Statistical Scale Space Methods

Holmström, Lasse; Pasanen, Leena

doi:10.1111/insr.12155

Cited by 18 publications

(6 citation statements)

References 126 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally, one interesting topic for future work would be to consider also a so-called scale space approach where, instead of a fixed level smoothing in a density estimate, a whole range of smooths are explored in order discover salient features of data in different scales [29,30]. Such a method for 2D circular data that uses kernel estimation with a von Mises-Fisher kernel has been proposed in [31].…”

Section: Discussionmentioning

confidence: 99%

Analyzing infant head flatness and asymmetry using kernel density estimation of directional surface data from a craniofacial 3D model

et al. 2016

Self Cite

View full text Add to dashboard Cite

Infant skull deformation is analyzed using the distribution of head normal vector directions computed from a 3D image. Severity of flatness and asymmetry are quantified by functionals of the kernel estimate of the normal vector direction density. Using image data from 99 infants and clinical deformation ratings made by experts, our approach is compared with some recently suggested methods. The results show that the proposed method performs competitively. Copyright © 2016 John Wiley & Sons, Ltd.

show abstract

Section: Discussionmentioning

confidence: 99%

Analyzing infant head flatness and asymmetry using kernel density estimation of directional surface data from a craniofacial 3D model

et al. 2016

Self Cite

View full text Add to dashboard Cite

show abstract

“…The development of scale-space methodology is typically regarded to start with two papers by Witkin [4, 5]. A recent review by Holmström and Pasanen [6] shows how scale-space methodology has been extended to a large number of areas. The goal of statistical scale-space methodology is to extract features from noisy data at several levels of resolution.…”

Section: Introductionmentioning

confidence: 99%

A novel scale-space approach for multinormality testing and the k-sample problem in the high dimension low sample size scenario

2019

View full text Add to dashboard Cite

Two classical multivariate statistical problems, testing of multivariate normality and the k-sample problem, are explored by a novel analysis on several resolutions simultaneously. The presented methods do not invert any estimated covariance matrix. Thereby, the methods work in the High Dimension Low Sample Size situation, i.e. when n ≤ p. The output, a significance map, is produced by doing a one-dimensional test for all possible resolution/position pairs. The significance map shows for which resolution/position pairs the null hypothesis is rejected. For the testing of multinormality, the Anderson-Darling test is utilized to detect potential departures from multinormality at different combinations of resolutions and positions. In the k-sample case, it is tested whether k data sets can be said to originate from the same unspecified discrete or continuous multivariate distribution. This is done by testing the k vectors corresponding to the same resolution/position pair of the k different data sets through the k-sample Anderson-Darling test. Successful demonstrations of the new methodology on artificial and real data sets are presented, and a feature selection scheme is demonstrated.

show abstract

“…The concept of a scale space has its origin in computer vision literature (Witkin ; Lindeberg, ). The idea was first introduced to statistics by Chaudhuri & Marron (), and it has subsequently developed into a versatile ensemble of techniques with many applications (Holmström & Pasanen, ). In traditional scale space analysis, increasing smoothing progressively suppresses smaller scale data features, thus revealing increasingly coarse structures in the data.…”

Section: Introductionmentioning

confidence: 99%

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

Pasanen

Aakala

Holmström

2018

Stat

Self Cite

View full text Add to dashboard Cite

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.We propose a two-step procedure for the analysis of such hierarchical data. First, the signal is decomposed into components that represent its variation in different levels of hierarchy, and second, the characteristic feature size of each hierarchical level is determined.In the first step, scale space multiresolution analysis (Holmström et al., 2011), an instance of statistical scale space methodology, is applied. Conventional scale space analysis considers smooths of a signal, interpreting each smooth

show abstract

Statistical Scale Space Methods

Cited by 18 publications

References 126 publications

Analyzing infant head flatness and asymmetry using kernel density estimation of directional surface data from a craniofacial 3D model

Analyzing infant head flatness and asymmetry using kernel density estimation of directional surface data from a craniofacial 3D model

A novel scale-space approach for multinormality testing and the k-sample problem in the high dimension low sample size scenario

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

Contact Info

Product

Resources

About