# Brain Extraction Using Active Contour Neighborhood-Based Graph Cuts Model

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Sets

#### 2.2. Graph Cuts

_{1},...,A

_{p},..., A

_{|}

_{$\mathcal{P}$}

_{|}) be a binary vector whose components A

_{p}specify assignments to pixels p in data set $\mathcal{P}$. Each A

_{p}can be either “obj” or “bkg” (abbreviations of “object” and “background”). In the graph described by Boykov and Jolly [26], an energy function was defined as below:

_{p}(“obj”) and R

_{p}(“bkg”) reflect how the intensity of the pixel p fits the histogram of the object ($\mathcal{O}$) and background ($\mathcal{B}$) models respectively. The boundary term B(A) was described by:

#### 2.3. Active Contour Neighborhood-Based Graph Cuts Model

#### 2.3.1. Description of ACN Model (ACNM)

#### 2.3.2. Edge Weights Assignment in ACNM

_{m}is the median intensity of the brain tissue on each slice, which is approximated from the pixels within the initial brain region. ${I}_{\mathrm{max}}$ increases the edge weights on the eyeball to avoid the brain boundary leaking through the eyeball tissue.

## 3. Results

#### 3.1. Evaluation Metrics

#### 3.2. Comparison to Other Methods

^{*}-values listed in Table 3, Table 4 and Table 5 are the adjusted P-values of paired t-tests with the Bonferroni-Holm correction to show the statistical difference between the compared methods and the proposed method. Most of the P*-values are below 0.05 except those of FN

_{RATE}and DS for BSE on IBSR18 and IBSR20 data sets, which means the performance of the proposed method was different with the compared methods. Figure 4 and Figure 5 display sample outputs from each method on both IBSR data sets and mark false negative and false positive voxels with different colors to show the extraction errors. To clearly and correctly show the visual extraction errors on all test images for each method, we first warped all the results and the ground truth to the atlas [19], thus every 3D brain extracted from different methods had the same size, and then the false positive and false negative voxels of each warped result could be obtained. The hot color map of the false positive and false negative voxels are shown in Figure 6 and Figure 7. The brighter the hot color in Figure 6 and Figure 7 is, the bigger the error on the corresponding area is. Because the ground truth of OASIS77 (see in Figure 8) is not as precise as those of IBSR18 and IBSR20 data sets, we do not show the errors for OASIS77 in Figure 4, Figure 5, Figure 6 and Figure 7, but directly display the sample outputs from each method on both IBSR data sets and OASIS77 data set in Figure 8 to show the differences among them.

_{Rate}and high FN

_{Rate}in Table 4 caused by a bad estimation of brain center. The obvious intensity inhomogeneity also makes it difficult for BET to obtain a good result with the same parameter for all slices of the MRI volume, leading to low DS and JS.

_{Rate}. A very high FP

_{Rate}shows that it tends to maintain non-brain tissue by GCUT. ROBEX performs equally on all data sets, as it is robust across different data. However, the DS and JS for ROBEX are not high in Table 3 and Table 4. By the proposed ACNM method, the average DS is 0.957 for IBSR18, 0.960 for IBSR20, and 0.936 for OASIS77. The proposed ACNM method shows the highest extraction accuracy on both IBSR data sets. Both FP

_{Rate}and FN

_{Rate}are lower than 5%, indicating that a balance of FN

_{Rate}and FP

_{Rate}is achieved by the proposed method on both IBSR data sets. From the coefficients in Table 5, it seems ACNM does not perform as well as ROBEX and GCUT on OASIS77 data set. It is important to note that the ground truth of OASIS77 data set is not as precise as IBSR data set and has the tendency to over cover the brain, which is similar to the result from ROBEX and GCUT. So, it is reasonable that ROBEX and GCUT obtain better evaluation on OASIS77 than ACNM does. In Figure 8, it is clear that ACNM does the best on OASIS77.

## 4. Discussion

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**The maps of $\mathcal{B}$, $\mathcal{O}$ and ACN. $\mathcal{B}$: background, $\mathcal{O}$: object, ACN: active contour neighborhood, Dash line: current brain boundary.

