ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences
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Articles | Volume V-1-2021
ISPRS Ann. Photogramm. Remote Sens. Spatial Inf. Sci., V-1-2021, 89–96, 2021
https://doi.org/10.5194/isprs-annals-V-1-2021-89-2021
ISPRS Ann. Photogramm. Remote Sens. Spatial Inf. Sci., V-1-2021, 89–96, 2021
https://doi.org/10.5194/isprs-annals-V-1-2021-89-2021

  17 Jun 2021

17 Jun 2021

A REVIEW OF THE ONE-PARAMETER DIVISION UNDISTORTION MODEL

B. Erdnüß1,2 B. Erdnüß
  • 1Institute of Photogrammetry and Remote Sensing (IPF), Karlsruhe Institute of Technology (KIT), Germany
  • 2Fraunhofer-IOSB (Institute of Optronics, System Technologies and Image Exploitation), Karlsruhe, Germany

Keywords: Projective Invariance, Cross-Ratio, Radial Distortion, Division Model, Rails Distance

Abstract. The one-parameter division undistortion model by (Lenz, 1987) and (Fitzgibbon, 2001) is a simple radial distortion model with beneficial algebraic properties that allows to reason about some problems analytically that can only be handled numerically in other distortion models. One property of this distortion model is that straight lines in the undistorted image correspond to circles in the distorted image. These circles are fully described by their center point, as the radius can be calculated from the position of the center and the distortion parameter only. This publication collects the properties of this distortion model from several sources and reviews them. Moreover, we show in this publication that the space of this center is projectively isomorphic to the dual space of the undistorted image plane, i.e. its line space. Therefore, projective invariant measurements on the undistorted lines are possible by the according measurements on the centers of the distorted circles. As an example of application, we use this to find the metric distance of two parallel straight rails with known track gauge in a single uncalibrated camera image with significant radial distortion.