'Institute of Electrical and Electronics Engineers (IEEE)'
Doi
Abstract
This paper presents a new intrinsic calibration method that allows us to calibrate a generic single-view point camera just
by waving it around. From the video sequence obtained while the camera undergoes random motion, we compute the pairwise time
correlation of the luminance signal for a subset of the pixels. We show that, if the camera undergoes a random uniform motion, then
the pairwise correlation of any pixels pair is a function of the distance between the pixel directions on the visual sphere. This leads to
formalizing calibration as a problem of metric embedding from non-metric measurements: we want to find the disposition of pixels on
the visual sphere from similarities that are an unknown function of the distances. This problem is a generalization of multidimensional
scaling (MDS) that has so far resisted a comprehensive observability analysis (can we reconstruct a metrically accurate embedding?)
and a solid generic solution (how to do so?). We show that the observability depends both on the local geometric properties (curvature)
as well as on the global topological properties (connectedness) of the target manifold. We show that, in contrast to the Euclidean case,
on the sphere we can recover the scale of the points distribution, therefore obtaining a metrically accurate solution from non-metric
measurements. We describe an algorithm that is robust across manifolds and can recover a metrically accurate solution when the metric
information is observable. We demonstrate the performance of the algorithm for several cameras (pin-hole, fish-eye, omnidirectional),
and we obtain results comparable to calibration using classical methods. Additional synthetic benchmarks show that the algorithm
performs as theoretically predicted for all corner cases of the observability analysis