Box-Counting Fractal Dimension Algorithm Variations on Retina Images

Azemin, Mohd Zulfaezal Che; Hamid, Fadilah Ab; Wang, Jie Jin; Kawasaki, Ryo; Kumar, Deepak

doi:10.1007/978-3-319-24584-3_27

Cited by 9 publications

(3 citation statements)

References 14 publications

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“…In the case of the analysis of human retinal vessels, it has been reported that a healthy eye has an FD of around 1.7 (Family, Masters, & Platt, 1989;Mainster, 1990;Popovic et al, 2018). However, it has also been shown that, due to its underlying dependence on the structural properties of the image, the FD is sensitive to a number of other factors from both biological origin e.g., age, cataracts, and lens opacity (Cheung et al, 2012), changes in blood pressure due different origins (Sng et al, 2010;Zhu et al, 2014), existing diabetic condition , and cognitive dysfunctions (Taylor et al, 2015), as well as numerical origin e.g., size and location of the region of interest Huang et al, 2015) or the specific stages in the pre-processing procedure (Che Azemin et al, 2016). Due to this overall 'instability' of the FD, which can be significant in some cases, one should not rely a quantitative analysis for diagnosis purposes solely on the value of the FD (Huang et al, 2015).…”

Section: Resultsmentioning

confidence: 99%

A proposal to measure the similarity between retinal vessel segmentations images

Escobar

Sepúlveda

Parra-Michel

et al. 2019

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Introduction: We propose a novel approach for the assessment of the similarity of retinal vessel segmentation images that is based on linking the standard performance metrics of a segmentation algorithm, with the actual structural properties of the images through the fractal dimension.Method: We apply our methodology to compare the vascularity extracted by automatic segmentation against manually segmented images.Results: We demonstrate that the strong correlation between the standard metrics and fractal dimension is preserved regardless of the size of the subimages analyzed.Discussion or Conclusion: We show that the fractal dimension is correlated to the segmentation algorithm’s performance and therefore it can be used as a comparison metric.

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Section: Resultsmentioning

confidence: 99%

A proposal to measure the similarity between retinal vessel segmentations images

Escobar

Sepúlveda

Parra-Michel

et al. 2019

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“…The second step involves the enumeration of the number of boxes (N) that overlap the matter. Estimation of the FD value can then be calculated from the slope of log Number (N) against log box-size (s) [32]. An example of 3D box-counting analysis is shown in Figure 2.…”

Section: Box-counting Fractal Dimension (Fd)mentioning

confidence: 99%

Volume of Interest-Based Fractal Analysis of Huffaz’s Brain

et al. 2022

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The robust process in memorising the Quran is expected to cause neuroplasticity changes in the brain. To date, the analysis of neuroplasticity is limited in binary images because greyscale analysis requires the usage of more robust processing techniques. This research work aims to explore and characterise the complexity of textual memorisation brain structures using fractal analysis between huffaz and non-huffaz applying global box-counting, global Fourier fractal dimension (FFD), and volume of interest (VOI)-based analysis. The study recruited 47 participants from IIUM Kuantan Campus. The huffaz group had their 18 months of systematic memorisation training. The brain images were acquired by using MRI. Global box-counting and FFD analysis were conducted on the brain. Magnetic resonance imaging (MRI) found no significant statistical difference between brains of huffaz and non-huffaz. VOI-based analysis found nine significant areas: two for box-counting analysis (angular gyrus and medial temporal gyrus), six for FFD analysis (BA20, BA30, anterior cingulate, fusiform gyrus, inferior temporal gyrus, and frontal lobe), and only a single area (BA33) showed significant volume differences between huffaz and non-huffaz. The results have highlighted the sensitivity of VOI-based analysis because of its local nature, as compared to the global analysis by box-counting and FFD.

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“…The equation system provides five equations for five parameters, so d i , the vertical scaling factor, is computed by using the fractal dimension (DF) calculated by the box-counting algorithm [54,55]. We can solve the above equations for a i ,c i , d i ,e i ,F i which are defined as…”

Section: Affine Transformationmentioning

confidence: 99%

Reconstruction of Three-Dimensional Blood Vessel Model Using Fractal Interpolation

Guedri¹,

Belmabrouk²

2020

Computer Methods and Programs in Biomedical Signal and Image Processing

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Fractal method is used in the image processing and studying the irregular and the complex shapes in the image. It is also used in the reconstruction and smoothing of one-, two-, and three-dimensional data. In this chapter, we present an interpolating fractal algorithm to reconstruct 3D blood vessels. Firstly, the proposed method determines the blood vessel centerline from the 2D retina image, and then it uses the Douglas-Peucker algorithm to detect the control points. Secondly, we use the 3D fractal interpolation and iterated function systems for the visualization and reconstruction of these blood vessels. The results showed that the obtained reduction rate is between 71 and 94% depending on the tolerance value. The 3D blood vessels model can be reconstructed efficiently by using the 3D fractal interpolation method.

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Box-Counting Fractal Dimension Algorithm Variations on Retina Images

Cited by 9 publications

References 14 publications

A proposal to measure the similarity between retinal vessel segmentations images

A proposal to measure the similarity between retinal vessel segmentations images

Volume of Interest-Based Fractal Analysis of Huffaz’s Brain

Reconstruction of Three-Dimensional Blood Vessel Model Using Fractal Interpolation

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