A1 Refereed original research article in a scientific journal
Ridge-based method for finding curvilinear structures from noisy data
Authors: Pulkkinen Seppo
Publisher: ELSEVIER SCIENCE BV
Publication year: 2015
Journal: Computational Statistics and Data Analysis
Journal name in source: COMPUTATIONAL STATISTICS & DATA ANALYSIS
Journal acronym: COMPUT STAT DATA AN
Volume: 82
First page : 89
Last page: 109
Number of pages: 21
ISSN: 0167-9473
eISSN: 1872-7352
DOI: https://doi.org/10.1016/j.csda.2014.08.007
Abstract
Extraction of curvilinear structures from noisy data is an essential task in many application fields such as data analysis, pattern recognition and machine vision. The proposed approach assumes a random process in which the samples are obtained from a generative model. The model specifies a set of generating functions describing curvilinear structures as well as sampling noise and background clutter. It is shown that ridge curves of the marginal density induced by the model can be used to estimate the generating functions. Given a Gaussian kernel density estimate for the marginal density, ridge curves of the density estimate are parametrized as the solution to a differential equation. Finally, a predictor corrector algorithm for tracing the ridge curve set of such a density estimate is developed. Efficiency and robustness of the algorithm are demonstrated by numerical experiments on synthetic datasets as well as observational datasets from seismology and cosmology. (C) 2014 Elsevier B.V. All rights reserved.
Extraction of curvilinear structures from noisy data is an essential task in many application fields such as data analysis, pattern recognition and machine vision. The proposed approach assumes a random process in which the samples are obtained from a generative model. The model specifies a set of generating functions describing curvilinear structures as well as sampling noise and background clutter. It is shown that ridge curves of the marginal density induced by the model can be used to estimate the generating functions. Given a Gaussian kernel density estimate for the marginal density, ridge curves of the density estimate are parametrized as the solution to a differential equation. Finally, a predictor corrector algorithm for tracing the ridge curve set of such a density estimate is developed. Efficiency and robustness of the algorithm are demonstrated by numerical experiments on synthetic datasets as well as observational datasets from seismology and cosmology. (C) 2014 Elsevier B.V. All rights reserved.
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