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Beyond Alhazen's Problem: Analytical Projection Model for Non-Central Catadioptric Cameras with Quadric Mirrors
 

Summary: Beyond Alhazen's Problem: Analytical Projection Model for
Non-Central Catadioptric Cameras with Quadric Mirrors
Amit Agrawal, Yuichi Taguchi, and Srikumar Ramalingam
Mitsubishi Electric Research Labs (MERL), Cambridge, MA, USA
{agrawal, taguchi, ramalingam} at merl.com
Abstract
Catadioptric cameras are widely used to increase the
field of view using mirrors. Central catadioptric systems
having an effective single viewpoint are easy to model and
use, but severely constraint the camera positioning with re-
spect to the mirror. On the other hand, non-central cata-
dioptric systems allow greater flexibility in camera place-
ment, but are often approximated using central or linear
models due to the lack of an exact model. We bridge this
gap and describe an exact projection model for non-central
catadioptric systems. We derive an analytical `forward pro-
jection' equation for the projection of a 3D point reflected
by a quadric mirror on the imaging plane of a perspective
camera, with no restrictions on the camera placement, and
show that it is an 8th

  

Source: Agrawal, Amit - Mitsubishi Electric Research Labs

 

Collections: Engineering