Statistical Uncertainty Analysis for Image Processing Algorithms in Metric Vision Systems

Research output: ThesisDoctoral Thesis

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Abstract

The work presented in this thesis addresses image processing algorithms as well as methods of statistical uncertainty analysis related to metric vision systems. The term metric vision covers the optical measurement of quantitative information for geometric objects, such as position, orientation, dimensions and shape. Thereby, three tasks are of particular interest: (1) estimation of plane-to-plane homographies based on point correspondences, (2) fitting of geometric models to sets of data points perturbed by measurement noise, and (3) derivation of measurement results from the model parameters. In order to specify the uncertainty associated with the measurement results of metric vision systems, two different methods of uncertainty analysis are investigated: a statistical and an analytical approach. The statistical method is based on evaluating data of repeated but independent measurements, whereby the analytical estimates are computed by application of the law of first order error propagation to the particular steps of the evaluation procedure. In the present work, the algorithms for fitting lines as well as pairs of parallel lines to sets of noisy data points are analyzed in detail concerning first order estimation of error propagation. Furthermore, the direct linear transformation (DLT) algorithm for computing the parameters of plane-to-plane homographies based on point correspondences is analyzed. All of the analytically computed uncertainty estimates are numerically verified with Monte-Carlo simulations. The methods of statistical uncertainty analysis described in this thesis are of general validity for metric vision systems. In order to illustrate the applicability of the approaches, the image processing algorithms of a video-extensometer system are examined. The system is designed to measure the deformation of polymer materials during tensile testing. The images acquired during the tests are evaluated offline. At first, points of interest are extracted using gradient-based techniques followed by center-of-gravity calculation. As a result, sets of data points are obtained at sub-pixel accuracy. Linear geometric models, concretely lines as well as pairs of parallel lines, are approximated to the sets of noisy data points by means of least-squares estimation of the model parameters. The measurement results, in particular the longitudinal as well as the transversal specimen dimensions, are derived from the fitted geometric models.
Translated title of the contributionStatistische Unsicherheitsanalyse für Algorithmen der metrischen Bildverarbeitung
Original languageEnglish
QualificationDr.mont.
Supervisors/Advisors
  • O'Leary, Paul, Assessor A (internal)
  • Gfrerrer, Anton, Co-Supervisor (external)
Publication statusPublished - 2008

Bibliographical note

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Keywords

  • statistical uncertainty analysis
  • digital image processing
  • metric vision

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