Title: A Generic Structure-from-Motion Algorithm for Cross-Camera Scenarios

Srikumar Ramalingam
Dept. of Computer Science,
University of California, Santa Cruz, USA
www.soe.ucsc.edu/~srikumar/
srikumar@soe.ucsc.edu

Suresh K.Lodha
Dept. of Computer Science,
University of California, Santa Cruz, USA
www.soe.ucsc.edu/~lodha/
lodha@soe.ucsc.edu

Peter Sturm
INRIA Rhône-Alpes, 38330 Montbonnot, France
Peter.Sturm@inrialpes.fr
http://www.inrialpes.fr/movi/people/Sturm/

Abstract:

We introduce a generic structure-from-motion approach based on a previously
introduced, highly general imaging model, where cameras are modeled as possibly unconstrained
sets of projection rays.
This allows to describe most existing camera types (at least
for those operating in the visible domain), including pinhole cameras,
sensors with radial or more general distortions, catadioptric cameras
(central or non-central), etc.
We introduce a structure-from-motion approach for this general
imaging model, that allows to reconstruct scenes from calibrated
images, possibly taken by cameras of different types
(cross-camera scenarios).
Structure-from-motion is naturally handled via camera independent
ray intersection problems, solved via linear or
simple polynomial equations.
We also propose two approaches for obtaining optimal solutions
using bundle adjustment, where camera motion, calibration and 3D point
coordinates are refined simultaneously.
One is relatively straightforward, minimizing distances between
3D points and projection rays.
The other minimizes reprojection error; the general imaging
model does not provide analytical expressions for the reprojection
error and its derivatives, which are desirable for efficient
optimization.
To achieve this, we propose to approximate the set of projection rays
of a general non-central camera by several clusters of central rays,
allowing us to formulate an analytical cost function.
% that can be minimized using non-linear iteration.
We present results for two cross-camera scenarios --
a pinhole used together with an omnidirectional camera and a stereo system
used with an omnidirectional camera. Using ground-truth
and 3D reconstruction results from classical techniques, we show that our
generic algorithm is simple, general and accurate for extensions to
various cross-camera and multi-camera scenarios.



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