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

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Abstract

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.

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Abbreviations

ANRAD:

Adaptive noise-reducing anisotropic diffusion filter

DPAD:

Detail preserving anisotropic diffusion

FBAD:

Flux-based anisotropic diffusion

NLF:

Noise level function

MLE:

Maximum likelihood estimator

\({\text{FPR}}\) :

False-positive rate

\({\text{MAA}}\) :

Maximum average accuracy

\({\text{MSSIM}}\) :

Mean structural similarity index measure

PMAD:

Anisotropic diffusion of perona and malik

\({\text{SNR}}\) :

Signal-to-noise ratio

SRAD:

Specle reducing anisotropic diffusion

\({\text{TPR}}\) :

True positive rate

x :

Image pixel

f :

Response function of a camera

L :

Irradiance image

I :

Image intensity

I N :

Noisy image

N s :

Multiplicative noise

N c :

Additive noise

σ 2 c :

Variance of additive noise

σ 2 s :

Variance of multiplicative noise

N q :

Quantization noise

∑2 :

Noise model

IE(.):

Expectation of a random variable

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

Mean of principal components

ω η :

Eigenvectors of principal components

m :

Number of retained eigenvectors

α η :

Unknown parameters of noise model

η :

Index of unknown parameters of noise model

i, j :

Spatial coordinates of current pixel x

w i,j :

Window centered at current pixel

c :

Instantaneous coefficient of the variation of the image

c 2 n :

Instantaneous coefficient of the variation of the noise

φ :

Diffusion function

Var:

Local variance

\(\overline{I}^{2}\) :

Square of local mean intensity

Δt :

Step time

iter:

Iteration number of ANRAD filter

∇:

Gradient operator

div:

Divergence operator

κ :

Discretization number

t :

Continuous scale parameter

G :

Convolution kernel

∂ :

Derivative operator

σ min :

Minimal scale

σ max :

Maximal scale

Θ :

Image orientation

Γ σ :

Response function at scale σ

Γ multi :

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

λ 1 :

First eigenvalue of Hessian matrix

λ 2 :

Second eigenvalue of Hessian matrix

r :

Radius vessel

[t min, t max]:

Scale range

\(I^{ '} \,\) :

Interpolated image

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

Four nearest pixel values of pixel \(x\)

di :

Displacement along i-axis

dj :

Displacement along j-axis

Thres:

Threshold on norm gradient of image

\(N\) :

Iteration number of PMAD method

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Authors and Affiliations

  1. Electronics and Micro-Electronic Laboratory, Monastir University, Monastir, Tunisia

    Mariem Ben Abdallah, Ahmad Taher Azar, Hichem Guedri, Jihene Malek & Hafedh Belmabrouk

  2. Faculty of Computers and Information, Benha University, Benha, Egypt

    Mariem Ben Abdallah, Ahmad Taher Azar, Hichem Guedri, Jihene Malek & Hafedh Belmabrouk

  3. Nanoelectronics Integrated Systems Center (NISC), Nile University, Cairo, Egypt

    Mariem Ben Abdallah & Ahmad Taher Azar

  4. Department of Physics, College of Science in Zulfi, Majmaah University, Al Majma’ah, Saudi Arabia

    Mariem Ben Abdallah, Ahmad Taher Azar, Hichem Guedri, Jihene Malek & Hafedh Belmabrouk

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  1. Mariem Ben Abdallah
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  2. Ahmad Taher Azar
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  3. Hichem Guedri
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Correspondence to Mariem Ben Abdallah.

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Ben Abdallah, M., Azar, A., Guedri, H. et al. Noise-estimation-based anisotropic diffusion approach for retinal blood vessel segmentation. Neural Comput & Applic 29, 159–180 (2018). https://doi.org/10.1007/s00521-016-2811-9

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