Sensor calibration with unknown correspondence: Solving AX=XB using Euclidean-group invariants

Martin Kendal Ackerman, Alexis Cheng, Bernard Shiffman, Emad Boctor, Gregory Chirikjian

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The AX = XB sensor calibration problem must often be solved in image guided therapy systems, such as those used in robotic surgical procedures. In this problem, A, X, and B are homogeneous transformations with A and B acquired from sensor measurements and X being the unknown. It has been known for decades that this problem is solvable for X when a set of exactly measured A's and B's, in a priori correspondence, is given. However, in practical problems, the data streams containing the A' and B's will be asynchronous and may contain gaps (i.e., the correspondence is unknown, or does not exist, for the sensor measurements) and temporal registration is required. For the AX = XB problem, an exact solution can be found when four independent invariant quantities exist between two pairs of A's and B's. We formally define these invariants, reviewing and elaborating results from classical screw theory. We then illustrate how they can be used, with sensor data from multiple sources that contain unknown or missing correspondences, to provide a solution for X.

Original languageEnglish (US)
Title of host publicationIROS 2013
Subtitle of host publicationNew Horizon, Conference Digest - 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems
Pages1308-1313
Number of pages6
DOIs
StatePublished - Dec 1 2013
Event2013 26th IEEE/RSJ International Conference on Intelligent Robots and Systems: New Horizon, IROS 2013 - Tokyo, Japan
Duration: Nov 3 2013Nov 8 2013

Publication series

NameIEEE International Conference on Intelligent Robots and Systems
ISSN (Print)2153-0858
ISSN (Electronic)2153-0866

Other

Other2013 26th IEEE/RSJ International Conference on Intelligent Robots and Systems: New Horizon, IROS 2013
CountryJapan
CityTokyo
Period11/3/1311/8/13

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Software
  • Computer Vision and Pattern Recognition
  • Computer Science Applications

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