A scale space approach for estimating the characteristic feature sizes in hierarchical signals
|Author:||Ruha (née Pasanen), Leena1; Aakala, Tuomas2; Holmström, Lasse1|
1Research Unit of Mathematical Sciences, University of Oulu, Oulu, Finland
2Department of Forest Sciences, University of Helsinki, Helsinki, Finland
|Persistent link:|| http://urn.fi/urn:nbn:fi-fe2018082834185
John Wiley & Sons,
|Publish Date:|| 2019-08-13
The temporal and spatial data analysed in, for example, ecology or climatology, are often hierarchically structured, carrying information in different scales. An important goal of data analysis is then to decompose the observed signal into distinctive hierarchical levels and to determine the size of the features that each level represents. Using differences of smooths, scale space multiresolution analysis decomposes a signal into additive components associated with different levels of scales present in the data. The smoothing levels used to compute the differences are determined by the local minima of the norm of the so‐called scale‐derivative of the signal. While this procedure accomplishes the first goal, the hierarchical decomposition of the signal, it does not achieve the second goal, the determination of the actual size of the features corresponding to each hierarchical level. Here, we show that the maximum of the scale‐derivative norm of an extracted hierarchical component can be used to estimate its characteristic feature size. The feasibility of the method is demonstrated using an artificial image and a time series of a drought index, based on climate reconstructions from long tree ring chronologies.
|Type of Publication:||
A1 Journal article – refereed
|Field of Science:||
112 Statistics and probability
This study was funded by the Academy of Finland under grant no. 276022 and by the Kone Foundation.
|Academy of Finland Grant Number:||
276022 (Academy of Finland Funding decision)
© 2018 John Wiley & Sons, Ltd. "This is the peer reviewed version of the following article: Pasanen, L., Aakala, T., and Holmström, L. (2018) A scale space approach for estimating the characteristic feature sizes in hierarchical signals. Stat, 7: e195, https://doi.org/10.1002/sta4.195, which has been published in final form at https://doi.org/10.1002/sta4.195. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.