2003 Reports

A General Framework for Designing Catadioptric Imaging and Projection Systems

Swaminathan, Rahul; Grossberg, Michael D.; Nayar, Shree K.

New vision applications have been made possible and old ones improved through the creation and design of novel catadioptric systems. Critical to the design of catadioptric imaging is determining the shape of one or more mirrors in the system. Almost all the previously designed mirrors for catadioptric systems used case specific tools and considerable effort on the part of the designer. Recently some new general methods have been proposed to automate the design process. However, all the methods presented so far determine the mirror shape by optimizing its geometric properties, such as surface normal orientations. A more principled approach is to determine a mirror that reduces image errors. In this paper we present a method for finding mirror shapes which meet user determined specifications while minimizing image error. We accomplish this by deriving a first order approximation of the image error. This permits us to compute the mirror shape using a linear approach that provides good results efficiently while avoiding the numerical problems associated with non-linear optimization. Since the design of mirrors can also be applied to projection systems, we also provide a method to approximate projection errors in the scene. We demonstrate our approach on various catadioptric systems and show our approach to provide much more accurate imaging characteristics. In some cases we achieved reduction in image error up to 80 percent.