Analytical forward projection for axial non-central dioptric and catadioptric cameras

  • Authors:

  • Amit Agrawal;Yuichi Taguchi;Srikumar Ramalingam

  • Affiliations:

  • Mitsubishi Electric Research Labs, Cambridge, MA;Mitsubishi Electric Research Labs, Cambridge, MA;Mitsubishi Electric Research Labs, Cambridge, MA

  • Venue:
  • ECCV'10 Proceedings of the 11th European conference on computer vision conference on Computer vision: Part III
  • Year:
  • 2010

Quantified Score

Hi-index 0.00

Visualization

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 analytical solution. This allows computation of the optical path from a given 3D point to the given viewpoint by solving a 6th degree forward projection 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 imaging 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 analytical forward projection leads to accurate and fast 3D reconstruction via bundle adjustment. Simulations and real results on single image sparse 3D reconstruction are presented. We demonstrate ∼ 100 times speed up using the analytical solution over iterative forward projection for 3D reconstruction using spherical mirrors.