A Bayesian method for fitting parametric and nonparametric models to noisy data

We present a simple paradigm for fitting models, parametric and nonparametric, to noisy data, which resolves some of the problems associated with classical MSE algorithms. This is done by considering each point on the model as a possible source for each data point. The paradigm can be used to solve...

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Bibliographic Details
Published inIEEE transactions on pattern analysis and machine intelligence Vol. 23; no. 5; pp. 528 - 534
Main Authors Werman, M., Keren, D.
Format Journal Article
LanguageEnglish
Published New York IEEE 01.05.2001
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Bayesian methods
Curve fitting
Data points
Discontinuity
Fittings
Gaussian
Gaussian noise
Image segmentation
Intelligence
Linear approximation
Mean square error methods
Parametric statistics
Pattern analysis
Polynomials
Rectangles
Segments
Surface fitting
Traveling salesman problems
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Summary:We present a simple paradigm for fitting models, parametric and nonparametric, to noisy data, which resolves some of the problems associated with classical MSE algorithms. This is done by considering each point on the model as a possible source for each data point. The paradigm can be used to solve problems which are ill-posed in the classical MSE approach, such as fitting a segment (as opposed to a line). It is shown to be nonbiased and to achieve excellent results for general curves, even in the presence of strong discontinuities. Results are shown for a number of fitting problems, including lines, circles, elliptic arcs, segments, rectangles, and general curves, contaminated by Gaussian and uniform noise.
Bibliography:ObjectType-Article-2
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content type line 23
ISSN:0162-8828
1939-3539
DOI:10.1109/34.922710