# Edge-Based Color Image Segmentation Using Particle Motion in a Vector Image Field Derived from Local Color Distance Images

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Background to Particle Motion in a Vector Image Field

## 3. Methodology

#### 3.1. Image Moments

#### 3.2. Local Color Distance Images

#### 3.3. The Normal Compressive Vector Field

#### 3.4. The Edge Vector Field

#### 3.5. Particle Motion in a Vector Image Field Derived from Local Color Distance Images

#### 3.6. Appropriate PMLCD Parameter Setting

#### 3.7. Overall Boundary Extraction Method

## 4. Experimental Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) $\nabla P$, (

**b**) ${\nabla}^{2}P$, (

**c**) an edge vector field $\overrightarrow{e}$, and (

**d**) a normal compressive vector field $\overrightarrow{n}$.

**Figure 2.**(

**a**) a combined vector field, $\alpha \overrightarrow{e}+\beta \overrightarrow{n}$, $\alpha =0.5$, $\beta =0.5$, and (

**b**) a boundary extraction result.

**Figure 3.**(

**a**) local color distance images and (

**b**) a normal compressive vector field obtained from (C-to-CT) vectors.

**Figure 7.**Image segmentation results obtained using (

**a**) PMVIF and (

**b**) PMLCD are evaluated using the same grayscale image and (

**c**) the PMLCD result evaluated using the original color image.

**Figure 8.**(

**a**) BSDS500 #3096, (

**b**) particle trajectory obtained from Equation (3), and (

**c**) zoom of (

**b**).

**Figure 10.**The ground truth object in Figure 9 and the corresponding segmented regions.

**Figure 11.**Color image segmentation results. (

**a**) dataset images, (

**b**) ground truths; results of (

**c**) PMLCD, (

**d**) PMVIF, (

**e**) watershed, (

**f**) SLIC, (

**g**) K-means, (

**h**) mean shift, and (

**i**) JSEG.

**Figure 13.**Noisy image segmentation results: (

**a**) VOC2012 #2007_001289 image with SNR = 0 dB (${\sigma}_{noise}$ = 0.21), (

**b**) particle trajectories obtained using PMLCD with a radius of LCD = 3, ${T}_{|\overrightarrow{e}|}$ = 0.27, $\gamma $ = −0.14 ($\alpha $ = 0.34, $\beta $ = 0.66), (

**c**) extracted boundaries (red lines), and (

**d**) segmented regions.

Dataset | Method | By Image | By Object | Parameter | ||||
---|---|---|---|---|---|---|---|---|

RI | GCE | NVI | BDE | Time | Dice | |||

VOC2012 #2007_000063 | PMLCD | 0.67 | 0.09 | 0.15 | 16.66 | 0.21s | 0.97 | LCD radius 1, ${T}_{|\overrightarrow{e}|}$0.17($Otsu$), $\gamma $0.06($\alpha $0.52,$\beta $0.48) |

PMVIF | 0.63 | 0.30 | 0.15 | 14.87 | 0.49s | 0.87 | ${T}_{|\overrightarrow{e}|}$0.16($Otsu$), $\gamma $0.06($\alpha $0.50,$\beta $0.50) | |

Watershed | 0.62 | 0.06 | 0.34 | 13.96 | 0.08s | 0.96 | Level 0.10 | |

SLIC | 0.64 | 0.15 | 0.20 | 13.87 | 12.99s | 0.88 | Number of SuperPixels 20 | |

K-means | 0.63 | 0.23 | 0.24 | 14.02 | 12.78s | 0.63 | Number of clusters 100 | |

Mean shift | 0.62 | 0.29 | 0.28 | 13.92 | 147.71s | 0.47 | Bandwidth 0.02 | |

JSEG | 0.66 | 0.30 | 0.12 | 18.69 | 84.38s | 0.79 | Color quantization 20 | |

VOC2012 #2007_001430 | PMLCD | 0.62 | 0.09 | 0.17 | 18.75 | 0.41s | 0.95 | LCD radius 2, ${T}_{|\overrightarrow{e}|}$0.22($Otsu$), $\gamma $0.00($\alpha $0.50,$\beta $0.50) |

PMVIF | 0.60 | 0.14 | 0.20 | 16.59 | 0.75s | 0.90 | ${T}_{|\overrightarrow{e}|}$0.13($Otsu$), $\gamma $0.00($\alpha $0.50,$\beta $0.50) | |

Watershed | 0.60 | 0.08 | 0.23 | 16.85 | 0.07s | 0.90 | Level 0.08 | |

SLIC | 0.60 | 0.11 | 0.18 | 16.05 | 3.92s | 0.90 | Number of SuperPixels 30 | |

K-means | 0.58 | 0.49 | 0.16 | 16.98 | 2.12s | 0.41 | Number of clusters 8 | |

Mean shift | 0.57 | 0.47 | 0.18 | 18.11 | 53.50s | 0.43 | Bandwidth 0.07 | |

JSEG | 0.62 | 0.16 | 0.13 | 21.92 | 60.72s | 0.83 | Color quantization 10 | |

VOC2012 #2010_005626 | PMLCD | 0.65 | 0.12 | 0.17 | 17.43 | 0.39s | 0.90 | LCD radius 2, ${T}_{|\overrightarrow{e}|}$0.16($Otsu$), $\gamma $0.30($\alpha $0.70,$\beta $0.30) |

