Ridge-based method for finding curvilinear structures from noisy data

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.