The Robotics Institute

Carnegie Mellon Robotics Institute

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Abstract

In computer vision we often estimate a 3D model of an object, and its uncertainty, up to an unknown scale factor. This unknown scale factor means that we cannot directly infer positions and lengths of the model, nor their uncertainties. In order to make quantitative distance measurements on this model, we must obtain the unknown scale factor. However, how we determine the scale factor will affect the accuracy of the rescaled model. In this paper we study the problem of estimating the absolute scale of an object and its uncertainty, starting from a 3D reconstruction up to a scale factor, and a reference length. The theory derived here can be used both to correctly transform a model covariance matrix under rescaling, and to select a good length on the object from which to obtain the scale, and so maximize accuracy.

Keywords

gauge freedoms, indeterminacy, uncertainty, covariance, ambiguity

Notes

Associated Project(s): Modeling by Videotape

Text Reference

Daniel D. Morris, Kenichi Kanatani, and Takeo Kanade, "3D Model Accuracy and Gauge Fixing," tech. report CMU-RI-TR-00-32, Robotics Institute, Carnegie Mellon University, December, 2000

BibTeX Reference

@techreport{Morris_2000_3424,
   author = "Daniel D. Morris and Kenichi Kanatani and Takeo Kanade",
   title = "3D Model Accuracy and Gauge Fixing",
   booktitle = "",
   institution = "Robotics Institute",
   month = "December",
   year = "2000",
   number= "CMU-RI-TR-00-32",
   address= "Pittsburgh, PA",
}

The Robotics Institute

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