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Calibration by correlation using metric embedding from non-metric similarities

Censi, Andrea and Scaramuzza, Davide (2013) Calibration by correlation using metric embedding from non-metric similarities. IEEE Transactions on Pattern Analysis and Machine Intelligence, 35 (10). pp. 2357-2370. ISSN 0162-8828. doi:10.1109/TPAMI.2013.34.

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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.

Item Type:Article
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URLURL TypeDescription Paper DOIArticle
Censi, Andrea0000-0001-5162-0398
Additional Information:© 2013 IEEE. A. Censi was supported by the US National Science Foundation (NRI program, grant #12018687) and US Defense Advanced Research Projects Agency (MSEE program, grant #FA8650-11-1-7156). D. Scaramuzza was suppported by the Swiss National Science Foundation through project #200021-143607 and the National Centre of Competence in Research Robotics.
Funding AgencyGrant Number
Defense Advanced Research Projects Agency (DARPA)FA8650-11-1-7156
Swiss National Science Foundation (SNSF)200021-143607
National Centre of Competence in Research RoboticsUNSPECIFIED
Subject Keywords:intrinsic camera calibration, metric embedding, catadioptric cameras, pin-hole cameras, fish-eye cameras
Issue or Number:10
Record Number:CaltechAUTHORS:20120805-103228127
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32927
Deposited By: Andrea Censi
Deposited On:06 Aug 2012 17:43
Last Modified:09 Nov 2021 21:31

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