PMVIF | 0.60 | 0.24 | 0.20 | 16.24 | 0.64s | 0.78 | ${T}_{|\overrightarrow{e}|}$0.12($Otsu$), $\gamma $0.30($\alpha $0.50,$\beta $0.50) | |

Watershed | 0.60 | 0.17 | 0.27 | 19.33 | 0.07s | 0.83 | Level 0.05 | |

SLIC | 0.64 | 0.13 | 0.17 | 15.54 | 4.35s | 0.88 | Number of SuperPixels 20 | |

K-means | 0.63 | 0.40 | 0.14 | 16.73 | 2.03s | 0.78 | Number of clusters 8 | |

Mean shift | 0.65 | 0.38 | 0.09 | 19.75 | 1.96s | 0.79 | Bandwidth 0.25 | |

JSEG | 0.64 | 0.20 | 0.14 | 20.19 | 71.54s | 0.85 | Color quantization 19 | |

VOC2012 #2010_005746 | PMLCD | 0.82 | 0.05 | 0.09 | 7.65 | 0.19s | 0.93 | LCD radius 1, ${T}_{|\overrightarrow{e}|}$0.21($Otsu$), $\gamma $0.00($\alpha $0.50,$\beta $0.50) |

PMVIF | 0.73 | 0.05 | 0.12 | 4.26 | 0.45s | 0.91 | ${T}_{|\overrightarrow{e}|}$0.18($Otsu$), $\gamma $0.00($\alpha $0.50,$\beta $0.50) | |

Watershed | 0.37 | 0.11 | 0.30 | 19.40 | 0.07s | 0.82 | Level 0.01 | |

SLIC | 0.46 | 0.16 | 0.15 | 7.59 | 4.13s | 0.75 | Number of SuperPixels 5 | |

K-means | 0.37 | 0.16 | 0.24 | 9.28 | 10.62s | 0.74 | Number of clusters 100 | |

Mean shift | 0.41 | 0.17 | 0.23 | 13.43 | 373.74s | 0.71 | Bandwidth 0.02 | |

JSEG | 0.46 | 0.14 | 0.14 | 14.47 | 36.85s | 0.77 | Color quantization 2 | |

BSDS500 #2018 | PMLCD | 0.90 | 0.21 | 0.09 | 5.43 | 0.20s | 0.92 | LCD radius 1, ${T}_{|\overrightarrow{e}|}$0.24($Otsu$), $\gamma $0.35($\alpha $0.86,$\beta $0.14) |

PMVIF | 0.75 | 0.46 | 0.14 | 4.32 | 0.49s | 0.92 | ${T}_{|\overrightarrow{e}|}$0.19($Otsu$), $\gamma $0.35($\alpha $0.52,$\beta $0.48) | |

Watershed | 0.84 | 0.31 | 0.16 | 7.88 | 0.05s | 0.83 | Level 0.04 | |

SLIC | 0.89 | 0.22 | 0.10 | 3.75 | 3.54s | 0.88 | Number of SuperPixels 10 | |

K-means | 0.82 | 0.61 | 0.16 | 4.14 | 2.33s | 0.69 | Number of clusters 10 | |

Mean shift | 0.74 | 0.36 | 0.12 | 5.01 | 8.34s | 0.73 | Bandwidth 0.10 | |

JSEG | 0.81 | 0.37 | 0.11 | 18.94 | 69.68s | 0.59 | Color quantization 30 | |

BSDS500 #81095 | PMLCD | 0.90 | 0.17 | 0.09 | 9.55 | 0.35s | 0.89 | LCD radius 2, ${T}_{|\overrightarrow{e}|}$0.21($Otsu$), $\gamma $0.12($\alpha $0.64,$\beta $0.36) |

PMVIF | 0.81 | 0.26 | 0.14 | 9.64 | 0.38s | 0.86 | ${T}_{|\overrightarrow{e}|}$0.18($Otsu$), $\gamma $0.12($\alpha $0.50,$\beta $0.50) | |

Watershed | 0.85 | 0.15 | 0.18 | 10.63 | 0.06s | 0.84 | Level 0.05 | |

SLIC | 0.85 | 0.20 | 0.11 | 9.99 | 2.50s | 0.86 | Number of SuperPixels 10 | |

K-means | 0.81 | 0.49 | 0.16 | 8.77 | 2.77s | 0.64 | Number of clusters 14 | |

Mean shift | 0.82 | 0.50 | 0.14 | 10.41 | 38.64s | 0.63 | Bandwidth 0.08 | |

JSEG | 0.84 | 0.30 | 0.11 | 16.63 | 47.30s | 0.80 | Color quantization 12 | |

BSDS500 #107072 | PMLCD | 0.85 | 0.18 | 0.10 | 12.78 | 0.16s | 0.93 | LCD radius 1, ${T}_{|\overrightarrow{e}|}$0.22($Otsu$), $\gamma $-0.05($\alpha $0.47,$\beta $0.53) |

