A generic structure-from-motion algorithm for cross-camera scenarios
Résumé
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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