Euclidean constraints for uncalibrated reconstruction

Proceedings of International Symposium on Computer Vision - ISCV, 1995

Previous work sh,ows that based on five noncoplanar correspondences of two uncalibrated cameras, 3 0 reconstruction can be achieved under projective models, or based on four non-coplanar correspon,dences of two uncalibrated cameras, 3 0 recon.struction, can be achieved m d e r a@ne models, with three unknoiun parameters. In th,is paper, we show that based on four coplanar correspondences of two externally uncalibrated cameras, SD reconstruction can be achieved in Euclidean. space with only one unknown s c a h g parameter. Moreover, the unknown, scale factor is the physical distance from the camera center to the plane formed b y the four points in SD space. If th.is distance is known a priori, then the 3D structure can be conzpletely recovered. Both simulated and real data experimental results show that our reconstruction algorithm works reasonably robustly.

Lecture Notes in Computer Science, 1994

It is possible to recover the three-dimensional structure of a scene using images taken with uncalibrated cameras and pixel correspondences. But such a reconstruction can only be computed up to a projective transformation of the 3D space. Therefore, constraints have to be added to the reconstructed data in order to get the reconstruction in the euclidean space. Such constraints arise from knowledge of the scene: location of points, geometrical constraints on lines, etc. We rst discuss here the type of constraints that have to be added then we show how they can be fed into a general framework. Experiments prove that the accuracy needed for industrial applications is reachable when measurements in the image have subpixel accuracy. Therefore, we show how a real camera can be mapped into an accurate projective camera and how accurate point detection improve the reconstruction results.

1996

To make a Euclidean reconstruction of the world seen through a stereo rig, we can either use a cal ibration grid, and the results will rely on the preci sion of the grid and the extracted points of interest, or use self-calibration. Past work on self-calibration is focussed on the use of only one camera, and gives sometimes very unstable results.

Image and Vision Computing, 2005

This paper mainly focuses on the problem of camera calibration and 3D reconstruction from a single view of structured scene. It is well known that three constraints on the intrinsic parameters of a camera can be obtained from the vanishing points of three mutually orthogonal directions. However, there usually exist one or several pairs of line segments, which are mutually orthogonal and lie in the pencil of planes defined by two of the vanishing directions in the structured scenes. It is proved in this paper that a new independent constraint to the image of the absolute conic can be obtained if the pair of line segments is of equal length or with known length ratio in space. The constraint is further studied both in terms of the vanishing points and the images of circular points. Hence, four independent constraints on a camera are obtained from one image, and the camera can be calibrated under the widely accepted assumption of zero-skew. This paper also presents a simple method for the recovery of camera extrinsic parameters and projection matrix with respect to a given world coordinate system. Furthermore, several methods are presented to estimate the positions and poses of space planar surfaces from the recovered projection matrix and scene constraints. Thus, a scene structure can be reconstructed by combining the planar patches. Extensive experiments on simulated data and real images, as well as a comparative test with other methods in the literature, validate our proposed methods.

Pattern Recognition, 2006

A new approach is proposed for reconstructing 3D lines and cameras from 2D corresponding lines across multiple uncalibrated views. There is no requirement that the 2D corresponding lines on different images represent the same segment of a 3D line, which may not appear on all images. A 3D line is reconstructed by minimizing a geometric cost function that measures the distance of the reprojected end points of the 3D segment from the measured 2D lines on different images. An algorithmic procedure is provided with guaranteed convergence to a solution where the geometric cost function achieves a (local) minimum.

We present a method for camera calibration and metric reconstruction of the three-dimensional structure of scenes with several, possibly small and nearly planar objects from one or more images. We formulate the projection of object models explicitly according to the pin-hole camera model in order to be able to estimate the pose parameters for all objects as well as relative poses and the focal lengths of the cameras. This is accomplished by minimising a multivariate non-linear cost function. The only information needed is simple geometric object models, the correspondence between model and image features, and the correspondence of objects in the images if more than one view of the scene is used. Additionally, we present a new method for the projection of circles using projective invariants. Results using both simulated and real images are presented. keywords: Least-squares model fitting, model-based vision, 3-D reconstruction, camera calibration, projective invariants. 1

1995

We present a method for camera calibration and metric reconstruction of the three-dimensional structure of scenes with several, possibly small and nearly planar objects from one or more images. We formulate the projection of object models explicitly according to the pin-hole camera model in order to be able to estimate the pose parameters for all objects as well as relative poses and the focal lengths of the cameras. This is accomplished by minimising a multivariate non-linear cost function. The only information needed is simple geometric object models, the correspondence between model and image features, and the correspondence of objects in the images if more than one view of the scene is used. Additionally, we present a new method for the projection of circles using projective invariants. Results using both simulated and real images are presented. keywords: Least-squares model fitting, model-based vision, 3-D reconstruction, camera calibration, projective invariants. 1 Introductio...

Proceedings. International Conference on Information Technology: Coding and Computing

An optimized linear factorization method for recovering both the 3D geometry of a scene and the camera parameters from multiple uncalibrated images is presented. In a first step, we recover a projective approximation using a well known iterative approach. Then, we are able to upgrade from projective to Euclidean structure by computing the projective distortion matrix in a way that is analogous to estimating the absolute quadric. Using the Singular Value Decomposition (SVD) as a main tool, and from the study of the ranks of the matrices involved in the process, we are able to enforce an accurate Euclidean reconstruction. Moreover, in contrast to other approaches our process is essentially a linear one and does not require an initial estimation of the solution. Examples of synthetic and real data reconstructions are presented.

1997

In this paper the special case of reconstruction from image sequences taken by cameras with skew equal to 0 and aspect ratio equal to 1 has been treated. These type of cameras, here called cameras with Euclidean image planes, represent rigid projections where neither the principal point nor the focal length is known. It will be shown that it is possible to reconstruct an unknown object from images taken by a camera with Euclidean image plane up to similarity transformations, i.e., Euclidean transformations plus changes in the global scale.

Proc. of the Vth Ibero-American Symposium on Pattern Recognition, Lisboa, 2000

A method of uncalibrated reconstruction through structured lighting is presented in this paper. The co-ordinates of 3-D points and the projection matrices are simultaneously determined in a parameter estimation approach The reconstruction is. performed in a projective frame, up to a projective transformation, by only using pixel correspondences. ït is shown that an Euclidean reconstmcüon can be recovered by constraining the projective transformation by using geometrical knowledge about the scene. Moreover, it is described ...