Paracatadioptric Camera Calibration Using The Images Of Relative Position Between Double Spheres

The central catadioptric cameras are widely used in robot navigation, visual surveillance and3D reconstruction because of their very large field of view. The camera calibration is a necessary and important procedure for a central catadioptric camera, and the selection of a suitable calibration method is critical to the calibration results. A sphere is a common geometric object of which occlusion itself is not the most important advantage, utilizing spherical image to complete camera calibration is a focus in recent years. This thesis mainly discusses the paracatadioptric camera calibration from the images of relative position between double spheres The main research contents can be summarized as follows:1. Analysis the projections of double spheres at different positions under the unit sphere model for paracatadioptric camera, found that their projections to satisfy three conditions:ⅰ) two real intersection points; ⅱ) a real intersection point; ⅲ) without real intersection point. For the three cases, the two groups of double spheres projection circles on the unit viewing sphere are caused to intersect points corresponding to form the antipodal points. At the same time, the intersection points of double spheres images and their antipodal sphere images corresponding to form the antipodal image points. Solving the principal point and determine the orthogonal vanishing points by the definition and properties of the antipodal image points.2. Based on the orthogonal vanishing points were determined, by utilizing the relationship between the orthogonal vanishing points and the intrinsic camera parameters as constraint conditions solving the intrinsic camera parameters. When the principal point is known, to complete camera calibration requires at least one image of double spheres for the above three kind of situations. When the principal point is unknown, to complete camera calibration requires at least one image of double spheres for the ⅰ) and ⅲ) of situations, and to complete camera calibration requires at least two images of double spheres for the ⅱ) of situations. When the principal point is known, we also can solve the camera intrinsic parameters by utilizing the relationship between the images of circular points and the intrinsic camera parameters. First, according to the sphere projection circle and antipodal circle on the unit viewing sphere at the corresponding point of tangent parallel determine the vanishing line of the base plane. Next, solving equations of the vanishing line equation and equation of sphere image to get the images of circular points in the plane containing the small circle. Finally, by taking the relationship between the images of circular points and the intrinsic camera parameters as constraint conditions, the rest of the camera intrinsic parameters can be obtained.3. We performed a number of experiments with simulated and real image data using Matlab software. The paracatadioptric images were corrected and obtained the corresponding perspective images in the real experiment. The experimental results show that the methods presented in this thesis is effective.