基于二次曲线的纯旋转摄像机自标定

研究探讨了一种基于平面二次曲线的纯旋转摄像机自标定方法.在不同的方位拍摄 三幅或三幅以上图像,每幅图像至少包含两个空间平面二次曲线、或两个二次曲面、或一个平 面二次曲线与一个二次曲面的投影,利用图像之间的二次曲线对应关系,可以确定摄像机的 内参数矩阵,同时可以获得摄像机不同方位之间的旋转矩阵.由于使用的定标基元为二次曲 线,是较点和直线包含更多信息的基元,因而基元之间的匹配容易自动实现,并有助于提高标 定算法的鲁棒性和在线实时性.模拟实验和真实图像实验表明文中所介绍的方法是可行的.     

Conic reconstruction and correspondence from two views

Conics are widely accepted as one of the most fundamental image features together with points and line segments. The problem of space reconstruction and correspondence of two conics from two views is addressed in this paper. It is shown that there are two independent polynomial conditions on the corresponding pair of conics across two views, given the relative orientation of the two views. These two correspondence conditions are derived algebraically and one of them is shown to be fundamental in establishing the correspondences of conics. A unified closed-form solution is also developed for both projective reconstruction of conics in space from two uncalibrated camera views and metric reconstruction from two calibrated camera views. Experiments are conducted to demonstrate the discriminality of the correspondence conditions and the accuracy and stability of the reconstruction both for simulated and real images     

Fitting conics to paracatadioptric projections of lines

The paracatadioptric camera is one of the most popular panoramic systems currently available in the market. It provides a wide field of view by combining a parabolic shaped mirror with a camera inducing an orthographic projection. Previous work proved that the paracatadioptric projection of a line is a conic curve, and that the sensor can be fully calibrated from the image of three or more lines. However, the estimation of the conic curves where the lines are projected is hard to accomplish because of the partial occlusion. In general only a small arc of the conic is visible in the image, and conventional conic fitting techniques are unable to accurately estimate the curve. The present work provides methods to overcome this problem. We show that in uncalibrated paracatadioptric views a set of conic curves is a set of line projections if and only if certain properties are verified. These properties are used to constrain the search space and correctly estimate the curves. The conic fitting is solved naturally by an eigensystem whenever the camera is skewless and the aspect ratio is known. For the general situation the line projections are estimated using non-linear optimization. The set of paracatadioptric lines is used in a geometric construction to determine the camera parameters and calibrate the system. We also propose an algorithm to estimate the conic locus corresponding to a line projection in a calibrated paracatadioptric image. It is proved that the set of all line projections is a hyperplane in the space of conic curves. Since the position of the hyperplane depends only on the sensor parameters, the accuracy of the estimation can be improved by constraining the search to conics lying in this subspace. We show that the fitting problem can be solved by an eigensystem, which leads to a robust and computationally efficient method for paracatadioptric line estimation.     

Self-Calibration of a Moving Camera from Point Correspondences and Fundamental Matrices

We address the problem of estimating three-dimensional motion, and structure from motion with an uncalibrated moving camera. We show that point correspondences between three images, and the fundamental matrices computed from these point correspondences, are sufficient to recover the internal orientation of the camera (its calibration), the motion parameters, and to compute coherent perspective projection matrices which enable us to reconstruct 3-D structure up to a similarity. In contrast with other methods, no calibration object with a known 3-D shape is needed, and no limitations are put upon the unknown motions to be performed or the parameters to be recovered, as long as they define a projective camera.The theory of the method, which is based on the constraint that the observed points are part of a static scene, thus allowing us to link the intrinsic parameters and the fundamental matrix via the absolute conic, is first detailed. Several algorithms are then presented, and their performances compared by means of extensive simulations and illustrated by several experiments with real images.     

Identical Projective Geometric Properties of Central Catadioptric Line Images and Sphere Images with Applications to Calibration

Central catadioptric cameras are imaging devices that use mirrors to enhance the field of view while preserving a single effective viewpoint. Lines and spheres in space are all projected into conics in the central catadioptric image planes, and such conics are called line images and sphere images, respectively. We discovered that there exists an imaginary conic in the central catadioptric image planes, defined as the modified image of the absolute conic (MIAC), and by utilizing the MIAC, the novel identical projective geometric properties of line images and sphere images may be exploited: Each line image or each sphere image is double-contact with the MIAC, which is an analogy of the discovery in pinhole camera that the image of the absolute conic (IAC) is double-contact with sphere images. Note that the IAC also exists in the central catadioptric image plane, but it does not have the double-contact properties with line images or sphere images. This is the main reason to propose the MIAC. From these geometric properties with the MIAC, two linear calibration methods for central catadioptric cameras using sphere images as well as using line images are proposed in the same framework. Note that there are many linear approaches to central catadioptric camera calibration using line images. It seems that to use the properties that line images are tangent to the MIAC only leads to an alternative geometric construction for calibration. However, for sphere images, there are only some nonlinear calibration methods in literature. Therefore, to propose linear methods for sphere images may be the main contribution of this paper. Our new algorithms have been tested in extensive experiments with respect to noise sensitivity.     

