6个已知空间点用最小二乘获取投影矩阵的最优解,在计算投影矩阵的基础上,利用旋转矩阵的正交性和摄像机参数之间的约束关系,用单幅图像即可实现摄像机内外参数的恢复。模拟和真实实验结果均表明了本文算法的可行性和鲁棒性。     

A branch-and-bound algorithm for globally optimal camera pose and focal length

This paper considers the problem of finding the global optimum of the camera rotation, translation and the focal length given a set of 2D–3D point pairs. The global solution is obtained under the L-infinity optimality by a branch-and-bound algorithm. To obtain the goal, we firstly extend the previous branch-and-bound formulation and show that the image space error (pixel distance) may be used instead of the angular error. Then, we present that the problem of camera pose plus focal length given the rotation is a quasi-convex problem. This provides a derivation of a novel inequality for the branch-and-bound algorithm for our problem. Finally, experimental results with synthetic and real data are provided.     

Fast and robust absolute camera pose estimation with known focal length

Some 3D computer vision techniques such as structure from motion (SFM) and augmented reality (AR) depend on a specific perspective-n-point (PnP) algorithm to estimate the absolute camera pose. However, existing PnP algorithms are difficult to achieve a good balance between accuracy and efficiency, and most of them do not make full use of the internal camera information such as focal length. In order to attack these drawbacks, we propose a fast and robust PnP (FRPnP) method to calculate the absolute camera pose for 3D compute vision. In the proposed FRPnP method, we firstly formulate the PnP problem as the optimization problem in the null space that can avoid the effects of the depth of each 3D point. Secondly, we can easily get the solution by the direct manner using singular value decomposition. Finally, the accurate information of camera pose can be obtained by optimization strategy. We explore four ways to evaluate the proposed FRPnP algorithm with synthetic dataset, real images, and apply it in the AR and SFM system. Experimental results show that the proposed FRPnP method can obtain the best balance between computational cost and precision, and clearly outperforms the state-of-the-art PnP methods.

     

Localization of a door handle of unknown geometry using a single camera for door-opening with a mobile manipulator

Door-opening by a robot is a challenging task. Current approaches to localization of door handles are only applicable to certain types of handles or require the use of learning algorithms. In this paper, a method for localizing a door handle of unknown geometry is presented. The localization is performed by fitting a bounding box around the door handle. The proposed method extracts a three-dimensional (3D) point cloud using the optical flow calculated from images taken with a single CCD camera. The point cloud is then segmented to separate the door and the handle points. A?bounding box is fitted to the door handle. The box is oriented along the principal components of the handle points after they are projected into the plane of the door, and the normal to the door. The box performs the function of both localizing the handle and estimating its pose. Experiments performed on a set of various door handles demonstrated the effectiveness of the proposed method.     

Adaptive control design for a class of nonsmooth nonlinear systems with matched and linearly parameterized uncertainty

This paper presents an adaptive control design for a class of nonsmooth nonlinear systems with matched uncertainty, which is linearly parameterized with a known discontinuous function. The design framework is based on the concept of the Filippov solution as the classical Lyapunov theory for smooth systems cannot be applied to establish the stability of the adaptive control system due to the presence of the discontinuity. It is proved that as an adaptive control system, the global Lyapunov stability with the convergence of the state of the controlled system to the origin can be achieved by evaluating the monotonicity of the Lyapunov function in the state space, particularly on the discontinuous surface, while the uniqueness of the solution of the closed‐loop system is not necessarily guaranteed. Some interesting numerical examples are demonstrated with simulation results. Copyright © 2008 John Wiley & Sons, Ltd.     

Automatic 3D model reconstruction of cutting tools from a single camera

Collision detection by machining simulation requires the 3D models of rotating cutters. However, the 3D models of a cutter and holder are not always available. In this paper, a new method is proposed to design an automatic vision-based 3D modeling system, which is able to quickly reconstruct the 3D model of a cutter and holder when they are installed onto the spindle. Only a single camera is mounted on the machine tool to capture the image of the rotating cutter and holder. By viewing the rotating cutter and holder as an object of surface of revolution, the contour of the imaged cutter and holder can be used to reconstruct the 3D model as a stack of circular cross-sections. Then the complete generating function of the cutter and holder can be recovered from the cross-sections. Finally, the 3D model of the cutter is built by rotating the generating function around the spindle axis. The effectiveness and accuracy of the proposed method are verified by experiments on-machine using 12 kinds of cutters and holders, which can satisfy the requirement of collision detection.     

Three kinds of particles on a single rationally parameterized world line

We consider the light cone (‘retardation’) equation (LCE) of an inertially moving observer and a single world line parameterized by arbitrary rational functions. Then a set of apparent copies, R- or C-particles, defined by (real or complex conjugate) roots of the LCE will be detected by the observer. For any rational world line the collective R-C dynamics is manifestly Lorentz-invariant and conservative; the latter property follows directly from the structure of Vieta formulas for the LCE roots. In particular, two Lorentz invariants, the square of total 4-momentum and total rest mass, are distinct and both integer-valued. Asymptotically, at large values of the observer’s proper time, one distinguishes three types of LCE roots and associated R-C particles, with specific locations and evolutions; each of three kinds of particles can assemble into compact large groups—clusters. Throughout the paper, we make no use of differential equations of motion, field equations, etc.: the collective R-C dynamics is purely algebraic.     

