Omnidirectional optoelectronic systems (OOES) find applications in many areas where a wide viewing angle is crucial. The disadvantage of these systems is the large distortion of the images, which makes it difficult to make wide use of them. The purpose of this study is the development an algorithm for the precision calibration of an omnidirectional camera using a statistical approach. The calibration approach comprises three basic stages. The first stage is the formation of a cloud of points characterizing the view field of the virtual perspective camera. In the second stage, a calibration procedure that provides the projection function for the camera calibration is performed. The projection functions of traditional perspective lenses and omnidirectional wide-angle fisheye lenses with a viewing angle of no less than 180° are compared. The construction of the corrected image is performed in the third stage. The developed algorithm makes it possible to obtain an image for part of the field of view of an OOES by correcting the distortion from the original omnidirectional image.Using the developed algorithm, a non-mechanical pivoting camera based on an omnidirectional camera is implemented. The achieved mean squared error of the reproducing points from the original omnidirectional image onto the image with corrected distortion is less than the size of a very few pixels.