Non-Single Viewpoint Catadioptric Cameras: Geometry and Analysis

Abstract.Conventional vision systems and algorithms assume the imaging system to have a single viewpoint. However, these imaging systems need not always maintain a single viewpoint. For instance, an incorrectly aligned catadioptric system could cause non-single viewpoints. Moreover, a lot of flexibility in imaging system design can be achieved by relaxing the need for imaging systems to have a single viewpoint. Thus, imaging systems with non-single viewpoints can be designed for specific imaging tasks, or image characteristics such as field of view and resolution. The viewpoint locus of such imaging systems is called a caustic.In this paper, we present an in-depth analysis of caustics of catadioptric cameras with conic reflectors. We use a simple parametric model for both, the reflector and the imaging system, to derive an analytic solution for the caustic surface. This model completely describes the imaging system and provides a map from pixels in the image to their corresponding viewpoints and viewing direction. We use the model to analyze the imaging system's properties such as field of view, resolution and other geometric properties of the caustic itself. In addition, we present a simple technique to calibrate the class of conic catadioptric cameras and estimate their caustics from known camera motion. The analysis and results we present in this paper are general and can be applied to any catadioptric imaging system whose reflector has a parametric form.

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