Unbiased estimation of ellipses by bootstrapping

Javier Cabrera; Peter Meer

doi:10.1109/34.506797

Unbiased estimation of ellipses by bootstrapping

Javier Cabrera, Peter Meer

Research output: Contribution to journal › Article › peer-review

50 Scopus citations

Abstract

A general method for eliminating the bias of nonlinear estimators using bootstrap is presented. Instead of the traditional mean bias we consider the definition of bias based on the median. The method is applied to the problem of fitting ellipse segments to noisy data. No assumption beyond being independent identically distributed (i.i.d.) is made about the error distribution and experiments with both synthetic and real data prove the effectiveness of the technique.

Original language	English (US)
Pages (from-to)	752-756
Number of pages	5
Journal	IEEE Transactions on Pattern Analysis and Machine Intelligence
Volume	18
Issue number	7
DOIs	https://doi.org/10.1109/34.506797
State	Published - 1996

All Science Journal Classification (ASJC) codes

Software
Computer Vision and Pattern Recognition
Computational Theory and Mathematics
Artificial Intelligence
Applied Mathematics

Keywords

Bootstrap
Curve fitting
Implicit models
Low-level processing

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10.1109/34.506797

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title = "Unbiased estimation of ellipses by bootstrapping",

abstract = "A general method for eliminating the bias of nonlinear estimators using bootstrap is presented. Instead of the traditional mean bias we consider the definition of bias based on the median. The method is applied to the problem of fitting ellipse segments to noisy data. No assumption beyond being independent identically distributed (i.i.d.) is made about the error distribution and experiments with both synthetic and real data prove the effectiveness of the technique.",

keywords = "Bootstrap, Curve fitting, Implicit models, Low-level processing",

author = "Javier Cabrera and Peter Meer",

note = "Funding Information: We would like to thank the associate editor and two anonymous referees for their comments and suggestions, which significantly improved this paper. A first version of this work was presented at the Performance versus Methodology in Computer Vision, NSF/ARPA workshop, Seattle, Washington, June 1994. Kyujin Cho created the real image example. Javier Cabrera would like to acknowledge the support of the National Science Foundation Grant No. DMS 92-12411, and Peter Meer Grant No. IN-9210861.",

year = "1996",

doi = "10.1109/34.506797",

language = "English (US)",

volume = "18",

pages = "752--756",

journal = "IEEE Transactions on Pattern Analysis and Machine Intelligence",

issn = "0162-8828",

publisher = "IEEE Computer Society",

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T1 - Unbiased estimation of ellipses by bootstrapping

AU - Cabrera, Javier

AU - Meer, Peter

N1 - Funding Information: We would like to thank the associate editor and two anonymous referees for their comments and suggestions, which significantly improved this paper. A first version of this work was presented at the Performance versus Methodology in Computer Vision, NSF/ARPA workshop, Seattle, Washington, June 1994. Kyujin Cho created the real image example. Javier Cabrera would like to acknowledge the support of the National Science Foundation Grant No. DMS 92-12411, and Peter Meer Grant No. IN-9210861.

PY - 1996

Y1 - 1996

N2 - A general method for eliminating the bias of nonlinear estimators using bootstrap is presented. Instead of the traditional mean bias we consider the definition of bias based on the median. The method is applied to the problem of fitting ellipse segments to noisy data. No assumption beyond being independent identically distributed (i.i.d.) is made about the error distribution and experiments with both synthetic and real data prove the effectiveness of the technique.

AB - A general method for eliminating the bias of nonlinear estimators using bootstrap is presented. Instead of the traditional mean bias we consider the definition of bias based on the median. The method is applied to the problem of fitting ellipse segments to noisy data. No assumption beyond being independent identically distributed (i.i.d.) is made about the error distribution and experiments with both synthetic and real data prove the effectiveness of the technique.

KW - Bootstrap

KW - Curve fitting

KW - Implicit models

KW - Low-level processing

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VL - 18

SP - 752

EP - 756

JO - IEEE Transactions on Pattern Analysis and Machine Intelligence

JF - IEEE Transactions on Pattern Analysis and Machine Intelligence

IS - 7

ER -

Unbiased estimation of ellipses by bootstrapping

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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