Ridge-based method for finding curvilinear structures from noisy data

: Pulkkinen Seppo

Publisher: ELSEVIER SCIENCE BV

: 2015

: Computational Statistics and Data Analysis

: COMPUTATIONAL STATISTICS & DATA ANALYSIS

: COMPUT STAT DATA AN

: 82

: 89

: 109

: 21

: 0167-9473

: 1872-7352

DOI: https://doi.org/10.1016/j.csda.2014.08.007

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.