# MR Brain Image Segmentation: A Framework to Compare Different Clustering Techniques

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## Abstract

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## 1. Introduction

## 2. The Image Segmentation Framework

- (a)
- Partitioning: divide into regions/sequences with coherent internal properties;
- (b)
- Grouping: identify sets of coherent tokens in the image.

- choosing the image
- choosing the color space
- choosing the segmentation method
- setting the running parameters of the specific method
- visualizing the segmented image
- computing the evaluation metrics

- User work section: This component gives the user the possibility to access the primary functions of the tool, which are the clustering method section and the evaluation section.
- Method section: For each implemented method, the user can configure its parameters such as color space conversion, number of cluster, maximum number of iterations, stopping condition and visualization mode.
- Evaluation section: The segmentation results can be evaluated both qualitatively and quantitatively. Qualitative evaluation is made by visualization of the segmented image compared to the ground truth image. Quantitative evaluation is made by computing the metrics described in Section 4.

- by the cluster centroid color: Each point of a cluster is labeled with the color of its centroid (in the case of color conversion, the color space is converted back to RGB);
- by a gray level: Each pixel is labeled with the number of the cluster it belongs to, and the range is stretched in 0–255;
- by a random RGB color: A random RGB value is generated for each cluster;
- by a binary stack: The clustering is represented as a stack of binary images. Each binary image represents a cluster; each pixel shows a hard cluster membership. Thus, it is possible to extract cluster regions from the original image by performing an AND operation between a slide of the stack and the original image.
- by using a fuzzy stack: A stack of gray level images is used to show the membership values of each pixel to each cluster. Each pixel represents the soft cluster membership value of that pixel in the original image according to the currently selected cluster.

## 3. Clustering Methods

#### 3.1. K-means

- Fix the number of clusters K, and initialize the cluster centers ${\mathbf{c}}_{k}$ ($k=1\dots K$), either randomly or based on some heuristic;
- Assign each pixel to the cluster that minimizes the distance between the pixel and the cluster center;
- Re-compute the cluster centers by averaging all of the pixels in the cluster, namely:$${\mathbf{c}}_{k}=\frac{1}{|{C}_{k}|}\sum _{{\mathbf{x}}_{i}\in {C}_{k}}{x}_{i}\mathrm{for}k=1\dots K$$
- Repeat Steps 2 and 3 until convergence is attained (i.e., the assignment of pixels to clusters does not change)

#### 3.2. Fuzzy C-Means

- Fix the number of clusters K and initialize the cluster centers ${\mathbf{c}}_{k}$ ($k=1\dots K$), either randomly or based on some heuristic;
- Compute membership values ${u}_{ik}$ using Equation (4)
- Re-compute the cluster centers ${\mathbf{c}}_{k}$ using Equation (5)
- Repeat Steps 2 and 3 until convergence is attained (i.e., the assignment of pixels to clusters does not change)

#### 3.3. Spatial FCM

- $m\ge 1$: fuzziness parameter used to control the fuzziness; if m is near one, the results are similar to those obtained by K-means
- p and q: parameters used to control the relative importance of membership and spatial functions
- Radius r: the spatial function is evaluated on a $(2r+1)\times (2r+1)$ window centered on the pixel

#### 3.4. Kernelized FCM

## 4. Evaluation Metrics

- $TP$ (True Positive) is the number of pixels that belong to tissue T in the ground truth image and are correctly classified as tissue T in the segmented image;
- $FN$ (False Negative) is the number pixels that are classified as tissue T in the ground truth image, but classified as different tissues in the segmented image;
- $TN$ (True Negatives) is the number of pixels that are classified as different tissues both in the segmented and ground truth images;
- $FP$ (False Positives) is the number of pixels incorrectly classified as tissue T in the segmented image compared to the ground truth image.

