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

Leena Pasanen, Tuomas Aakala, Lasse Holmström

Tutkimustuotos: ArtikkelijulkaisuArtikkeliTieteellinenvertaisarvioitu

Kuvaus

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.
Alkuperäiskielienglanti
Artikkelie195
LehtiStat : the ISI's journal for rapid dissemination of statistics research
Vuosikerta7
Numero1
Sivumäärä17
ISSN2049-1573
DOI - pysyväislinkit
TilaJulkaistu - 2018
OKM-julkaisutyyppiA1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä, vertaisarvioitu

Tieteenalat

  • 4112 Metsätiede
  • 112 Tilastotiede

Lainaa tätä

@article{1fda844ff9074be3a86ee8b99fd20982,
title = "A scale space approach for estimating the characteristic feature sizes in hierarchical signals",
abstract = "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.",
keywords = "4112 Forestry, environmetrics, image analysis, smoothing, time series, visualization, multiresolution analysis, temperature, extraction, view, 112 Statistics and probability",
author = "Leena Pasanen and Tuomas Aakala and Lasse Holmstr{\"o}m",
year = "2018",
doi = "10.1002/sta4.195",
language = "English",
volume = "7",
journal = "Stat : the ISI's journal for rapid dissemination of statistics research",
issn = "2049-1573",
publisher = "Wiley",
number = "1",

}

A scale space approach for estimating the characteristic feature sizes in hierarchical signals. / Pasanen, Leena; Aakala, Tuomas ; Holmström, Lasse.

julkaisussa: Stat : the ISI's journal for rapid dissemination of statistics research, Vuosikerta 7, Nro 1, e195, 2018.

Tutkimustuotos: ArtikkelijulkaisuArtikkeliTieteellinenvertaisarvioitu

TY - JOUR

T1 - A scale space approach for estimating the characteristic feature sizes in hierarchical signals

AU - Pasanen, Leena

AU - Aakala, Tuomas

AU - Holmström, Lasse

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - 4112 Forestry

KW - environmetrics

KW - image analysis

KW - smoothing

KW - time series

KW - visualization

KW - multiresolution analysis

KW - temperature

KW - extraction

KW - view

KW - 112 Statistics and probability

U2 - 10.1002/sta4.195

DO - 10.1002/sta4.195

M3 - Article

VL - 7

JO - Stat : the ISI's journal for rapid dissemination of statistics research

JF - Stat : the ISI's journal for rapid dissemination of statistics research

SN - 2049-1573

IS - 1

M1 - e195

ER -