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Scale space methods

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Abstract We discuss methods that use multiscale smoothing for explorative data analysis and inference. The problems considered involve nonparametric density estimation and regression, time series analysis, image analysis, and more general spatial data analysis settings. Copyright © 2010 John Wiley & Sons, Inc. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Statistical Graphics and Visualization

Three slices of a scale space of a rose image.

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First row: the reconstructed image difference E (μ|y) of two satellite images (first panel) together with three smooths obtained as posterior means E (Sλμ|y). The effective size of the smoother is indicated by the yellow circle. Second row: credibility maps that show the salient features in different spatial resolutions.

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Left panel: the noisy example image. Middle panel: arrows indicate significant gradient direction and different colors flag different types of local curvature. Right hand panel: streamlines computed from significant gradient directions.

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BSiZer analysis of a diatom‐ based temperature reconstruction in northern Fennoscandia for the last 800 years. The upper panel: the reconstructed temperatures shown as asterisks together with three smooths obtained as posterior means. The lower panel: BSiZer map with the three smoothing levels shown using the same colors as in the upper panel. For details see Ref 24.

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SiZer analysis of the Hidalgo stamp data. In the upper panel several smooths of data are shown and the SiZer map is in the lower panel.

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