## 5. Application and Results

## 6. Conclusions

## Author Contributions

## Conflicts of Interest

## References

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**Figure 3.**(

**a**) Original image of Subject 202-3, Slice 20 and (

**b**) its ground truth; (

**c**) original image of Subject 205-3, Slice 20 and (

**d**) its ground truth.

**Figure 4.**Average trend of the entropy-based measure. The dotted line refers to the average value computed on the ground truth segmented images.

**Figure 5.**Entropy-based evaluation measure for the clustering algorithms on Image 202-3 and on Image 205-3 using the optimal parameter setting.

**Figure 8.**The 202-3 (

**a**) and 205-3 (

**b**) images with added noise and the pre-processed images using the median filter (

**c**,

**d**).

K-means | FCM | SFCM | KFCM | |
---|---|---|---|---|

K | 4, 6, 8, 10 | 4, 6, 8, 10 | 4, 6, 8, 10 | 4, 6, 8, 10 |

m | - | 1.0, 1.5, 2.0 | 1.0, 1.5, 2.0 | 1.0, 1.5, 2.0 |

p | - | - | 1.0, 2.0 | - |

q | - | - | 1.0, 2.0 | - |

r | - | - | 2.0, 3.0, 4.0 | - |

$Ws$ | - | - | - | 1, 3, 5 |

$opt$ | - | - | - | average, median, weighted |

**Table 2.**Average segmentation results obtained by different clustering algorithms on the test images.

K-means | FCM | SFCM | KFCM | |
---|---|---|---|---|

E-measure | 0.5374 ± 0.0763 | 0.5381 ± 0.0750 | 0.5363 ± 0.0742 | 0.5348 ± 0.0761 |

Subject | Method | JS | DSC | Sensitivity | Specificity | Accuracy |
---|---|---|---|---|---|---|

K-means | $0.8997$ | $0.9472$ | $96.12\%$ | $98.77\%$ | $97.77$% | |

202-3 | $FCM$ | $0.9015$ | $0.9482$ | $96.07\%$ | $98.80\%$ | $97.82\%$ |

$SFCM$ | $0.9022$ | $0.9486$ | $96.03\%$ | $98.88\%$ | $97.84\%$ | |

$KFCM$ | 0.8938 | 0.9486 | $95.47\%$ | $98.93\%$ | $97.77\%$ | |

K-means | $0.9017$ | $0.9483$ | $96.94\%$ | $98.71\%$ | $97.91\%$ | |

205-3 | $FCM$ | $0.9028$ | $0.9489$ | $97.09\%$ | $98.72\%$ | $97.93\%$ |

$SFCM$ | $0.9043$ | $0.9497$ | $97.11\%$ | $98.75\%$ | $97.97\%$ | |

$KFCM$ | $0.8830$ | $0.9408$ | $95.89\%$ | $98.69\%$ | $97.62\%$ |

**Table 4.**Average segmentation results obtained by different clustering algorithms on the test images.

Segmented Image | K-means | FCM | SFCM | KFCM |
---|---|---|---|---|

202-3 original | 0.5842 | 0.5850 | 0.5832 | 0.5889 |

202-3 with noise | 0.5859 | 0.5873 | 0.5856 | 0.5845 |

205-3 original | 0.5793 | 0.5781 | 0.5758 | 0.5761 |

205-3 with noise | 0.5763 | 0.5787 | 0.5761 | 0.5782 |

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Caponetti, L.; Castellano, G.; Corsini, V.
MR Brain Image Segmentation: A Framework to Compare Different Clustering Techniques. *Information* **2017**, *8*, 138.
https://doi.org/10.3390/info8040138

**AMA Style**

Caponetti L, Castellano G, Corsini V.
MR Brain Image Segmentation: A Framework to Compare Different Clustering Techniques. *Information*. 2017; 8(4):138.
https://doi.org/10.3390/info8040138

**Chicago/Turabian Style**

Caponetti, Laura, Giovanna Castellano, and Vito Corsini.
2017. "MR Brain Image Segmentation: A Framework to Compare Different Clustering Techniques" *Information* 8, no. 4: 138.
https://doi.org/10.3390/info8040138