Issues on the Geometry of Central Catadioptric Image Formation

An imaging system with a single effective viewpoint is called a central projection system. The conventional perspective camera is an example of a central projection system. Systems using mirrors to enhance the field of view while keeping a unique center of projection are also examples of central projection systems. Perspective image formation can be described by a linear model with well known properties. In general central catadioptric imaging the mapping between points in the world and in the image is highly nonlinear. This paper establishes a general model for central catadioptric image formation made up of three functions: a linear function mapping the world into an oriented projective plane, a non-linear transformation between two oriented projective planes, and a collineation in the plane. The model is used to study issues in the projection of lines. The equations and geometric properties of general catadioptric imaging of lines are derived. The application of the results in auto-calibration of central catadioptric systems and reconstruction are discussed. A method to calibrate the system using three line images is presented.