# 3D Flow Entropy Contour Fitting Segmentation Algorithm Based on Multi-Scale Transform Contour Constraint

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. The Determination of the Initial Contour by Multi-Scale Morphological Fitting

#### 2.1. Improved Top-Hat and Bottom-Hat Transform Sample Pretreatment

#### 2.2. Improved Morphological Watershed Segmentation Method

## 3. Flow Entropy Resegmentation Algorithm Based on Three-Dimensional Information Constraints

#### 3.1. The Establishment of Three-Dimensional Information Segmentation Model

#### 3.2. Using the Energy Theory and the Maximum Information Entropy to Fit the Contour of the Target

- (1)
- Randomly select N points on the obtained contour from the pre-segmentation as the initial iteration data source $({v}_{11},{v}_{12},{v}_{13},\dots ,{v}_{1n})$. ${v}_{1i}$ represents the ith pixel of the edge line and ${v}_{1i}$ is the ith 5 × 5 pixels window center.
- (2)
- Pixels belonging to the 1,3 quadrant region in $({v}_{11},{v}_{12},{v}_{13},\dots ,{v}_{1n})$ are selected to compose the set $({v}_{11},{v}_{12},{v}_{13},\dots ,{v}_{1k})$. ${v}_{11(ij)}$ expresses pixel at (i, j) in the 5 × 5 pixels window of ${v}_{11}$. The pixels at the same place of the 5 × 5 neighborhood of each pixel in $({v}_{11},{v}_{12},{v}_{13},\dots ,{v}_{1k})$ reform 25 sets of k-dimensional vector. When $k\ge N/2$, calculate the flow entropy of pixel points belong to 1,3 quadrant of the three-dimensional coordinates. When $k\le N/2$, repeat (1) process.
- (3)
- After one calculation, the set of pixels that $({v}_{11(ij)},{v}_{12(ij)},{v}_{13(ij)},\dots ,{v}_{1k(ij)})(1\le i,j\le 5)$ with the maximum flow entropy in the 5 × 5 neighborhood is selected as the final contour of the object.

## 4. Experimental Results

#### 4.1. Computer Simulation Experiment

#### 4.2. Physical Image Experiment

^{2})) determines the computational efficiency of the proposed method. There is no uniform computational complexity in the deep learning based method, and the operation time of image segmentation can be obtained according to the connection design of the network.