**Figure 4.**Outputs from two scans in IBSR18 data set. Blue voxels represent the segmentation results of the corresponding brain extraction methods. Green voxels indicate the false negatives and red voxels indicate the false positives.

**Figure 5.**Outputs from two scans in IBSR20 data set. Blue voxels represent the segmentation results of the corresponding brain extraction methods. Green voxels indicate the false negatives and red voxels indicate the false positives.

**Figure 6.**Average of the false positive and false negative voxels for each method on IBSR18 data set.

**Figure 7.**Average of the false positive and false negative voxels for each method on IBSR20 data set.

Edge | Weight | for |
---|---|---|

$\{p,q\}$ | $B\{p,q\}$ | $\{p,q\}\in \mathcal{N}$ |

$\{p,\mathcal{S}\}$ | $\lambda {R}_{p}(\u201c\mathrm{bkg}\u201d)$ | $p\in \mathcal{P},p\notin \mathcal{O}\cup \mathcal{B}$ |

K | $p\in \mathcal{O}$ | |

0 | $p\in \mathcal{B}$ | |

$\{p,\mathcal{T}\}$ | $\lambda {R}_{p}(\u201c\mathrm{obj}\u201d)$ | $p\in \mathcal{P},p\notin \mathcal{O}\cup \mathcal{B}$ |

0 | $p\in \mathcal{O}$ | |

K | $p\in \mathcal{B}$ |

Edge | Weight | for |
---|---|---|

$\{p,q\}$ | $B\{p,q\}$ | $\{p,q\}\in \mathcal{N}$ |

$\{p,\mathcal{S}\}$ | $\lambda {R}_{p}(\u201cbrain\u201d)$ | $p\in ACN$ |

$\lambda \underset{p\in ACN}{\mathrm{min}}{R}_{p}(\u201cbrain\u201d)$ | $p\in \mathcal{O}$ | |

$\lambda \underset{p\in ACN}{\mathrm{max}}{R}_{p}(\u201cbrain\u201d)$ | $p\in \mathcal{B}$ | |

$\{p,\mathcal{T}\}$ | $\lambda {R}_{p}(\u201cnonbrain\u201d)$ | $p\in ACN$ |

$\lambda \underset{p\in ACN}{\mathrm{max}}{R}_{p}(\u201cnonbrain\u201d)$ | $p\in \mathcal{O}$ | |

$\lambda \underset{p\in ACN}{\mathrm{min}}{R}_{p}(\u201cnonbrain\u201d)$ | $p\in \mathcal{B}$ |

Method | DS Mean (SD) | JS Mean (SD) | FP_{RATE} (%) Mean (SD) | FN_{RATE} (%) Mean (SD) |
---|---|---|---|---|

BET P ^{*}-value | 0.946(0.012) 3.0 × 10 ^{−4} | 0.898(0.021) 3.3 × 10 ^{−4} | 8.36(2.77) 4.65 × 10 ^{−7} | 2.83(2.92) 1.09 × 10 ^{−4} |

BSE P ^{*}-value | 0.943(0.039)5.0 × 10^{−2} | 0.895(0.066) 4.87 × 10 ^{−2} | 7.82(6.20) 8.71 × 10 ^{−3} | 3.68(6.30)2.71 × 10^{−1} |

GCUT P ^{*}-value | 0.911(0.015) 8.72 × 10 ^{−8} | 0.837(0.025) 7.08 × 10 ^{−8} | 18.47(3.89) 1.02 × 10 ^{−12} | 0.92(0.04) 1.34 × 10 ^{−6} |

ROBEX P ^{*}-value | 0.927(0.032) 2.42 × 10 ^{−3} | 0.865(0.054) 2.0 × 10 ^{−3} | 14.74(8.14) 2.0 × 10 ^{−5} | 1.1(0.81) 1.34 × 10 ^{−6} |

