ultra wide-angle optical systems
video surveillance systems
the coefficient of spherical distortion
K. V. Kolobov, V. Ya. Kolyuchkin
The article suggests the approach for projection with the specified quality indicators on the basis of the analysis of the process of image formation in ultra wide-angle optical systems of panoramic video surveillance systems. To estimate the geometric distortion of ultra wide-angle optical systems instead of the coefficient of relative distortion is suggested to use the coefficient of deformation. Cameras with ultra wide-angle optical systems are becoming more and more popular in video surveillance systems, herewith the geometric distortions presented in images generated by such systems can impair visual perception of images by an operator. Therefore, the problems of synthesis of the ultra wide-angle optical systems with higher quality indicators are still relevant. To describe the projection of the objects in the image for ultra wide-angle optical system (OS) the concept mapping can be used, which defines the relationship between the linear coordinate r` point of the image plane and the angular coordinate , the corresponding point in space (see Picture 1). Mapping function can be determined by integration of the dependence of the angular resolution of the OS dα from the angle of sight α. In the case of the ultra wide-angle OS the equidistant («FTheta») mapping function is mostly used that projects a subject area to the image plane, and provides equal angular resolution over the entire angular field . At the initial stage of synthesis of ultra wide-angle lens, the original optical scheme is presented, it consists a composition of two OS’, precisely, the photographic lens, that forms an image on the sensor and the afocal system. As in the ultra wide-angle OS in items’ space not items’ plane is considered, but the sphere, so that to estimate the geometric distortion one cannot use the coefficient of relative distortion, the use of the coefficient of spherical distortion is suggested (7). The coefficient of spherical distortion gives a more common evaluation of geometric distortions as it may be used for all angles. It is proposed to assess geometric distortion by the coefficient that characterizes the difference of the image of an ideal that is generated with a given mapping function. This coefficient is defined as (10). Accordingly, the geometric distortions alter the angular resolution of the OS, compared with a given mapping function. In the synthesis of ultra wide-angle OS with a given mapping function, the requirement to the dependence of the angle increasing of the OS on the angle of sight is formulated upon condition that of the absence of geometric distortion. The synthesis was carried out for ultra wide-angle OS with gnomonic and «FTheta» mapping function.