# Segmentation of Brain Tumors in MRI Images Using Three-Dimensional Active Contour without Edge

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Proposed Method

#### 2.1. Data Collection

#### 2.2. Image Preprocessing

#### 2.2.1. Resizing the Dimensions of MRI (Magnetic Resonance Imaging) Slices

#### 2.2.2. MRI Enhancement Algorithm

#### 2.2.3. Intensity Normalization

#### 2.2.4. Background Segmentation

#### 2.2.5. Mid-Sagittal Plane Detection and Correction

#### 2.3. Feature Extraction

#### 2.3.1. Feature Aggregation

#### 2.3.2. Feature Selection

#### 2.4. Classification

#### 2.5. Brain Tumors Location Identification

_{1}, x

_{2}, y

_{1}, y

_{2}, z

_{1}, and z

_{2}). In this case, x

_{1}and x

_{2}represent the height of the 3D box and are subject to the constraints 1 ≤ x

_{1}< 512 and x

_{1}< x

_{2}≤ 512. Meanwhile, y

_{1}and y

_{2}signify the width of the 3D box and are subject to the constraints 1 ≤ y

_{1}< 256 and y

_{1}< y

_{2}≤ 256. Finally, z

_{1}and z

_{2}represent the depth of the 3D box and are subject to the constraints 1 ≤ z

_{1}< 32 and z

_{1}< z

_{2}≤ 32. Herein, we assume that the maximum number of MRI slices is 32. Figure 4 shows an example of how the coordinates of 3D box (x

_{1}, x

_{2}, y

_{1}, y

_{2}, z

_{1}, z

_{2}) are mapped to the individual of GA in a binary form.

#### 2.6. Three-Dimensional Brain Tumors Segmentation

#### 2.6.1. Level Set Method

#### 2.6.2. 3DACWE (Three-Dimensional Active Contour without Edge)

#### 2.6.3. Evaluation of the Segmentation

## 3. Experimental Results

#### 3.1. Classification Results

_{1}= 0 and θ

_{2}= 0 is shown in Table 1. All features seemed acceptable except the weighted mean predictor. Nevertheless, significant variation existed in the F-statistic values between features, indicating a degree of significant difference between the selected features. The p-value does not actually signify the degree of separation of each group from others and ignores feature redundancy [35]. This drawback is overcome by the F-statistic to determine the power of feature discrimination through thresholding, in which different threshold values are taken to ignore the redundant features and evaluate the selected features at each time by observing the performance of the classifier. When the F-statistic threshold value increases, the numbers of selected predictors and the vector of the features decrease. The optimal threshold value that can provide the highest accuracy is 35 (Figure 6). Under this condition, only one normal patient was classified incorrectly as pathological, and three pathological patients were classified incorrectly as normal. Thus, some patients may be misclassified in both ways, but the high classification accuracy (97.8%) reduces these cases to a very small number. These cases are not treated and are passed to the segmentation phase as “erroneous cases.”

#### 3.2. Tumor Identification Results

^{3}. Moreover, tiny tumors hold a spatial scale relatively similar to normal anatomic variability [39].

#### 3.3. Tumor Segmentation Results

_{1}= λ

_{2}= 1 and length penalty μ = 106.

#### 3.4. Discussion

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 6.**Optimal F-statistic threshold value. The achievable accuracy was 97.8% ± 0.1% for the classification of the collected dataset into normal and abnormal brain scans with sensitivity and specificity rates of 98.1% ± 0.3% and 97.6% ± 0.4%, respectively.

**Figure 9.**Comparative segmentation results on MRI T2-w (normalized) scan (matching images in Figure 7) by 3DACWE. The ground truth is marked in green, and the output of 3DACWE is marked in red.

**Figure 11.**Results after applying the consistency verification algorithm. (

**A**) original MRI slices; (

**B**) segmented MRI brain slices by 3DACWE; (

**C**) output of consistency verification algorithm.

**Figure 13.**Comparison of tumor segmentation of the average Dice scores of four MRI modalities under 2DACWE and 3DACWE.

**Figure 15.**Comparison between clinical and experimental MRI slice identification features (mean ± SD).

**Figure 16.**Scatterplot of segmentation accuracy to the summation of slice thickness and space between slices, showing the mean accuracy (R-squared) as the dotted brown line.

**Table 1.**Comparison of MRI brain scan features (mean ± standard deviation (SD)) between normal and abnormal patients.

Features | Abnormal MRI Scans | Normal MRI Scans | F-Statistic | p-Value |
---|---|---|---|---|