Geometry of single axis motions using conic fitting

Previous algorithms for recovering 3D geometry from an uncalibrated image sequence of a single axis motion of unknown rotation angles are mainly based on the computation of two-view fundamental matrices and three-view trifocal tensors. We propose three new methods that are based on fitting a conic locus to corresponding image points over multiple views. The main advantage is that determining only five parameters of a conic from one corresponding point over at least five views is simpler and more robust than determining a fundamental matrix from two views or a trifocal tensor from three views. It is shown that the geometry of single axis motion can be recovered either by computing one conic locus and one fundamental matrix or by computing at least two conic loci. A maximum likelihood solution based on this parametrization of the single axis motion is also described for optimal estimation using three or more loci. The experiments on real image sequences demonstrate the simplicity, accuracy, and robustness of the new methods.     

Hypercatadioptric line images for 3D orientation and image rectification

In central catadioptric systems 3D lines are projected into conics. In this paper we present a new approach to extract conics in the raw catadioptric image, which correspond to projected straight lines in the scene. Using the internal calibration and two image points we are able to compute analytically these conics which we name hypercatadioptric line images. We obtain the error propagation from the image points to the 3D line projection in function of the calibration parameters. We also perform an exhaustive analysis on the elements that can affect the conic extraction accuracy. Besides that, we exploit the presence of parallel lines in man-made environments to compute the dominant vanishing points (VPs) in the omnidirectional image. In order to obtain the intersection of two of these conics we analyze the self-polar triangle common to this pair. With the information contained in the vanishing points we are able to obtain the 3D orientation of the catadioptric system. This method can be used either in a vertical stabilization system required by autonomous navigation or to rectify images required in applications where the vertical orientation of the catadioptric system is assumed. We use synthetic and real images to test the proposed method. We evaluate the 3D orientation accuracy with a ground truth given by a goniometer and with an inertial measurement unit (IMU). We also test our approach performing vertical and full rectifications in sequences of real images.     

A calibration method for paracatadioptric camera from sphere images

For paracatadioptric camera, the estimation of intrinsic parameters from sphere images is still an open and challenging problem. In this paper, we propose a calibration method for paracatadioptric camera based on sphere images, which only requires that the projected contour of parabolic mirror is visible on the image plane in one view. We have found that, under central catadioptric camera, a sphere is projected to two conics on the image plane, which are defined as a pair of antipodal sphere images. The conic that is visible on the image plane is called the sphere image, while the other invisible conic is called the antipodal sphere image. In the other aspect, according to the image formation of central catadioptric camera, these two conics can also be considered as the projections of two parallel circles on the viewing sphere by a virtue camera. That is to say, if three pairs of antipodal sphere images are known, central catadioptric camera can be directly calibrated by the calibration method based on two parallel circles. Therefore, the problem of calibrating central catadioptric camera is transferred to the estimations of sphere images and their antipodal sphere images. Based on this idea, we first initialize the intrinsic parameters of the camera by the projected contour of parabolic mirror, and use them to initialize the antipodal sphere images. Next, we study properties of several pairs of antipodal sphere images under paracatadioptric camera. Then, these properties are used to optimize sphere images and their antipodal sphere images, so as to calibrate the paracatadioptric camera. Experimental results on both simulated and real image data have demonstrated the effectiveness of our method.     

Paraperspective ≡ affine

It is shown that the set of all paraperspective images with arbitrary reference point and the set of all affine images of a 3-D object are identical. Consequently, all uncalibrated paraperspective images of an object can be constructed from a 3-D model of the object by applying an affine transformation to the model, and every affine image of the object represents some uncalibrated paraperspective image of the object. It follows that the paraperspective images of an object can be expressed as linear combinations of any two non-degenerate images of the object. When the image position of the reference point is given the parameters of the affine transformation (and, likewise, the coefficients of the linear combinations) satisfy two quadratic constraints. Conversely, when the values of parameters are given the image position of the reference point is determined by solving a bi-quadratic equation.     

