Neural Computing and Applications

, Volume 29, Issue 8, pp 159–180 | Cite as

Noise-estimation-based anisotropic diffusion approach for retinal blood vessel segmentation

  • Mariem Ben Abdallah
  • Ahmad Taher Azar
  • Hichem Guedri
  • Jihene Malek
  • Hafedh Belmabrouk
New Trends in data pre-processing methods for signal and image classification


Recently, numerous research works in retinal-structure analysis have been performed to analyze retinal images for diagnosing and preventing ocular diseases such as diabetic retinopathy, which is the first most common causes of vision loss in the world. In this paper, an algorithm for vessel detection in fundus images is employed. First, a denoising process using the noise-estimation-based anisotropic diffusion technique is applied to restore connected vessel lines in a retinal image and eliminate noisy lines. Next, a multi-scale line-tracking algorithm is implemented to detect all the blood vessels having similar dimensions at a selected scale. An openly available dataset, called “the STARE Project’s dataset,” has been firstly utilized to evaluate the accuracy of the proposed method. Accordingly, our experimental results, performed on the STARE dataset, depict a maximum average accuracy of around 93.88%. Then, an experimental evaluation on another dataset, named DRIVE database, demonstrates a satisfactory performance of the proposed technique, where the maximum average accuracy rate of 93.89% is achieved.


Segmentation Filtering RGB noise model Anisotropic diffusion Vessel Retina 



Adaptive noise-reducing anisotropic diffusion filter


Detail preserving anisotropic diffusion


Flux-based anisotropic diffusion


Noise level function


Maximum likelihood estimator


False-positive rate


Maximum average accuracy


Mean structural similarity index measure


Anisotropic diffusion of perona and malik


Signal-to-noise ratio


Specle reducing anisotropic diffusion


True positive rate

List of symbols


Image pixel


Response function of a camera


Irradiance image


Image intensity


Noisy image


Multiplicative noise


Additive noise


Variance of additive noise


Variance of multiplicative noise


Quantization noise


Noise model


Expectation of a random variable

\(\overline{{\sum^{2} }}\)

Mean of principal components


Eigenvectors of principal components


Number of retained eigenvectors


Unknown parameters of noise model


Index of unknown parameters of noise model

i, j

Spatial coordinates of current pixel x


Window centered at current pixel


Instantaneous coefficient of the variation of the image


Instantaneous coefficient of the variation of the noise


Diffusion function


Local variance


Square of local mean intensity


Step time


Iteration number of ANRAD filter

Gradient operator


Divergence operator


Discretization number


Continuous scale parameter


Convolution kernel


Derivative operator


Minimal scale


Maximal scale


Image orientation


Response function at scale σ


Multi-scale response

\(\overrightarrow {d}\)

Unitary vector of direction Θ

\(\overrightarrow {v}_{1}\)

First eigenvector of Hessian matrix

\(\overrightarrow {v}_{2}\)

Second eigenvector of Hessian matrix


First eigenvalue of Hessian matrix


Second eigenvalue of Hessian matrix


Radius vessel


Scale range

\(I^{ '} \,\)

Interpolated image

\(Q_{11} \, , \, Q_{12} \, , \, Q_{21} \, , \, Q_{22}\)

Four nearest pixel values of pixel \(x\)


Displacement along i-axis


Displacement along j-axis


Threshold on norm gradient of image


Iteration number of PMAD method


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Copyright information

© The Natural Computing Applications Forum 2017

Authors and Affiliations

  • Mariem Ben Abdallah
    • 1
    • 2
    • 3
    • 4
  • Ahmad Taher Azar
    • 1
    • 2
    • 3
    • 4
  • Hichem Guedri
    • 1
    • 2
    • 4
  • Jihene Malek
    • 1
    • 2
    • 4
  • Hafedh Belmabrouk
    • 1
    • 2
    • 4
  1. 1.Electronics and Micro-Electronic LaboratoryMonastir UniversityMonastirTunisia
  2. 2.Faculty of Computers and InformationBenha UniversityBenhaEgypt
  3. 3.Nanoelectronics Integrated Systems Center (NISC)Nile UniversityCairoEgypt
  4. 4.Department of Physics, College of Science in ZulfiMajmaah UniversityAl Majma’ahSaudi Arabia

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