Auto correlation (×10^{3}) | 5.62 ± 1.2 | 4.92 ± 1.24 | 13.67 | <0.001 |

Contrast (×10^{3}) | 1.89 ± 0.618 | 0.918 ± 0.22 | 166.2 | <0.001 |

Correlation (÷10) | 7.1 ± 0.91 | 8.07 ± 0.72 | 291.5 | <0.001 |

Cluster Prominence (×10^{8}) | 3.6 ± 1.87 | 2.7 ± 1.09 | 14.62 | <0.001 |

Cluster Shade (×10^{5}) | 7.6 ± 4.26 | 5.5 ± 2.9 | 13.14 | <0.001 |

Dissimilarity (×10) | 2.42 ± 0.47 | 1.58 ± 0.21 | 209 | <0.001 |

Energy (÷10) | 1.02 ± 0.2 | 1.05 ± 0.18 | 368.15 | <0.001 |

Entropy | 7.07 ± 0.336 | 6.87 ± 0.25 | 15.21 | <0.001 |

Homogeneity (÷10) | 3.55 ± 0.34 | 3.76 ± 0.26 | 451.3 | <0.001 |

Max. Probability (÷10) | 3.17 ± 0.33 | 3.23 ± 0.28 | 444.96 | <0.001 |

Sum of Square Variance (×10^{3}) | 6.5 ± 1.6 | 5.38 ± 1.23 | 24.36 | <0.001 |

Sum Average (×10^{2}) | 1.15 ± 0.112 | 1.06 ± 0.15 | 20.84 | <0.001 |

Sum Variance (×10^{4}) | 2.33 ± 0.47 | 1.97 ± 0.48 | 24.25 | <0.001 |

Sum Entropy | 4.46 ± 0.177 | 4.16 ± 0.147 | 35.98 | <0.001 |

Difference Entropy | 3.64 ± 0.2 | 3.34 ± 0.124 | 132.2 | <0.001 |

Information Measure of Correlation I (÷10) | −2.24 ± 0.3 | −2.53 ± 0.26 | 430.15 | <0.001 |

Information Measure of Correlation II (÷10) | 9.11 ± 0.2 | 9.26 ± 0.18 | 355.48 | <0.001 |

Inverse difference Normalized (÷10) | 9.25 ± 0.12 | 9.48 ± 0.06 | 407.8 | <0.001 |

Inverse difference Moment Normalized (÷10) | 9.78 ± 0.07 | 9.87 ± 0.028 | 316.89 | <0.001 |

Weighted Mean (÷10) | −8.73 ± 84 | 0.53 ± 18.7 | 0.92 | 0.339 |

Weighted Distance | 3.05 ± 2.91 | 0.77 ± 0.52 | 46.1 | <0.001 |

Cross Correlation (÷10) | 7.1 ± 0.91 | 8.07 ± 0.72 | 291.5 | <0.001 |

Results | Sensitivity | Specificity | Accuracy | Dice Index | Jaccard | Matching |
---|---|---|---|---|---|---|

Average | 0.854 | 0.999 | 0.998 | 0.890 | 0.804 | 0.854 |

STD | 0.069 | 0.001 | 0.002 | 0.047 | 0.075 | 0.069 |

Min | 0.690 | 0.996 | 0.994 | 0.764 | 0.619 | 0.690 |

Max | 0.971 | 1.000 | 1.000 | 0.956 | 0.915 | 0.971 |

Results | Sensitivity | Specificity | Accuracy | Dice Index | Jaccard | Matching |
---|---|---|---|---|---|---|

Average | 0.909 | 1.000 | 0.999 | 0.893 | 0.809 | 0.909 |

STD | 0.076 | 0.000 | 0.000 | 0.043 | 0.068 | 0.076 |

Min | 0.736 | 0.998 | 0.998 | 0.768 | 0.624 | 0.736 |

Max | 0.999 | 1.000 | 1.000 | 0.947 | 0.899 | 0.999 |

Method | T2-w | T1-w | T1c-w | FLAIR |
---|---|---|---|---|

2DACWE | 83.73% ± 4.6% | 84.43% ± 5.3% | 86.6% ± 3.4% | 82% ± 4.5% |

3DACWE | 88.11% ± 4.4% | 89.92% ± 4.9% | 90.3% ± 3.6% | 88.8% ± 6.9% |

Reference | MRI Modalities | Approach | No. of Patients | Accuracy (100%) | Match (100%) | Jaccard (100%) | Dice (100%) |
---|---|---|---|---|---|---|---|

[33] | T_{1}, T_{2}, and PD | Fuzzy clustering | 6 | - | 53–91 | - | - |

[41] | T_{1} | Template-moderated classification | 20 | 95 | - | - | - |

[42] | T_{1}, and T_{1}-c | Level-sets | 5 | - | - | 85–93 | - |

[43] | T_{2} | Generative model | 3 | - | - | 59–89 | - |

[44] | T_{1}, T_{1}-C, T_{2}, and FLAIR | Weighted aggregation | 20 | - | - | 62–69 | - |

[12] | T_{1}, T_{1}-c, T_{2}, and FLAIR | SVM | 14 | 34–93 | - | - | - |

[45] | T_{1}, T_{1}-c, T_{2}, and FLAIR | Generative model | 25 | - | - | - | 40–70 |

Proposed System | T_{1}, T_{1}-c, T_{2}, and FLAIR | 3D-ACWE | 50 (collected) | 99.8 ± 0.2 | 85.4 ± 6.9 | 80.4 ± 7.4 | 89 ± 4.7 |

25 (BRATS 2013) | 99.9 | 91 ± 7.6 | 81 ± 6.8 | 89.3 ± 4.2 |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Hasan, A.M.; Meziane, F.; Aspin, R.; Jalab, H.A.
Segmentation of Brain Tumors in MRI Images Using Three-Dimensional Active Contour without Edge. *Symmetry* **2016**, *8*, 132.
https://doi.org/10.3390/sym8110132

**AMA Style**

Hasan AM, Meziane F, Aspin R, Jalab HA.
Segmentation of Brain Tumors in MRI Images Using Three-Dimensional Active Contour without Edge. *Symmetry*. 2016; 8(11):132.
https://doi.org/10.3390/sym8110132

**Chicago/Turabian Style**

Hasan, Ali M., Farid Meziane, Rob Aspin, and Hamid A. Jalab.
2016. "Segmentation of Brain Tumors in MRI Images Using Three-Dimensional Active Contour without Edge" *Symmetry* 8, no. 11: 132.
https://doi.org/10.3390/sym8110132