PMVIF | 0.48 | 0.33 | 0.13 | 15.34 | 0.27s | 0.47 | ${T}_{|\overrightarrow{e}|}$0.23($Otsu$), $\gamma $-0.05($\alpha $0.50,$\beta $0.50) | |

Watershed | 0.75 | 0.12 | 0.25 | 15.50 | 0.05s | 0.92 | Level 0.15 | |

SLIC | 0.76 | 0.12 | 0.16 | 12.27 | 3.89s | 0.88 | Number of SuperPixels 25 | |

K-means | 0.75 | 0.34 | 0.17 | 12.33 | 3.61s | 0.43 | Number of clusters 20 | |

Mean shift | 0.74 | 0.32 | 0.27 | 13.58 | 79.77s | 0.41 | Bandwidth 0.02 | |

JSEG | 0.82 | 0.22 | 0.10 | 8.99 | 47.27s | 0.73 | Color quantization 10 | |

BSDS500 #238025 | PMLCD | 0.86 | 0.10 | 0.09 | 13.60 | 0.37s | 0.96 | LCD radius 2, ${T}_{|\overrightarrow{e}|}$0.19($Otsu$), $\gamma $0.15($\alpha $0.64,$\beta $0.36) |

PMVIF | 0.69 | 0.31 | 0.10 | 15.95 | 0.28s | 0.93 | ${T}_{|\overrightarrow{e}|}$0.18($Otsu$), $\gamma $0.15($\alpha $0.50,$\beta $0.50) | |

Watershed | 0.65 | 0.06 | 0.29 | 19.30 | 0.06s | 0.94 | Level 0.05 | |

SLIC | 0.67 | 0.08 | 0.17 | 15.49 | 3.73s | 0.95 | Number of SuperPixels 30 | |

K-means | 0.68 | 0.35 | 0.15 | 12.80 | 2.94s | 0.67 | Number of clusters 16 | |

Mean shift | 0.71 | 0.47 | 0.12 | 13.41 | 50.11s | 0.61 | Bandwidth 0.05 | |

JSEG | 0.73 | 0.24 | 0.11 | 15.27 | 42.22s | 0.61 | Color quantization 10 | |

Average (Standard Deviation) | PMLCD | 0.78(0.11) | 0.13(0.05) | 0.12(0.04) | 12.73 (4.52) | 0.29s (0.10) | 0.93(0.03) | LCD radius 1.50(0.50), $\gamma $0.14(0.15) |

PMVIF | 0.66 (0.10) | 0.26 (0.12) | 0.15 (0.03) | 12.15 (4.98) | 0.47s (0.16) | 0.83 (0.14) | $\gamma $0.14(0.15) | |

Watershed | 0.66 (0.15) | 0.13(0.08) | 0.25 (0.06) | 15.36 (4.03) | 0.06s(0.01) | 0.88 (0.05) | Level 0.0.07(0.04) | |

SLIC | 0.69 (0.13) | 0.15 (0.04) | 0.16 (0.03) | 11.82(4.12) | 4.88s (3.11) | 0.87 (0.05) | Number of SuperPixels 18.75(8.93) | |

K-means | 0.66 (0.14) | 0.38 (0.14) | 0.18 (0.04) | 11.88 (4.05) | 4.90s (3.99) | 0.62 (0.13) | Number of clusters 34.50(38.01) | |

Mean shift | 0.66 (0.13) | 0.37 (0.10) | 0.18 (0.07) | 13.45 (4.21) | 94.22s (113.90) | 0.60 (0.14) | Bandwidth 0.08(0.07) | |

JSEG | 0.70 (0.12) | 0.24 (0.07) | 0.12(0.01) | 16.89 (3.78) | 57.50s (15.60) | 0.75 (0.09) | Color quantization 14.13(8.01) |

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**MDPI and ACS Style**

Phornphatcharaphong, W.; Eua-Anant, N.
Edge-Based Color Image Segmentation Using Particle Motion in a Vector Image Field Derived from Local Color Distance Images. *J. Imaging* **2020**, *6*, 72.
https://doi.org/10.3390/jimaging6070072

**AMA Style**

Phornphatcharaphong W, Eua-Anant N.
Edge-Based Color Image Segmentation Using Particle Motion in a Vector Image Field Derived from Local Color Distance Images. *Journal of Imaging*. 2020; 6(7):72.
https://doi.org/10.3390/jimaging6070072

**Chicago/Turabian Style**

Phornphatcharaphong, Wutthichai, and Nawapak Eua-Anant.
2020. "Edge-Based Color Image Segmentation Using Particle Motion in a Vector Image Field Derived from Local Color Distance Images" *Journal of Imaging* 6, no. 7: 72.
https://doi.org/10.3390/jimaging6070072