用于室内环境建模的基于形状一致性的立体视觉匹配算法

本文针对室内环境水平特征丰富的特点，提出借助图象变换，使立体视觉图象对中对应水平特征呈现形状一致性，以利于实现特征匹配，并获取物体三维结构的新颖算法，本文地在标定图象及非标定图象两种条件下如何获取所需变换参数进行了深入的理论分析，并对适用于基于形状一致性匹配算法的图象预处理及匹配算法进行了分析与实验研究。从初步获取的实验结果来看，这是一种对室内环境建模较为有效的方法。     

View and Time Interpolation in Image Space

The ability to interpolate between images taken at different time and viewpoints directly in image space opens up new possiblities. The goal of our work is to create plausible in‐between images in real time without the need for an intermediate 3D reconstruction. This enables us to also interpolate between images recorded with uncalibrated and unsynchronized cameras. In our approach we use a novel discontiniuity preserving image deformation model to robustly estimate dense correspondences based on local homographies. Once correspondences have been computed we are able to render plausible in‐between images in real time while properly handling occlusions. We discuss the relation of our approach to human motion perception and other image interpolation techniques.     

Robust automated multiple view inspection

Recently, Automated Multiple View Inspection (AMVI) has been developed for automated defect detection of manufactured objects, and the framework was successfully implemented for calibrated image sequences. However, it is not easy to be implemented in industrial environments because the calibration is a difficult and an unstable process. To overcome these disadvantages, the robust AMVI strategy, which assumes that an unknown affine transformation exists between each pair of uncalibrated images, is proposed. This transformation is estimated using two complementary robust procedures: a global approximation of the affine mapping is computed by creating candidate correspondences via B-splines and selecting those which better satisfy the epipolar constraint for uncalibrated images. Then, we use this approximation as initial estimate of a robust intensity-based matching approach, which is applied locally on each potential defect. The result is that false alarms are discarded, and the defects of an industrial object are actually tracked along the uncalibrated image sequence. The method is successful as shown in our experiments on aluminum die castings.     

Fast and robust numerical solutions to minimal problems for cameras with radial distortion

A number of minimal problems of structure from motion for cameras with radial distortion have recently been studied and solved in some cases. These problems are known to be numerically very challenging and in several cases there were no practical algorithms yielding solutions in floating point arithmetic. We make some crucial observations concerning the floating point implementation of Gröbner basis computations and use these new insights to formulate fast and stable algorithms for two minimal problems with radial distortion previously solved in exact rational arithmetic only: (i) simultaneous estimation of essential matrix and a common radial distortion parameter for two partially calibrated views and six image point correspondences and (ii) estimation of fundamental matrix and two different radial distortion parameters for two uncalibrated views and nine image point correspondences. We demonstrate that these two problems can be efficiently solved in floating point arithmetic in simulated and real experiments. For comparison we have also invented a new non-minimal algorithm for estimating fundamental matrix and two different radial distortion parameters for two uncalibrated views and twelve image point correspondences based on a generalized eigenvalue problem.     

Automatic Registration of Multi‐Projector Domes Using a Single Uncalibrated Camera

In this paper we present a novel technique for easily calibrating multiple casually aligned projectors on spherical domes using a single uncalibrated camera. Using the prior knowledge of the display surface being a dome, we can estimate the camera intrinsic and extrinsic parameters and the projector to display surface correspondences automatically using a set of images. These images include the image of the dome itself and a projected pattern from each projector. Using these correspondences we can register images from the multiple projectors on the dome. Further, we can register displays which are not entirely visible in a single camera view using multiple pan and tilted views of an uncalibrated camera making our method suitable for displays of different size and resolution. We can register images from any arbitrary viewpoint making it appropriate for a single head‐tracked user in a 3D visualization system. Also, we can use several cartographic mapping techniques to register images in a manner that is appropriate for multi‐user visualization. Domes are known to produce a tremendous sense of immersion and presence in visualization systems. Yet, till date, there exists no easy way to register multiple projectors on a dome to create a high‐resolution realistic visualizations. To the best of our knowledge, this is the first method that can achieve accurate geometric registration of multiple projectors on a dome simply and automatically using a single uncalibrated camera.     

The Geometry and Matching of Lines and Curves Over Multiple Views

This paper describes the geometry of imaged curves in two and three views. Multi-view relationships are developed for lines, conics and non-algebraic curves. The new relationships focus on determining the plane of the curve in a projective reconstruction, and in particular using the homography induced by this plane for transfer from one image to another. It is shown that given the fundamental matrix between two views, and images of the curve in each view, then the plane of a conic may be determined up to a two fold ambiguity, but local curvature of a curve uniquely determines the plane. It is then shown that given the trifocal tensor between three views, this plane defines a homography map which may be used to transfer a conic or the curvature from two views to a third. Simple expressions are developed for the plane and homography in each case.A set of algorithms are then described for automatically matching individual line segments and curves between images. The algorithms use both photometric information and the multiple view geometric relationships. For image pairs the homography facilitates the computation of a neighbourhood cross-correlation based matching score for putative line/curve correspondences. For image triplets cross-correlation matching scores are used in conjunction with line/curve transfer based on the trifocal geometry to disambiguate matches. Algorithms are developed for both short and wide baselines. The algorithms are robust to deficiencies in the segment extraction and partial occlusion.Experimental results are given for image pairs and triplets, for varying motions between views, and for different scene types. The methods are applicable to line/curve matching in stereo and trinocular rigs, and as a starting point for line/curve matching through monocular image sequences.     

