Effect of Noise in Estimation of Fractal Dimension of Digital Images

Pant, Triloki

doi:10.14257/ijsip.2013.6.5.10

Cited by 8 publications

(3 citation statements)

References 24 publications

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“…The highest values were around 1.4 but these are sometimes found in fields with very low column densities where the values are affected by observational noise and even the extragalactic background. Both act as noise, which tends to increase the D P values (Vogelaar & Wakker 1994;Pant 2013).…”

Section: Fractal Dimensionmentioning

confidence: 99%

Galactic cold cores

Juvela

Malinen

Montillaud

et al. 2018

A&A

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Context. The Galactic Cold Cores (GCC) project has made Herschel photometric observations of interstellar clouds where Planck detected compact sources of cold dust emission. The fields are in different environments and stages of star formation. Aims. Our aim is to characterise the structure of the clumps and their parent clouds, and to study the connections between the environment and the formation of gravitationally bound objects. We also examine the accuracy to which the structure of dense clumps can be determined from sub-millimetre data. Methods. We use standard statistical methods to characterise the GCC fields. Individual clumps are extracted using column density thresholding. Based on sub-millimetre measurements, we construct a three-dimensional radiative transfer (RT) model for each field. These are used to estimate the relative radiation field intensities, to probe the clump stability, and to examine the uncertainty of column density estimates. We examine the structural parameters of the clumps, including their radial column density profiles. Results. In the GCC fields, the structure noise follows the relations previously established at larger scales and in lower-density clouds. The fractal dimension has no significant dependence on column density and the values DP = 1.25 ± 0.07 are only slightly lower than in typical molecular clouds. The column density probability density functions (PDFs) exhibit large variations, for example, in the case of externally compressed clouds. At scales r > 0.1 pc, the radial column density distributions of the clouds follow an average relation of N ~ r−1. In spite of a great variety of clump morphologies (and a typical aspect ratio of 1.5), clumps tend to follow a similar N ~ r−1 relation below r ~ 0.1 pc. RT calculations indicate only factor 2.5 variation in the local radiation field intensity. The fraction of gravitationally bound clumps increases significantly in regions with AV > 5 mag but most bound objects appear to be pressure-confined. Conclusions. The host clouds of the cold clumps in the GCC sample have statistical properties similar to general molecular clouds. The gravitational stability, peak column density, and clump orientation are connected to the cloud background while most other statistical clump properties (e.g. DP and radial profiles) are insensitive to the environment. The study of clump morphology should be continued with a comparison with numerical simulations.

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Section: Fractal Dimensionmentioning

confidence: 99%

Galactic cold cores

Juvela

Malinen

Montillaud

et al. 2018

A&A

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“…Note that both of these objects are self-similar. We may break a line segment into 4 self-similar intervals, each with the same length, and each of which can be magnified by a factor of 4 to yield the original segment [1,16]. We can also break a line segment into 7 self-similar pieces, each with magnification factor 7, or 20 self-similar pieces with magnification factor 20.…”

Section: Fractal Dimensionmentioning

confidence: 99%

A Review of Fractals Properties: Mathematical Approach

Nurujjaman¹,

Hossain²,

Ahmed³

2017

SJAMS

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Abstract:In this article, we will discuss some spectacularly beautiful images known as Fractals such as Sierpiński Triangle, Koch Curve, Dragon Curve, Koch Island, H Fractal, The Levy Curve Fractal, Box Fractal etc. We will investigate and calculate the area, perimeter and self-similar dimension of fractals. Observing the results we see some similarities about the said properties for some fractals those are generated by particular method. Our attention is restricted to find the mathematical behavior of Fractals so that we can establish mathematical formulas concerning the fractals.

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“…Manoj Kumar et.al [12] modified Clarke's original Triangular Prism Surface Area Method to estimate fractal dimensions of gray scale images. The effects of noise on the values of fractal dimensions of digital images were discussed by T. Pant [13]. Gaussian noise, salt and pepper noise and speckle noise were applied to the digital images to generate noisy images.…”

Section: A Literature Reviewmentioning

confidence: 99%

A Novel Approach to Diagnose Diabetic Retinopathy

Lamani¹,

Manjunath²,

M³

et al. 2015

IJIGSP

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Early identification of diabetic retinopathy is highly beneficial for preventing the progression of disease. Appearance of blood vessels & retinal surface is a good ophthalmological sign of diabetic retinopathy in fundus images. In this paper, a novel method involving two approaches has been proposed for diagnosis of diabetic retinopathy. The first approach deals with estimation of fractal dimension of lesions by applying power spectral fractal dimension algorithms. For healthy retinas, fractal dimensions are found to be in the range of 2.00 to 2.069, whereas for retinas with diabetic retinopathy, fractal dimensions exceed upper limit. In the second approach, Gray Level Co-occurrence Matrix method is used to analyze the extracted regions from healthy and diabetes affected fundus retinal images. Texture features such as entropy & contrast are computed for healthy and unhealthy regions. These texture features are compared with fractal dimensions. The authors observed positive correlation between entropy and fractal dimensions, whereas negative correlation with contrast and fractal dimensions. Detailed implementations of the proposed work are presented.

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Effect of Noise in Estimation of Fractal Dimension of Digital Images

Abstract: In present paper the effect of noise on fractal dimension of digital images has been tested.

Cited by 8 publications

References 24 publications

Galactic cold cores

Galactic cold cores

A Review of Fractals Properties: Mathematical Approach

A Novel Approach to Diagnose Diabetic Retinopathy

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