## 5. Conclusions and Future Works

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Image preprocessing. (

**a**) Initial image, (

**b**) Original background image, (

**c**) Results of traditional top-hat and bottom-hat transform, (

**d**) Gauss filter processing results, (

**e**) Wavelet transform enhancement results, (

**f**) Algorithm processing results of this paper.

**Figure 3.**Comparison results of initial contour detection. (

**a**) Initial image, (

**b**) watershed segmentation, (

**c**) The proposed method.

**Figure 10.**Lena noise simulation image and experimental result curve. (

**a**) $\varsigma =0$, (

**b**) $\varsigma =1$, (

**c**) $\varsigma =3$, (

**d**) $\varsigma =5$, (

**e**) $\varsigma =7$, (

**f**) The evaluation index curve.

**Figure 11.**Cameraman noise simulation image and experimental result curve. (

**a**) $\varsigma =0$, (

**b**) $\varsigma =1$, (

**c**) $\varsigma =3$, (

**d**) $\varsigma =5$, (

**e**) $\varsigma =7$, (

**f**) The evaluation index curve.

**Figure 12.**Saturn noise simulation image and experimental result curve. (

**a**) $\varsigma =0$, (

**b**) $\varsigma =1$, (

**c**) $\varsigma =3$, (

**d**) $\varsigma =5$, (

**e**) $\varsigma =7$, (

**f**) The evaluation index curve.

**Figure 13.**Cell noise simulation image and experimental result curve. (

**a**) $\varsigma =0$, (

**b**) $\varsigma =1$, (

**c**) $\varsigma =3$, (

**d**) $\varsigma =5$, (

**e**) $\varsigma =7$, (

**f**) The evaluation index curve.

**Figure 14.**Segmentation results of license plate image under low contrast condition. (

**a**) Original image, (

**b**) SPW algorithm, (

**c**) Two-dimensional OTSU algorithm, (

**d**) Fuzzy C-mean algorithm, (

**e**) Markov Random Model of multiscale edge detection and image segmentation (MRM), (

**f**) adaptive active contour method (AAC), (

**g**) 3D OTSU algorithm, (

**h**) Semi-Supervised Learning With Deep Embedded Clustering for Image Classification and Segmentation (S’s) method, (

**i**) Bayesian Polytrees With Learned Deep Features (BL) method, (

**j**) The proposed method.

**Figure 15.**Segmentation results of aircraft in uneven illumination background. (

**a**) Original image, (

**b**) SPW algorithm, (

**c**) Two-dimensional OTSU algorithm, (

**d**) Fuzzy C-mean algorithm, (

**e**) MRM, (

**f**) AAC, (

**g**) 3D OTSU algorithm, (

**h**) S’s method, (

**i**) BL method, (

**j**) The proposed method.

**Figure 16.**Segmentation results of fighter image under low illumination. (

**a**) Original image, (

**b**) SPW algorithm, (

**c**) Two-dimensional OTSU algorithm, (

**d**) Fuzzy C-mean algorithm, (

**e**) MRM, (

**f**)AAC, (

**g**) 3D OTSU algorithm, (

**h**) S’s method, (

**i**) BL method, (

**j**) The proposed method.

**Figure 17.**The segmentation results of the object image. (

**a**) Original image, (

**b**) SPW algorithm, (

**c**) Two-dimensional OTSU algorithm, (

**d**) Fuzzy C-mean algorithm, (

**e**) MRM, (

**f**) AAC, (

**g**) 3D OTSU algorithm, (

**h**) S’s method, (

**i**) BL method, (

**j**) The proposed method.

**Figure 18.**The segmentation results of the Lighthouse image. (

**a**) Original image, (

**b**) SPW algorithm, (

**c**) Two-dimensional OTSU algorithm, (

**d**) Fuzzy C-mean algorithm, (

**e**) MRM, (

**f**) AAC, (

**g**) 3D OTSU algorithm, (

**h**) S’s method, (

**i**) BL method, (

**j**) The proposed method.

**Figure 19.**The segmentation results of crane. (

**a**) Original image, (

**b**) SPW algorithm, (

**c**) Two-dimensional OTSU algorithm, (

**d**) Fuzzy C-mean algorithm, (

**e**) MRM, (

**f**) AAC, (

**g**) 3D OTSU algorithm, (

**h**) S’s method, (

**i**) BL method, (

**j**) The proposed method.

**Figure 20.**The segmentation results of dolphin image with local weak contrast. (

**a**) Original image, (

**b**) SPW algorithm, (

**c**) Two-dimensional OTSU algorithm, (

**d**) Fuzzy C-mean algorithm, (

**e**) MRM, (

**f**) AAC, (

**g**) 3D OTSU algorithm, (

**h**) S’s method, (

**i**) BL method, (

**j**) The proposed method.

Segmentation Algorithms | License Plate Image | Aircraft Image | Fighter Image | The Object Image | The Lighthouse Image | Crane Image | Dolphin Image |
---|---|---|---|---|---|---|---|

The proposed method | 0.9011 | 0.9523 | 0.9435 | 0.9501 | 0.8913 | 0.9042 | 0.9098 |

SPW | 0.8016 | 0.4121 | 0.3117 | 0.5131 | 0.5962 | 0.6858 | 0.8714 |

2D-Otsu | 0.4036 | 0.5271 | 0.4015 | 0.7254 | 0.6525 | 0.6555 | 0.8544 |

Fuzzy C-means | 0.5542 | 0.4651 | 0.4754 | 0.7541 | 0.7288 | 0.7359 | 0.4653 |

MRM | 0.6654 | 0.4553 | 0.4573 | 0.7252 | 0.7075 | 0.7459 | 0.4943 |

AAC | 0.7956 | 0.5152 | 0.5565 | 0.7752 | 0.7586 | 0.8785 | 0.7789 |

3D-Otsu | 0.8656 | 0.7815 | 0.7153 | 0.7963 | 0.8848 | 0.8796 | 0.8906 |

S’s method | 0.8215 | 0.9245 | 0.8978 | 0.8645 | 0.8875 | 0.8632 | 0.8514 |

BL method | 0.8773 | 0.8998 | 0.9015 | 0.9096 | 0.8563 | 0.8731 | 0.8721 |

Segmentation Algorithms | License Plate Image | Aircraft Image | Fighter Image | The Object Image | The Lighthouse Image | Crane Image | Dolphin Image |
---|---|---|---|---|---|---|---|

The proposed method | 92.11% | 94.54% | 90.87% | 95.52% | 89.15% | 90.95% | 84.11% |

