Robust Methodology for Fractal Analysis of the Retinal Vasculature

Abstract

We have developed a robust method to perform retinal vascular fractal analysis from digital retina images. The technique preprocesses the green channel retina images with Gabor wavelet transforms to enhance the retinal images. Fourier Fractal dimension is computed on these preprocessed images and does not require any segmentation of the vessels. This novel technique requires human input only at a single step; the allocation of the optic disk center. We have tested this technique on 380 retina images from healthy individuals aged 50+ years, randomly selected from the Blue Mountains Eye Study population. To assess its reliability in assessing retinal vascular fractals from different allocation of optic center, we performed pair-wise Pearson correlation between the fractal dimension estimates with 100 simulated region of interest for each of the 380 images. There was Gaussian distribution variation in the optic center allocation in each simulation. The resulting mean correlation coefficient (standard deviation) was 0.93 (0.005). The repeatability of this method was found to be better than the earlier box-counting method. Using this method to assess retinal vascular fractals, we have also confirmed a reduction in the retinal vasculature complexity with aging, consistent with observations from other human organ systems.

Fractal, multifractal and lacunarity analysis applied in retinal regionsof diabetic patients with and without non-proliferative diabetic retinopathy

“…A fractal object or process is characterized by the following properties: self-similarity, scaling, fractal dimension [5,6]. Several works have used the fractal geometry to study the retinal vascular network [7,8]. Doubal et al [9] have obrtained the fractal dimension of retinal vessels in the lacunar stroke and Cavallari et al [10] in the cerebral autosomal dominant arteriopathy with subcortical infarcts and leukoencephalopathy (CADASIL).…”

Segmentation and texture analysis with multimodel inference for the automatic detection of exudates in early diabetic retinopathy

“…Measuring fractal dimension has previously attempted to quantify small changes to the human retinal vasculature, not immediately apparent by human observation, and act as an early marker of disease [28][29][30]. Monofractal analysis is an indicator of vascular change or disease has achieved limited success as retinal vessels may have different properties in different regions and different characteristics can be found depending on the location or scale of the measurement considered.…”

“…We first applied box-counting algorithm (with Hausdorff dimension) approach to calculate fractal dimension in binary type of image (segmentation of vessels) and then the Fourier fractal dimension (FFD) approach, which have been proposed by [28][29][30]. FFD has been used to quantify the grayscale images projected on to 3-D fractal surface [31].…”

“…It has also been found to be relatively insensitive to noise and it is believed to work effectively with data having low signal-to-noise ratio [31,32]. We adapted the similar FFD approach proposed by Azemin M. and et al [30]. The parameters related such as slope and intercept are generated based on this approach.…”

Fundus image analysis for automatic screening of ophthalmic pathologies.

“…In (MacGillivray et al, 2007), a blood vessel segmentation method based on fractal analysis was proposed and a comparison of the fractal dimension (extracted from the blood vessels) between hypertension and non-hypertension groups was carried out without significant evidences of discrimination ability. Azemin et al (2011) proposed a semiautomatic method to compute the fractal dimension of fundus images. They established a comparison between their method and the box-counting method.…”