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A scale space approach for estimating the characteristic feature sizes in hierarchical signals
Author(s) -
Pasanen Leena,
Aakala Tuomas,
Holmström Lasse
Publication year - 2018
Publication title -
stat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.61
H-Index - 18
ISSN - 2049-1573
DOI - 10.1002/sta4.195
Subject(s) - smoothing , scale (ratio) , pattern recognition (psychology) , maxima and minima , norm (philosophy) , signal (programming language) , computer science , hierarchical database model , feature (linguistics) , mathematics , scale space , data mining , algorithm , artificial intelligence , biological system , statistics , image (mathematics) , image processing , geography , cartography , mathematical analysis , political science , linguistics , philosophy , law , programming language , biology
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. © 2018 John Wiley & Sons, Ltd.