SPW | 82.16% | 37.65% | 44.65% | 55.27% | 54.89% | 60.27% | 64.98% |

2D-Otsu | 57.14% | 45.15% | 45.63% | 60.16% | 63.86% | 59.88% | 55.48% |

Fuzzy C-means | 53.16% | 36.19% | 59.61% | 68.15% | 73.02% | 65.19% | 57.46% |

MRM | 59.15% | 63.03% | 55.30% | 65.48% | 65.53% | 59.05% | 45.89% |

AAC | 47.51% | 53.43% | 57.15% | 56.57% | 69.51% | 60.12% | 65.88% |

3D-Otsu | 80.19% | 77.64% | 79.65% | 80.22% | 83.91% | 87.51% | 79.81% |

S’s method | 84.54% | 89.89% | 82.05% | 83.79% | 86.13% | 81.15% | 81.03% |

BL method | 85.13% | 89.25% | 81.25% | 85.94% | 80.82% | 84.12% | 80.09% |

Segmentation Algorithms | License Plate Image | Aircraft Image | Fighter Image | The Object Image | The Lighthouse Image | Crane Image | Dolphin Image |
---|---|---|---|---|---|---|---|

The proposed method | 0.91 | 0.92 | 0.89 | 0.95 | 0.89 | 0.90 | 0.84 |

SPW | 0.65 | 0.74 | 0.75 | 0.55 | 0.54 | 0.60 | 0.64 |

2D-Otsu | 0.57 | 0.66 | 0.70 | 0.60 | 0.63 | 0.59 | 0.55 |

Fuzzy C-means | 0.53 | 0.58 | 0.61 | 0.68 | 0.73 | 0.65 | 0.57 |

MRM | 0.59 | 0.65 | 0.55 | 0.64 | 0.61 | 0.59 | 0.46 |

AAC | 0.48 | 0.56 | 0.54 | 0.56 | 0.62 | 0.60 | 0.66 |

3D-Otsu | 0.80 | 0.78 | 0.83 | 0.80 | 0.81 | 0.86 | 0.77 |

S’s method | 0.82 | 0.88 | 0.80 | 0.81 | 0.85 | 0.84 | 0.80 |

BL method | 0.81 | 0.85 | 0.85 | 0.83 | 0.86 | 0.81 | 0.81 |

Segmentation Algorithms | License Plate Image | Aircraft Image | Fighter Image | The Object Image | The Lighthouse Image | Crane Image | Dolphin Image |
---|---|---|---|---|---|---|---|

the proposed algorithm | 9.25 | 9.19 | 8.97 | 8.98 | 9.01 | 9.19 | 8.49 |

SPW | 8.17 | 8.81 | 8.74 | 7.25 | 7.19 | 8.57 | 8.23 |

2D-Otsu | 4.72 | 5.23 | 6.16 | 3.29 | 4.64 | 4.52 | 5.54 |

Fuzzy C-means | 7.64 | 8.05 | 8.01 | 7.59 | 7.03 | 6.98 | 8.45 |

MRM | 9.12 | 9.36 | 10.14 | 11.73 | 9.69 | 9.42 | 10.57 |

AAC | 8.97 | 8.14 | 8.02 | 5.95 | 6.14 | 7.59 | 8.42 |

3D-Otsu | 10.12 | 12.14 | 9.69 | 11.37 | 12.49 | 10.91 | 9.56 |

S’s method | 8.98 | 9.19 | 8.39 | 8.19 | 8.19 | 8.94 | 9.11 |

BL method | 8.17 | 8.29 | 9.01 | 8.55 | 9.14 | 9.33 | 9.67 |

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**MDPI and ACS Style**

Wu, H.; Liu, L.; Lan, J.
3D Flow Entropy Contour Fitting Segmentation Algorithm Based on Multi-Scale Transform Contour Constraint. *Symmetry* **2019**, *11*, 857.
https://doi.org/10.3390/sym11070857

**AMA Style**

Wu H, Liu L, Lan J.
3D Flow Entropy Contour Fitting Segmentation Algorithm Based on Multi-Scale Transform Contour Constraint. *Symmetry*. 2019; 11(7):857.
https://doi.org/10.3390/sym11070857

**Chicago/Turabian Style**

Wu, Hongtao, Liyuan Liu, and Jinhui Lan.
2019. "3D Flow Entropy Contour Fitting Segmentation Algorithm Based on Multi-Scale Transform Contour Constraint" *Symmetry* 11, no. 7: 857.
https://doi.org/10.3390/sym11070857