ACNM | 0.957(0.013) | 0.917(0.024) | 4.06(1.24) | 4.55(2.48) |

Method | DS Mean (SD) | JS Mean (SD) | FP_{RATE} (%) Mean (SD) | FN_{RATE} (%) Mean (SD) |
---|---|---|---|---|

BET P ^{*}-value | 0.849(0.076) 2.96 × 10 ^{−6} | 0.745(0.110) 9.93 × 10 ^{−7} | 22.87(7.95) 1.21 × 10 ^{−8} | 9.00(11.30) 2.76 × 10 ^{−2} |

BSE P ^{*}-value | 0.933(0.054) 2.02 × 10 ^{−2} | 0.878(0.084) 1.58 × 10 ^{−2} | 6.43(2.43) 1.27 × 10 ^{−8} | 6.57(9.46)7.41 × 10^{−2} |

GCUT P ^{*}-value | 0.88(0.015) 1.62 × 10 ^{−12} | 0.786(0.024) 1.0 × 10 ^{−12} | 27.34(3.91) 1.57 × 10 ^{−15} | 0.01(0.02) 1.89 × 10 ^{−6} |

ROBEX P ^{*}-value | 0.94(0.012) 1.33 × 10 ^{−6} | 0.888(0.021) 9.93 × 10 ^{−7} | 11.9(2.75) 6.72 × 10 ^{−12} | 0.67(0.46) 1.86 × 10 ^{−6} |

ACNM | 0.960(0.009) | 0.924(0.016) | 4.61(2.08) | 3.40(2.40) |

Method | DS Mean(SD) | JS Mean(SD) | FP_{RATE} (%)Mean(SD) | FN_{RATE} (%)Mean(SD) |
---|---|---|---|---|

BET P ^{*}-value | 0.931(0.019) 2.64 × 10 ^{−2} | 0.871(0.033) 2.54 × 10 ^{−2} | 11.0(3.70) 1.14 × 10 ^{−35} | 3.45(2.94) 2.95 × 10 ^{−33} |

BSE P ^{*}-value | 0.923(0.060) 3.80 × 10 ^{−2} | 0.862(0.090) 4.99 × 10 ^{−2} | 14.1(18.2) 5.32 × 10 ^{−8} | 3.29(2.02) 2.22 × 10 ^{−33} |

GCUT P ^{*}-value | 0.950(0.008) 3.57 × 10 ^{−8} | 0.904(0.015) 2.90 × 10 ^{−8} | 7.55(2.82) 1.13 × 10 ^{−40} | 2.76(1.79) 9.57 × 10 ^{−6} |

ROBEX P ^{*}-value | 0.955(0.008) 1.02 × 10 ^{−21} | 0.914(0.015) 1.36 × 10 ^{−22} | 2.54(1.3) 4.22 × 10 ^{−10} | 6.23(2.1) 6.16 × 10 ^{−23} |

ACNM | 0.936(0.018) | 0.879(0.031) | 1.95(1.30) | 10.32(3.87) |

Method | DS Mean | SE Mean | SP Mean |
---|---|---|---|

CNN | 0.958 | 0.943 | 0.994 |

ACNM | 0.951 | 0.940 | 0.994 |

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## Share and Cite

**MDPI and ACS Style**

Jiang, S.; Wang, Y.; Zhou, X.; Chen, Z.; Yang, S.
Brain Extraction Using Active Contour Neighborhood-Based Graph Cuts Model. *Symmetry* **2020**, *12*, 559.
https://doi.org/10.3390/sym12040559

**AMA Style**

Jiang S, Wang Y, Zhou X, Chen Z, Yang S.
Brain Extraction Using Active Contour Neighborhood-Based Graph Cuts Model. *Symmetry*. 2020; 12(4):559.
https://doi.org/10.3390/sym12040559

**Chicago/Turabian Style**

Jiang, Shaofeng, Yu Wang, Xuxin Zhou, Zhen Chen, and Suhua Yang.
2020. "Brain Extraction Using Active Contour Neighborhood-Based Graph Cuts Model" *Symmetry* 12, no. 4: 559.
https://doi.org/10.3390/sym12040559