# An Efficient Image Segmentation Algorithm Using Neutrosophic Graph Cut

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## Abstract

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## 1. Introduction

## 2. Previous Works

## 3. Proposed Method

#### 3.1. Neutrosophic Image

_{i}is $\left\{T\left({A}_{i}\right),\text{}I\left({A}_{i}\right),F\left({A}_{i}\right)\right\}/{A}_{i}$, where $T\left({A}_{i}\right)$, $I\left({A}_{i}\right)$ and $F\left({A}_{i}\right)$ are the membership values to the true, indeterminate and false set.

_{m}in NS is called neutrosophic image, denoted as I

_{NS}which is interpreted using Ts, Is and Fs. Given a pixel P(x,y) in I

_{NS}, it is interpreted as ${P}_{NS}\left(x,y\right)=\left\{Ts\left(x,y\right),Is\left(x,y\right),Fs\left(x,y\right)\right\}$. $Ts\left(x,y\right)$, $Is\left(x,y\right)$ and $Fs\left(x,y\right)$ represent the memberships belonging to foreground, indeterminate set and background, respectively.

_{ij}. They are updated at each iteration until $\left|{T}_{{n}_{ij}}^{(k+1)}-{T}_{{n}_{ij}}^{(k)}\right|<\epsilon $, where $\epsilon $ is a termination criterion.

#### 3.2. Indeterminacy Filtering

_{s}and $m$ is the size of the filter kernel. $T{n}_{ij}^{\prime}$ is employed to construct a graph, and a maximum-flow algorithm is used to segment the image.

#### 3.3. Neutrosophic Graph Cut

- Step 1: Compute the local neutrosophic value ${T}_{s}$ and ${I}_{s}$.
- Step 2: Take indeterminate filtering on ${T}_{s}$ using ${I}_{s}$.
- Step 3: Use NCM algorithm on the filtered ${T}_{s}$ subset to obtain ${T}_{n}$ and ${I}_{n}$.
- Step 4: Filter ${T}_{n}$ using indeterminate filter based on ${I}_{n}$.
- Step 5: Define the energy function based on the ${T}_{n}{}^{\prime}$ value.
- Step 6: Partition the image using the maximum flow algorithm.

## 4. Experimental Results

#### 4.1. Quantitatively Evaluation

_{o}, B

_{o}, F

_{T}, and B

_{T}are the object and background pixels on the ground truth image and the resulting image, respectively.

_{th}actual pixel to the nearest segmented result pixel. $\beta $ is a constant and set as 1/9 in [31].

_{n}(r,c)and I(r,c) are the intensities of point (r,c) in the noisy and original images, respectively.

#### 4.2. Performance on Natural Images

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Intermediate results for “Lena” image: (

**a**) Original image; (

**b**) Result of Ts; (

**c**) Result of Is; (

**d**) Filtered result of Ts; (

**e**) Filter result of Tn; (

**f**) Final result.

**Figure 3.**Segmentation comparison on a low contrast synthetic noisy image: (

**a**) Artificial image with different levels of Gaussian noises; (

**b**) Results of the NSC; (

**c**) Results of the GC; (

**d**) Results of the NGC.

**Figure 6.**Comparison results on “Lena” image: (

**a**) “Lena” image with different Gaussian noise level: variance: 0, 10, 20, 30; (

**b**) Segmentation results of NSC; (

**c**) Segmentation results of GC; (

**d**) Segmentation results of KGC; (

**e**) Segmentation results of NGC.

**Figure 7.**Comparison results on “Peppers” image: (

**a**) “Peppers” image with different Gaussian noise level: variance: 0, 10, 20, 30; (

**b**) Segmentation results of NSC; (

**c**) Segmentation results of GC; (

**d**) Segmentation results of KGC; (

**e**) Segmentation results of NGC.

**Figure 8.**Comparison results on “Woman” image: (

**a**) “Woman” image with different Gaussian noise level: variance: 0, 10, 20, 30; (

**b**) Segmentation results of NSC; (

**c**) Segmentation results of GC; (

**d**) Segmentation results of KGC; (

**e**) Segmentation results of NGC.

**Figure 9.**Comparison results on “Lake” image: (

**a**) “Lake” image with different Gaussian noise level: variance: 0, 10, 20, 30; (

**b**) Segmentation results of NSC; (

**c**) Segmentation results of GC; (

**d**) Segmentation results of KGC; (

**e**) Segmentation results of NGC.

**Figure 10.**Comparison results on “Blood” image: (

**a**) “Blood” image with different Gaussian noise level: variance: 0, 10, 20, 30, 40; (

**b**) Segmentation results of NSC; (

**c**) Segmentation results of GC; (

**d**) Segmentation results of KGC; (

**e**) Segmentation results of NGC.

Metrics | NSC | GC | NGC |
---|---|---|---|

ME | 0.247 ± 0.058 | 0.062 ± 0.025 | 0.015 ± 0.011 |

FOM | 0.771 ± 0.025 | 0.897 ± 0.027 | 0.987 ± 0.012 |

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**MDPI and ACS Style**

Guo, Y.; Akbulut, Y.; Şengür, A.; Xia, R.; Smarandache, F.
An Efficient Image Segmentation Algorithm Using Neutrosophic Graph Cut. *Symmetry* **2017**, *9*, 185.
https://doi.org/10.3390/sym9090185

**AMA Style**

Guo Y, Akbulut Y, Şengür A, Xia R, Smarandache F.
An Efficient Image Segmentation Algorithm Using Neutrosophic Graph Cut. *Symmetry*. 2017; 9(9):185.
https://doi.org/10.3390/sym9090185

**Chicago/Turabian Style**

Guo, Yanhui, Yaman Akbulut, Abdulkadir Şengür, Rong Xia, and Florentin Smarandache.
2017. "An Efficient Image Segmentation Algorithm Using Neutrosophic Graph Cut" *Symmetry* 9, no. 9: 185.
https://doi.org/10.3390/sym9090185