Single
Image Calibration of MultiAxial
Imaging Systems
Amit Agrawal and Srikumar Ramalingam Mitsubishi Electric Research Labs (MERL) CVPR 2013
Summary
Calibration and 3D reconstruction for multiaxial imaging systems. Our paper shows that calibration can be done using a single photo of a checkerboard. Abstract Imaging systems consisting of
a camera looking at multiple spherical mirrors
(reflection) or multiple refractive spheres
(refraction) have been used for wideangle imaging
applications. We describe such setups as multiaxial
imaging systems, since a single sphere results in an
axial system. Assuming an internally calibrated
camera, calibration of such multiaxial systems
involves estimating the sphere radii and locations in
the camera coordinate system. However, previous
calibration approaches require manual intervention or
constrained setups. We present a fully automatic
approach using a single photo of a 2D calibration
grid. The pose of the calibration grid is assumed to
be unknown and is also recovered. Our approach can
handle unconstrained setups, where the
mirrors/refractive balls can be arranged in any
fashion, not necessarily on a grid.
The axial nature of rays allows us to compute the axis of each sphere separately. We then show that by choosing rays from two or more spheres, the unknown pose of the calibration grid can be obtained linearly and independently of sphere radii and locations. Knowing the pose, we derive analytical solutions for obtaining the sphere radius and location. This leads to an interesting result that $6$DOF pose estimation of a multiaxial camera can be done without the knowledge of full calibration. Simulations and real experiments demonstrate the applicability of our algorithm. Supplementary pdf Matlab Code