Circular motion geometry using minimal data

Circular motion or single axis motion is widely used in computer vision and graphics for 3D model acquisition. This paper describes a new and simple method for recovering the geometry of uncalibrated circular motion from a minimal set of only two points in four images. This problem has been previously solved using nonminimal data either by computing the fundamental matrix and trifocal tensor in three images or by fitting conics to tracked points in five or more images. It is first established that two sets of tracked points in different images under circular motion for two distinct space points are related by a homography. Then, we compute a plane homography from a minimal two points in four images. After that, we show that the unique pair of complex conjugate eigenvectors of this homography are the image of the circular points of the parallel planes of the circular motion. Subsequently, all other motion and structure parameters are computed from this homography in a straighforward manner. The experiments on real image sequences demonstrate the simplicity, accuracy, and robustness of the new method.     

Extracting 3D facial animation parameters from multiview video clips

We propose an accurate and inexpensive procedure that estimates 3D facial motion parameters from mirror-reflected multiview video clips. We place two planar mirrors near a subject's cheeks and use a single camera to simultaneously capture a marker's front and side view images. We also propose a novel closed-form linear algorithm to reconstruct 3D positions from real versus mirrored point correspondences in an uncalibrated environment. Our computer simulations reveal that exploiting mirrors' various reflective properties yields a more robust, accurate, and simpler 3D position estimation approach than general-purpose stereo vision methods that use a linear approach or maximum-likelihood optimization. Our experiments show a root mean square (RMS) error of less than 2 mm in 3D space with only 20-point correspondences. For semiautomatic 3D motion tracking, we use an adaptive Kalman predictor and filter to improve stability and infer the occluded markers' position. Our approach tracks more than 50 markers on a subject's face and lips from 30-frame-per-second video clips. We've applied the facial motion parameters estimated from the proposed method to our facial animation system.     

基于仿射点对应的分层重构

提出了一种基于仿射点对应的分层重构方法,所谓仿射点对应是指相差一个仿射变换的两个空间点集的图像对应．该方法主要分为以下三个步骤：首先,从点对应计算准仿射重构;然后,由仿射点对应的准仿射重构建立一个三维射影变换,并利用这个射影变换的特征向量来确定无穷远平面,从而得到仿射重构;最后,从仿射重构所获得的无穷远平面单应矩阵标定摄像机内参数,进而得到度量重构．在上述三个步骤中,第二个步骤是最关键的,即如何确定对应于无穷远平面的特征向量,这也是该文的新思想和主要贡献所在．仿真和真实图像实验均表明,该文的方法是有效的,并且有很好的鲁棒性．     

Affine Structure and Motion from Points,Lines and Conics

In this paper several new methods for estimating scene structure and camera motion from an image sequence taken by affine cameras are presented. All methods can incorporate both point, line and conic features in a unified manner. The correspondence between features in different images is assumed to be known.Three new tensor representations are introduced describing the viewing geometry for two and three cameras. The centred affine epipoles can be used to constrain the location of corresponding points and conics in two images. The third order, or alternatively, the reduced third order centred affine tensors can be used to constrain the locations of corresponding points, lines and conics in three images. The reduced third order tensors contain only 12 components compared to the 16 components obtained when reducing the trifocal tensor to affine cameras.A new factorization method is presented. The novelty lies in the ability to handle not only point features, but also line and conic features concurrently. Another complementary method based on the so-called closure constraints is also presented. The advantage of this method is the ability to handle missing data in a simple and uniform manner. Finally, experiments performed on both simulated and real data are given, including a comparison with other methods.     

Self-calibration of a stereo rig using monocular epipolar geometries

This paper addresses the problem of self-calibration from one unknown motion of an uncalibrated stereo rig. Unlike the existing methods for stereo rig self-calibration, which have been focused on applying the autocalibration paradigm using both motion and stereo correspondences, our method does not require the recovery of stereo correspondences. Our method combines purely algebraic constraints with implicit geometric constraints. Assuming that the rotational part of the stereo geometry has two unknown degrees of freedom (i.e., the third dof is roughly known), and that the principle point of each camera is known, we first show that the computation of the intrinsic and extrinsic parameters of the stereo rig can be recovered from the motion correspondences only, i.e., the monocular fundamental matrices. We then provide an initialization procedure for the proposed non-linear method. We provide an extensive performance study for the method in the presence of image noise. In addition, we study some of the aspects related to the 3D motion that govern the accuracy of the proposed self-calibration method. Experiments conducted on synthetic and real data/images demonstrate the effectiveness and efficiency of the proposed method.