Non-Single Viewpoint Catadioptric Cameras: Geometry and Analysis

Conventional vision systems and algorithms assume the camera to have a single viewpoint. However, sensors need not always maintain a single viewpoint. For instance, an incorrectly aligned system could cause non-single viewpoints. Also, systems could be designed to specifically deviate from a single viewpoint to trade-off image characteristics such as resolution and field of view. In these cases, a locus of viewpoints is formed, called a caustic. In this paper, we present an in-depth analysis of the viewpoint loci for catadioptric cameras with conic reflectors. Properties of these viewpoint loci with regard to field of view, resolution and other geometric properties are presented. In addition, we present a simple technique to calibrate such non-single viewpoint catadioptric cameras and estimate their viewpoint loci (caustics) from known camera motion