Catadioptric Camera Calibration Research Articles

Self-Localization of Mobile Robots Using a Single Catadioptric Camera with Line Feature Extraction.

This paper presents a novel self-localization technique for mobile robots using a central catadioptric camera. A unified sphere model for the image projection is derived by the catadioptric camera calibration. The geometric property of the camera projection model is utilized to obtain the intersections of the vertical lines and ground plane in the scene. Different from the conventional stereo vision techniques, the feature points are projected onto a known planar surface, and the plane equation is used for depth computation. The 3D coordinates of the base points on the ground are calculated using the consecutive image frames. The derivation of motion trajectory is then carried out based on the computation of rotation and translation between the robot positions. We develop an algorithm for feature correspondence matching based on the invariability of the structure in the 3D space. The experimental results obtained using the real scene images have demonstrated the feasibility of the proposed method for mobile robot localization applications.

Using concurrent lines in central catadioptric camera calibration

Central catadioptric cameras have been extensively adopted in robotics and surveillance due to their extensive field of view. To attain precise 3D information in these applications, it is important to calibrate the catadioptric cameras accurately. The existing calibration techniques either require prior knowledge of the mirror types, or highly depend on a conic estimation procedure, which might be ruined if there are only small portions of the conic visible on calibration images. In this paper, we design a novel planar pattern with concurrent lines as a calibration rig, which is more robust in conic estimation since the relationship among lines is taken into account. Based on the line properties, we propose a rough-to-fine approach suitable for the new planar pattern to calibrate central catadioptric cameras. This method divides the nonlinear optimization calibration problem into several linear sub-problems that are much more robust against noise. Our calibration method can estimate intrinsic parameters and the mirror parameter simultaneously and accurately, without a priori knowledge of the mirror type. The performance is demonstrated by both simulation and a real hyperbolic catadioptric imaging system.

Measurement of three-dimensional mirror parameters by polarization imaging applied to catadioptric camera calibration

We present a new efficient method for calibration of catadioptric sensors. The method is based on an accurate measurement of the three-dimensional parameters of the mirror through polarization imaging. While inserting a rotating polarizer between the camera and the mirror, the system is automatically calibrated without any calibration patterns. Moreover, this method permits most of the constraints related to the calibration of catadioptric systems to be relaxed. We show that, contrary to our system, the traditional methods of calibration are very sensitive to misalignment of the camera axis and the symmetry axis of the mirror. From the measurement of three-dimensional parameters, we apply the generic calibration concept to calibrate the catadioptric sensor. We also show the influence of the disturbed measurement of the parameters on the reconstruction of a synthetic scene. Finally, experiments prove the validity of the method with some preliminary results on three-dimensional reconstruction.

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.

Low-cost method for the estimation of the shape of quadric mirrors and calibration of catadioptric cameras

This paper tackles the problem of quadric mirror estimation for omnidirectional imaging systems, as well as the poses of the camera relative to the mirror and to the world reference system. These estimates are obtained for quadric-shaped mirrors (including elliptic, parabolic, hyperbolic, and spherical mirrors) where the positions of the camera and mirror are unconstrained (fully noncentral configurations). The apparent contour of the mirror can be used to reduce the uncertainty in the estimation. Although it can enhance both the accuracy of the estimation (allowing the method to converge from farther initial configurations) and also its performance, its use is not strictly required. The intrinsic parameters of the camera model (pinhole or orthographic) are assumed to be known, as well as the structure of a calibration object in local coordinates. The method is nonlinear, and we use a genetic algorithm in conjunction with the Nelder-Mead simplex algorithm to minimize the objective function. Experimental results using real data are presented, demonstrating the accuracy of this calibration method, comparing its accuracy with and without the apparent contour, and computing its reprojection error. Because the mirror quadric is estimated, this method can also be used to identify and classify the mirror.

Calibration Method for Misaligned Catadioptric Camera

This paper proposes a calibration method for catadioptric camera systems consisting of a mirror whose reflecting surface is the surface of revolution and a perspective camera as typified by HyperOmni Vision. The proposed method is based on conventional camera calibration and mirror posture estimation. Many methods for camera calibration have been proposed and during the last decade, methods for catadioptric camera calibration have also been proposed. The main problem with catadioptric camera calibration is that the degree of freedom of mirror posture is limited or the accuracy of the estimated parameters is inadequate due to nonlinear optimization. On the other hand, our method can estimate five degrees of freedom of mirror posture and is free from the volatility of nonlinear optimization. The mirror posture has five degrees of freedom, because the mirror surface has a surface of revolution. Our method uses the mirror boundary and can estimate up to four mirror postures. We apply an extrinsic parameter calibration method based on conic fitting for this estimation method. Because an estimate of the mirror posture is not unique, we also propose a selection method for finding the best one. By using the conic-based analytical method we can avoid the initial value problem arising from nonlinear optimization. We conducted experiments on synthesized images and real images to evaluate the performance of our method, and discuss its accuracy.

Catadioptric camera calibration using geometric invariants

Central catadioptric cameras are imaging devices that use mirrors to enhance the field of view while preserving a single effective viewpoint. In this paper, we propose a novel method for the calibration of central catadioptric cameras using geometric invariants. Lines and spheres in space are all projected into conics in the catadioptric image plane. We prove that the projection of a line can provide three invariants whereas the projection of a sphere can only provide two. From these invariants, constraint equations for the intrinsic parameters of catadioptric camera are derived. Therefore, there are two kinds of variants of this novel method. The first one uses projections of lines and the second one uses projections of spheres. In general, the projections of two lines or three spheres are sufficient to achieve catadioptric camera calibration. One important conclusion in this paper is that the method based on projections of spheres is more robust and has higher accuracy than that based on projections of lines. The performances of our method are demonstrated by both the results of simulations and experiments with real images.