Catadioptric Sensors that Approximate Wide-Angle Perspective Projections

• Authors: R. Andrew Hicks;Ruzena Bajcsy
• Venue: OMNIVIS '00 Proceedings of the IEEE Workshop on Omnidirectional Vision
• Year: 2000

We present two families of reflective surfaces that are capable of providing a wide field of view, and yet still approximate a perspective projection to a high degree. These surfaces are derived by considering a plane perpendicular to the axis of a surface of revolution and finding the equations governing the distortion of the image of the plane in this surface.We then view this relation as a differential equation and prescribe the distortion term to be linear. By choosing appropriate initial conditions for the differential equation and solving it numerically, we derive the surface shape and obtain a precise estimate as to what degree the resulting sensor can approximate a perspective projection. Thus, these surfaces act as computational sensors, allowing for a wide-angle perspective view of a scene without processing the image in software. The applications of such a sensor should be numerous, including surveillance, robotics and traditional photography.Recently, many researchers in the robotics and vision community have begun to consider visual sensors that are able to obtain wide fields of view. Such devices are the natural solution to various difficulties encountered with conventional imaging systems.The two most common means of obtaining wide fields of view are fish-eye lenses and reflective surfaces, also known as catoptrics. When catoptrics are combined with conventional lens systems, known as dioptrics, the resulting sensors are known as catadioptrics. The possible uses of these systems include applications such as robot control and surveillance. In this paper, we will consider only catadioptri-based sensors. Often such systems consist of a camera pointing at a convex mirror.How to interpret and make use of the visual information obtained by such systems, e.g. how they should be used to control robots is not at all obvious. There are infinitely many different shapes that a mirror can have, and at least two different camera models (perspective and orthographic projection) with which to combine each mirror.The properties of the resulting sensors are very sensitive to these choices. The classic need for wide-angle lenses have, of course been in photography. In particular, underwater and architectural photography are two examples in which having a wide-angle lens is often crucial. The commercially available lens with the widest field of view (without radial distortion) that the authors are aware of is the Nikon 13mm f/5.6 Nikkor AIS, which provides a field of view of 118 degrees at a cost of $(US) 12000. Note that our prototype orthographic sensor provides a field of view of 142 degrees.