A scale space approach for estimating the characteristic feature sizes in hierarchical signals

Leena Pasanen, Tuomas Aakala, Lasse Holmström

Research output: Contribution to journalArticleScientificpeer-review


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. (c) 2018 John Wiley & Sons, Ltd.
Original languageEnglish
Article numbere195
JournalStat : the ISI's journal for rapid dissemination of statistics research
Issue number1
Number of pages17
Publication statusPublished - 2018
MoE publication typeA1 Journal article-refereed

Fields of Science

  • 4112 Forestry
  • environmetrics
  • image analysis
  • smoothing
  • time series
  • visualization
  • multiresolution analysis
  • temperature
  • extraction
  • view
  • 112 Statistics and probability

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