Measuring homogeneity of planar point-patterns by using kurtosis

Johansson, Jan-Olof

doi:10.1016/s0167-8655(00)00076-3

Cited by 12 publications

(5 citation statements)

References 2 publications

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“…The variance of the PDF, for example, is an interesting measure of colour richness because it is influenced both by the area in the space occupied by colours, and by the homogeneity of colour distribution. The kurtosis is a better estimate of homogeneity independent of the area (Johansson, ). With a fixed bandwidth of the kernel, it is further possible to compare PDFs between data sets, for example to identify the regions in a colour space where two communities or taxa differ maximally (or minimally) in densities.…”

Section: Colour Diversitymentioning

confidence: 99%

Colour spaces in ecology and evolutionary biology

2015

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The recognition that animals sense the world in a different way than we do has unlocked important lines of research in ecology and evolutionary biology. In practice, the subjective study of natural stimuli has been permitted by perceptual spaces, which are graphical models of how stimuli are perceived by a given animal. Because colour vision is arguably the best-known sensory modality in most animals, a diversity of colour spaces are now available to visual ecologists, ranging from generalist and basic models allowing rough but robust predictions on colour perception, to species-specific, more complex models giving accurate but context-dependent predictions. Selecting among these models is most often influenced by historical contingencies that have associated models to specific questions and organisms; however, these associations are not always optimal. The aim of this review is to provide visual ecologists with a critical perspective on how models of colour space are built, how well they perform and where their main limitations are with regard to their most frequent uses in ecology and evolutionary biology. We propose a classification of models based on their complexity, defined as whether and how they model the mechanisms of chromatic adaptation and receptor opponency, the nonlinear association between the stimulus and its perception, and whether or not models have been fitted to experimental data. Then, we review the effect of modelling these mechanisms on predictions of colour detection and discrimination, colour conspicuousness, colour diversity and diversification, and for comparing the perception of colour traits between distinct perceivers. While a few rules emerge (e.g. opponent log-linear models should be preferred when analysing very distinct colours), in general model parameters still have poorly known effects. Colour spaces have nonetheless permitted significant advances in ecology and evolutionary biology, and more progress is expected if ecologists compare results between models and perform behavioural experiments more routinely. Such an approach would further contribute to a better understanding of colour vision and its links to the behavioural ecology of animals. While visual ecology is essentially a transfer of knowledge from visual sciences to evolutionary ecology, we hope that the discipline will benefit both fields more evenly in the future.

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Section: Colour Diversitymentioning

confidence: 99%

Colour spaces in ecology and evolutionary biology

2015

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“…Cherkassky (1998) used the homogeneity and the inhomogeneity theory of irregular random fields to indicate deviations that would suggest degrees of non-uniformity [13]. Johansson (2000) recommended that Kurtosis can be used as a scale to gauge the non-uniformity of each quantifiable characteristic on a flat surface [14]. To determine the level of non-uniformity, wavelet analysis and LVQ neural network [15], Bayesian [16], and the generalized Gaussian density model [17] were used.…”

Section: Tensile Testmentioning

confidence: 99%

Measurement of the Uniformity of Thermally Bonded Points in Polypropylene Spunbonded Non-Wovens Using Image Processing and its Relationship With Their Tensile Properties

Emadi

Tavanaie

Payvandy

2018

Autex Research Journal

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This article aims at the image processing of surface uniformity and thermally bonded points uniformity in polypropylene spunbonded non-wovens. The investigated samples were at two different weights and three levels of non-uniformity. An image processing method based on the k-means clustering algorithm was applied to produce clustered images. The best clustering procedure was selected by using the lowest Davies-Bouldin index. The peak signal-to-noise ratio (PSNR) image quality evaluation method was used to choose the best binary image. Then, the non-woven surface uniformity was calculated using the quadrant method. The uniformity of thermally bonded points was calculated through an image processing method based on morphological operators. The relationships between the numerical outcomes and the empirical results of tensile tests were investigated. The results of image processing and tensile behavior showed that the surface uniformity and the uniformity of thermally bonded points have great impacts on tensile properties at the selected weights and non-uniformity levels. Thus, a sample with a higher level of uniformity and, consequently, more regular bonding points with further bonding percentage depicts the best tensile properties.

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“…Johansson describes how kurtosis can be used to measure the homogeneity of any property on a given area [15]. This approach is, however, not applicable to our scenario as it assumes some knowledge of the given distribution (e.g.…”

Section: Related Workmentioning

confidence: 99%

Measuring Inhomogeneity in Spatial Distributions

Schilcher

Gyarmati

Bettstetter

et al. 2008

VTC Spring 2008 - IEEE Vehicular Technology Conference

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Abstract-The spatial distribution of nodes in wireless networks has important impact on network performance properties, such as capacity and connectivity. Although random sample models based on a uniform distribution are widely used in the research community, they are inappropriate for scenarios with clustered, inhomogeneous node distribution. This paper proposes a well-defined measure for the level of inhomogeneity of a node distribution. It is based on the local deviation of the actual value of the density of nodes from its expected value. Desired properties of the measure are defined and mathematically proven to be fulfilled. The inhomogeneity measure is also compared to human perception of inhomogeneity gained via an online survey. The results reveal that the measure well fits human perception, although there are notable deviations if linear operations are applied.

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Measuring homogeneity of planar point-patterns by using kurtosis

Cited by 12 publications

References 2 publications

Colour spaces in ecology and evolutionary biology

Colour spaces in ecology and evolutionary biology

Measurement of the Uniformity of Thermally Bonded Points in Polypropylene Spunbonded Non-Wovens Using Image Processing and its Relationship With Their Tensile Properties

Measuring Inhomogeneity in Spatial Distributions

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