未知主点条件的相机焦距自标定方法

对于双目相机焦距自标定,当前研究方法均假定相机主点位置已知,而相机主点在实际中却通常是未知的,提出一种主点和场景均未知的条件下相机焦距自标定的新方法,通过严格的数学分析表明相机的坐标系尺度对焦距标定具有重要影响,并在坐标系尺度影响的定量分析的基础上提出了一种选择合适的坐标系尺度算法。模拟和实际实验都验证了坐标系尺度的重要性,且该方法较传统方法可获得更好的标定精度。     

Self-calibration with varying focal length from two images obtained by a stereo head

The self-calibration approach based on the absolute conic or its dual, the absolute dual quadric, has the merit of allowing the intrinsic camera parameters to vary in image sequence. In this paper, we show that certain linear equations resulting from the infinity homography can be added to a system of originally undetermined linear equations to find the absolute dual quadric for a stereo head. The special stereo configurations considered here allow one camera to rotate around either one or two of the coordinate axes defined by another camera. Experiments with synthetic images show that satisfactory results can be obtained with only the proposed linear methods. For real images obtained with non-ideal stereo configurations, and possibly with measurement noises, results obtained from the proposed linear methods may serve as reasonable initial guesses for some non-linear optimization procedure.     

Human tracking from single RGB-D camera using online learning

Human detection and tracking is an essential component in several robotics applications, especially in indoor built environments where humans and robots are expected to coexist or collaborate. Due to their low cost and capability to capture both color and depth data, RGB-D cameras have shown significant promise in human detection and tracking for robotic applications. In this paper, a new human tracking method is proposed to detect and track a specific individual from a single RGB-D sensor using online learning classifiers with no ground plane assumption. Given a previous target human position, a candidate sampling method is designed to find potential positive samples while negative samples are obtained by a random sampling process. The kernelized Support Vector Machine (SVM) is employed as the online classifier to recognize the target human and updated using both the positive and negative examples. The experimental results on six RGB-D videos of a public dataset demonstrate that the proposed method achieves higher success rates compared to a 2D tracker and a 3D human detection method at a frame rate of 3.8 fps, and is capable of efficiently retrieving the target human following intermittent occlusion.     

Switching adaptive learning control for nonlinearly parameterized systems with disturbance of unknown periods

In this paper, a logic‐based switching adaptive learning control mechanism is proposed for a class of nonlinearly parameterized systems with disturbance of unknown periods. The switching algorithms include two parts: one is to stabilize the nonlinearly parameterized uncertainties, the other is to learn the periodic bounded disturbance. An adaptive control method with fully saturated periodic adaptation law is presented to take advantage of the periodic and bounded property of the disturbance. It is shown that under the proposed control designs, the asymptotic convergence is ensured irrespective of initial conditions with all the signals in the closed‐loop system bounded. An illustrative example is given to show the validity of the switching adaptive learning control. Copyright © 2014 John Wiley & Sons, Ltd.     

Towards the standardized exchange of parameterized feature-based CAD models

The paper describes the status of work aimed at extending the international standard ISO 10303 (STEP) to permit the exchange of parameterized feature-based models between different CAD systems, in terms of the constructional history of the models concerned. Such procedural models have the advantage of being easy to edit following an exchange, by contrast with the models that can be exchanged using current STEP methodology, which prove to be difficult or impossible to edit in the receiving system. The use of the approach described has already been demonstrated in the exchange of realistic procedural shape models of mechanical parts, and the paper includes a brief account of some of the tests performed and the projected benefits of the use of this extension of STEP technology.     

Face recognition from a single training image under arbitrary unknown lighting using spherical harmonics

In this paper, we propose two novel methods for face recognition under arbitrary unknown lighting by using spherical harmonics illumination representation, which require only one training image per subject and no 3D shape information. Our methods are based on the result which demonstrated that the set of images of a convex Lambertian object obtained under a wide variety of lighting conditions can be approximated accurately by a low-dimensional linear subspace. We provide two methods to estimate the spherical harmonic basis images spanning this space from just one image. Our first method builds the statistical model based on a collection of 2D basis images. We demonstrate that, by using the learned statistics, we can estimate the spherical harmonic basis images from just one image taken under arbitrary illumination conditions if there is no pose variation. Compared to the first method, the second method builds the statistical models directly in 3D spaces by combining the spherical harmonic illumination representation and a 3D morphable model of human faces to recover basis images from images across both poses and illuminations. After estimating the basis images, we use the same recognition scheme for both methods: we recognize the face for which there exists a weighted combination of basis images that is the closest to the test face image. We provide a series of experiments that achieve high recognition rates, under a wide range of illumination conditions, including multiple sources of illumination. Our methods achieve comparable levels of accuracy with methods that have much more onerous training data requirements. Comparison of the two methods is also provided.