Optimal Line Fitting and Reliability Evaluation

Yasushi KANAZAWA; Kenichi KANATANI

Optimal Line Fitting and Reliability Evaluation

Yasushi KANAZAWA, Kenichi KANATANI

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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.

Publication: IEICE TRANSACTIONS on Information Vol.E79-D No.9 pp.1317-1322

Publication Date: 1996/09/25

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Type of Manuscript: PAPER

Category: Image Processing,Computer Graphics and Pattern Recognition

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Yasushi KANAZAWA, Kenichi KANATANI, "Optimal Line Fitting and Reliability Evaluation" in IEICE TRANSACTIONS on Information, vol. E79-D, no. 9, pp. 1317-1322, September 1996, doi: .
Abstract: 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.
URL: https://globals.ieice.org/en_transactions/information/10.1587/e79-d_9_1317/_p

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@ARTICLE{e79-d_9_1317,
author={Yasushi KANAZAWA, Kenichi KANATANI, },
journal={IEICE TRANSACTIONS on Information},
title={Optimal Line Fitting and Reliability Evaluation},
year={1996},
volume={E79-D},
number={9},
pages={1317-1322},
abstract={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.},
keywords={},
doi={},
ISSN={},
month={September},}

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TY - JOUR
TI - Optimal Line Fitting and Reliability Evaluation
T2 - IEICE TRANSACTIONS on Information
SP - 1317
EP - 1322
AU - Yasushi KANAZAWA
AU - Kenichi KANATANI
PY - 1996
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E79-D
IS - 9
JA - IEICE TRANSACTIONS on Information
Y1 - September 1996
AB - 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.
ER -