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Analytical Forward Projection for Axial Non-Central Dioptric & Catadioptric Cameras

Summary: Analytical Forward Projection for Axial
Non-Central Dioptric & Catadioptric Cameras
Amit Agrawal, Yuichi Taguchi, and Srikumar Ramalingam
Mitsubishi Electric Research Labs (MERL), Cambridge, MA, USA
Abstract. We present a technique for modeling non-central catadioptric
cameras consisting of a perspective camera and a rotationally symmetric
conic reflector. While previous approaches use a central approximation
and/or iterative methods for forward projection, we present an analyt-
ical solution. This allows computation of the optical path from a given
3D point to the given viewpoint by solving a 6th
degree forward pro-
jection equation for general conic mirrors. For a spherical mirror, the
forward projection reduces to a 4th
degree equation, resulting in a closed
form solution. We also derive the forward projection equation for imag-
ing through a refractive sphere (non-central dioptric camera) and show
that it is a 10th
degree equation. While central catadioptric cameras
lead to conic epipolar curves, we show the existence of a quartic epipolar
curve for catadioptric systems using a spherical mirror. The analyti-


Source: Agrawal, Amit - Mitsubishi Electric Research Labs


Collections: Engineering