Optimal Line Fitting and Reliability Evaluation

Yasushi KANAZAWA  Kenichi KANATANI  

IEICE TRANSACTIONS on Information and Systems   Vol.E79-D   No.9   pp.1317-1322
Publication Date: 1996/09/25
Online ISSN: 
Print ISSN: 0916-8532
Type of Manuscript: PAPER
Category: Image Processing,Computer Graphics and Pattern Recognition
line fitting,  statistical model of noise,  optimization technique,  image processing,  reliability evaluation,  edge detection,  

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Introducing a mathematical model of image noise, we formalize the problem of fitting a line to point data as statistical estimation. It is shown that the reliability of the fitted line can be evaluated quantitatively in the form of the covariance matrix of the parameters. We present a numerical scheme called renormalization for computing an optimal fit and at the same time evaluating its reliability. We also present a scheme for visualizing the reliability of the fit by means of the primary deviation pair and derive an analytical expression for the reliability of a line fitted to an edge segment by using an asymptotic approximation. Our method is illustrated by showing simulations and real-image examples.