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1.
We consider the self-calibration problem for a generic imaging model that assigns projection rays to pixels without a parametric mapping. We consider the central variant of this model, which encompasses all camera models with a single effective viewpoint. Self-calibration refers to calibrating a camera’s projection rays, purely from matches between images, i.e. without knowledge about the scene such as using a calibration grid. In order to do this we consider specific camera motions, concretely, pure translations and rotations, although without the knowledge of rotation and translation parameters (rotation angles, axis of rotation, translation vector). Knowledge of the type of motion, together with image matches, gives geometric constraints on the projection rays. We show for example that with translational motions alone, self-calibration can already be performed, but only up to an affine transformation of the set of projection rays. We then propose algorithms for full metric self-calibration, that use rotational and translational motions or just rotational motions.  相似文献   

2.
Observability of 3D Motion   总被引:2,自引:2,他引:0  
This paper examines the inherent difficulties in observing 3D rigid motion from image sequences. It does so without considering a particular estimator. Instead, it presents a statistical analysis of all the possible computational models which can be used for estimating 3D motion from an image sequence. These computational models are classified according to the mathematical constraints that they employ and the characteristics of the imaging sensor (restricted field of view and full field of view). Regarding the mathematical constraints, there exist two principles relating a sequence of images taken by a moving camera. One is the epipolar constraint, applied to motion fields, and the other the positive depth constraint, applied to normal flow fields. 3D motion estimation amounts to optimizing these constraints over the image. A statistical modeling of these constraints leads to functions which are studied with regard to their topographic structure, specifically as regards the errors in the 3D motion parameters at the places representing the minima of the functions. For conventional video cameras possessing a restricted field of view, the analysis shows that for algorithms in both classes which estimate all motion parameters simultaneously, the obtained solution has an error such that the projections of the translational and rotational errors on the image plane are perpendicular to each other. Furthermore, the estimated projection of the translation on the image lies on a line through the origin and the projection of the real translation. The situation is different for a camera with a full (360 degree) field of view (achieved by a panoramic sensor or by a system of conventional cameras). In this case, at the locations of the minima of the above two functions, either the translational or the rotational error becomes zero, while in the case of a restricted field of view both errors are non-zero. Although some ambiguities still remain in the full field of view case, the implication is that visual navigation tasks, such as visual servoing, involving 3D motion estimation are easier to solve by employing panoramic vision. Also, the analysis makes it possible to compare properties of algorithms that first estimate the translation and on the basis of the translational result estimate the rotation, algorithms that do the opposite, and algorithms that estimate all motion parameters simultaneously, thus providing a sound framework for the observability of 3D motion. Finally, the introduced framework points to new avenues for studying the stability of image-based servoing schemes.  相似文献   

3.
Ambiguity in Structure from Motion: Sphere versus Plane   总被引:1,自引:1,他引:0  
If 3D rigid motion can be correctly estimated from image sequences, the structure of the scene can be correctly derived using the equations for image formation. However, an error in the estimation of 3D motion will result in the computation of a distorted version of the scene structure. Of computational interest are these regions in space where the distortions are such that the depths become negative, because in order for the scene to be visible it has to lie in front of the image, and thus the corresponding depth estimates have to be positive. The stability analysis for the structure from motion problem presented in this paper investigates the optimal relationship between the errors in the estimated translational and rotational parameters of a rigid motion that results in the estimation of a minimum number of negative depth values. The input used is the value of the flow along some direction, which is more general than optic flow or correspondence. For a planar retina it is shown that the optimal configuration is achieved when the projections of the translational and rotational errors on the image plane are perpendicular. Furthermore, the projection of the actual and the estimated translation lie on a line through the center. For a spherical retina, given a rotational error, the optimal translation is the correct one; given a translational error, the optimal rotational negative deptherror depends both in direction and value on the actual and estimated translation as well as the scene in view. The proofs, besides illuminating the confounding of translation and rotation in structure from motion, have an important application to ecological optics. The same analysis provides a computational explanation of why it is easier to estimate self-motion in the case of a spherical retina and why shape can be estimated easily in the case of a planar retina, thus suggesting that nature's design of compound eyes (or panoramic vision) for flying systems and camera-type eyes for primates (and other systems that perform manipulation) is optimal.  相似文献   

4.
Recovery of ego-motion using region alignment   总被引:2,自引:0,他引:2  
A method for computing the 3D camera motion (the ego-motion) in a static scene is described, where initially a detected 2D motion between two frames is used to align corresponding image regions. We prove that such a 2D registration removes all effects of camera rotation, even for those image regions that remain misaligned. The resulting residual parallax displacement field between the two region-aligned images is an epipolar field centered at the FOE (Focus-of-Expansion). The 3D camera translation is recovered from the epipolar field. The 3D camera rotation is recovered from the computed 3D translation and the detected 2D motion. The decomposition of image motion into a 2D parametric motion and residual epipolar parallax displacements avoids many of the inherent ambiguities and instabilities associated with decomposing the image motion into its rotational and translational components, and hence makes the computation of ego-motion or 3D structure estimation more robust  相似文献   

