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Ridge-based method for finding curvilinear structures from noisy data

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  • Pulkkinen, Seppo

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.

Suggested Citation

  • Pulkkinen, Seppo, 2015. "Ridge-based method for finding curvilinear structures from noisy data," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 89-109.
    • Handle: RePEc:eee:csdana:v:82:y:2015:i:c:p:89-109
    DOI: 10.1016/j.csda.2014.08.007
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    References listed on IDEAS

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    1. Delicado, Pedro, 2001. "Another Look at Principal Curves and Surfaces," Journal of Multivariate Analysis, Elsevier, vol. 77(1), pages 84-116, April.
    2. J. Chacón & T. Duong, 2010. "Multivariate plug-in bandwidth selection with unconstrained pilot bandwidth matrices," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 375-398, August.
    3. Christopher R. Genovese & Marco Perone-Pacifico & Isabella Verdinelli & Larry Wasserman, 2012. "The Geometry of Nonparametric Filament Estimation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 788-799, June.
    4. Seppo Pulkkinen & Marko Mäkelä & Napsu Karmitsa, 2013. "A continuation approach to mode-finding of multivariate Gaussian mixtures and kernel density estimates," Journal of Global Optimization, Springer, vol. 56(2), pages 459-487, June.
    5. Jang, Woncheol, 2006. "Nonparametric density estimation and clustering in astronomical sky surveys," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 760-774, February.
    6. Seppo Pulkkinen & Marko Mäkelä & Napsu Karmitsa, 2014. "A generative model and a generalized trust region Newton method for noise reduction," Computational Optimization and Applications, Springer, vol. 57(1), pages 129-165, January.
    7. Tarn Duong & Martin L. Hazelton, 2005. "Cross‐validation Bandwidth Matrices for Multivariate Kernel Density Estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(3), pages 485-506, September.
    8. Su, J. & Srivastava, A. & Huffer, F.W., 2013. "Detection, classification and estimation of individual shapes in 2D and 3D point clouds," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 227-241.
    9. Pedro Delicado & Mario Huerta, 2003. "Principal Curves of Oriented Points: theoretical and computational improvements," Computational Statistics, Springer, vol. 18(2), pages 293-315, July.
    10. Duong, Tarn, 2007. "ks: Kernel Density Estimation and Kernel Discriminant Analysis for Multivariate Data in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 21(i07).
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