5.
A unified approach to the linear camera calibration problem   总被引:4,自引:0,他引:4  
The camera calibration process relates camera system measurements (pixels) to known reference points in a three-dimensional world coordinate system. The calibration process is viewed as consisting of two independent phases: the first is removing geometrical camera distortion so that rectangular calibration grids are straightened in the image plane, and the second is using a linear affine transformation as a map between the rectified camera coordinates and the geometrically projected coordinates on the image plane of known reference points. Phase one is camera-dependent, and in some systems may be unnecessary. Phase two is concerned with a generic model that includes 12 extrinsic variables and up to five intrinsic parameters. General methods handling additional constraints on the intrinsic variables in a manner consistent with explicit satisfaction of all six constraints on the orthogonal rotation matrix are presented. The use of coplanar and noncoplanar calibration points is described  相似文献   

6.
Due to the aperture problem, the only motion measurement in images, whose computation does not require any assumptions about the scene in view, is normal flow—the projection of image motion on the gradient direction. In this paper we show how a monocular observer can estimate its 3D motion relative to the scene by using normal flow measurements in a global and qualitative way. The problem is addressed through a search technique. By checking constraints imposed by 3D motion parameters on the normal flow field, the possible space of solutions is gradually reduced. In the four modules that comprise the solution, constraints of increasing restriction are considered, culminating in testing every single normal flow value for its consistency with a set of motion parameters. The fact that motion is rigid defines geometric relations between certain values of the normal flow field. The selected values form patterns in the image plane that are dependent on only some of the motion parameters. These patterns, which are determined by the signs of the normal flow values, are searched for in order to find the axes of translation and rotation. The third rotational component is computed from normal flow vectors that are only due to rotational motion. Finally, by looking at the complete data set, all solutions that cannot give rise to the given normal flow field are discarded from the solution space.Research supported in part by NSF (Grant IRI-90-57934), ONR (Contract N00014-93-1-0257) and ARPA (Order No. 8459).  相似文献   

7.
Multi-frame estimation of planar motion   总被引:4,自引:0,他引:4  
Traditional plane alignment techniques are typically performed between pairs of frames. We present a method for extending existing two-frame planar motion estimation techniques into a simultaneous multi-frame estimation, by exploiting multi-frame subspace constraints of planar surfaces. The paper has three main contributions: 1) we show that when the camera calibration does not change, the collection of all parametric image motions of a planar surface in the scene across multiple frames is embedded in a low dimensional linear subspace; 2) we show that the relative image motion of multiple planar surfaces across multiple frames is embedded in a yet lower dimensional linear subspace, even with varying camera calibration; and 3) we show how these multi-frame constraints can be incorporated into simultaneous multi-frame estimation of planar motion, without explicitly recovering any 3D information, or camera calibration. The resulting multi-frame estimation process is more constrained than the individual two-frame estimations, leading to more accurate alignment, even when applied to small image regions.  相似文献   

8.
This paper addresses the problem of recovering both the intrinsic and extrinsic parameters of a camera from the silhouettes of an object in a turntable sequence. Previous silhouette-based approaches have exploited correspondences induced by epipolar tangents to estimate the image invariants under turntable motion and achieved a weak calibration of the cameras. It is known that the fundamental matrix relating any two views in a turntable sequence can be expressed explicitly in terms of the image invariants, the rotation angle, and a fixed scalar. It will be shown that the imaged circular points for the turntable plane can also be formulated in terms of the same image invariants and fixed scalar. This allows the imaged circular points to be recovered directly from the estimated image invariants, and provide constraints for the estimation of the imaged absolute conic. The camera calibration matrix can thus be recovered. A robust method for estimating the fixed scalar from image triplets is introduced, and a method for recovering the rotation angles using the estimated imaged circular points and epipoles is presented. Using the estimated camera intrinsics and extrinsics, a Euclidean reconstruction can be obtained. Experimental results on real data sequences are presented, which demonstrate the high precision achieved by the proposed method.  相似文献   

9.
基于二次曲线的线阵相机标定技术   总被引:1,自引:0,他引:1       下载免费PDF全文
针对绕固定轴旋转的线阵相机,提出一种基于二次曲线的相机标定方法。该方法只需要相机在2个或更多不同的方位拍摄图像,通过相机的转动在每个方位拍摄多帧图像。靶标采用一个包含3个或更多二次曲线的平板。相机和靶标可以自由移动,不需要知道运动参数。通过坐标变换,把每个方位所拍摄的多帧线阵图像排列成面阵图像。从面阵图像中提取二次曲线作为标定基元,以此简化基元对应问题。仿真实验结果表明,该方法精度较高,鲁棒性较好。  相似文献   

10.
3-D translational motion and structure from binocular image flows   总被引:1,自引:0,他引:1  
Image flow fields from parallel stereo cameras are analyzed to determine the relative 3-D translational motion of the camera platform with respect to objects in view and to establish stereo correspondence of features in the left and right images. A two-step procedure is suggested. In the first step, translational motion parameters are determined from linear equations the coefficients of which consist of the sums of measured quantities in the two images. Separate equations are developed for cases when measurements of either the full optical flow or the normal flow are available. This computation does not require feature-to-feature correspondence. In addition, no assumption is made about the surfaces being viewed. In the second step of the calculation, with the knowledge of the estimated translational motion parameters, the binocular flow information is used to find features in one image that correspond to given features in the other image. Experimental results with synthetic and laboratory images indicate that the method provides accurate results even in the presence of noise  相似文献   

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