# BSLIC: SLIC Superpixels Based on Boundary Term

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## Abstract

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## 1. Introduction

## 2. Overview of BSIC

## 3. Algorithm of BSLIC

#### 3.1. Distribution of Cluster Centers

#### 3.2. Initialization of Edge Centers

- If there exist image edges in the ${S}_{0}\times {S}_{0}$ searching region of plane center (like ${C}_{i1}$), choose a median edge pixel as the edge center (like ${E}_{i1}$);
- If there is no image edge within the ${S}_{0}\times {S}_{0}$ region (like ${C}_{i4}$), no edge center is generated;
- To avoid any noisy pixel being chosen as cluster center, modify the edge center to the lowest gradient position in the corresponding $3\times 3$ local neighborhood;
- Edge center is introduced to reduce the negativity of edge-across superpixels. It is necessary to keep it near to the image edges. During the 10 iterations, edge centers remain unalterable, and only plane centers are updated to the mean value.

#### 3.3. Distance Measurement

## 4. Experimental Results

#### 4.1. BSLIC Superpixels

#### 4.2. Qualitative Comparisons

#### 4.3. Quantitative Comparisons

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Superpixel segmentation results of four algorithms. (

**a**) SEEDS; (

**b**) SuperPB; (

**c**) simple linear iterative clustering (SLIC); (

**d**) Turbopixels. The second row is the partial enlarged superpixels defined by the green rectangles.

**Figure 3.**Distribution of Cluster Centers. (

**a**) Square distribution; (

**b**) Hexagon distribution; (

**c**) Diamond distribution.

**Figure 4.**Edge-across superpixels. (

**a**) Original image with slender rod; (

**b**) Edge image with canny filter operator; (

**c**) Partial enlarged superpixels with only plane centers initialized in hexagon distribution; (

**d**) Partial enlarged superpixels with only plane centers initialized in square distribution.

**Figure 5.**Plane center and edge center. Dots in solid black ${C}_{i0}$, ${C}_{i1}$, ${C}_{i2}$, ${C}_{i3}$, ${C}_{i4}$, ${C}_{i5}$ and ${C}_{i6}$ are “plane center”; Square in solid red ${E}_{i1}$ is “edge center”.

**Figure 6.**Partial enlarged superpixels segmentation with edge cluster centers initialized. (

**a**) Plane centers initialized in a hexagon distribution; (

**b**) Plane centers initialized in a square distribution.

**Figure 7.**Boundary term incorporation. (

**a**) Partial enlarged superpixels on original image; (

**b**) Partial enlarged superpixels on logical edge image.

**Figure 9.**BSLIC iterating process. (

**a**) Superpixels with only plane centers; (

**b**) Superpixels with both plane and edge centers; (

**c**) First iterating result of BSLIC; (

**d**) Final segmentation result of BSLIC.

**Figure 11.**BSLIC superpixels segmentation results. Superpixels number $k=\left[100,\text{}500,\text{}1000\right]$, weighting factor $m=\left[5,\text{}15,\text{}30\right]$. (

**a**) BSLIC segments when $m=5$; Column (

**b**) BSLIC segments when $m=15$; Column (

**c**) BSLIC segments when $m=30$.

**Figure 12.**Part of experimental results. (

**a**) BSLIC segments; (

**b**) Partial enlarged superpixels of BSLIC; (

**c**) Partial enlarged superpixels of SEEDS; (

**d**) Partial enlarged superpixels of SuperPB; (

**e**) Partial enlarged superpixels of SLIC; (

**f**) Partial enlarged superpixels of Turbopixles.

**Table 1.**Experimental data of $\mathrm{boundary}\text{}\mathrm{recall}\text{}\left(\mathrm{BR}\right)$.

${\mathit{k}}^{\prime}$ | 500 | 1000 | 1500 | 2000 | 2500 | |
---|---|---|---|---|---|---|

$\mathrm{m}=5$ | SLIC | 0.5932 | 0.6346 | 0.6245 | 0.6791 | 0.6782 |

BSLIC | 0.5849 | 0.6858 | 0.6888 | 0.6981 | 0.7193 | |

Improving Rate | −0.0083 | 0.0512 | 0.0623 | 0.0190 | 0.0411 | |

$\mathrm{m}=15$ | SLIC | 0.5646 | 0.6035 | 0.6504 | 0.6798 | 0.6957 |

BSLIC | 0.6501 | 0.6672 | 0.7055 | 0.7139 | 0.7397 | |

Improving Rate | 0.0856 | 0.0638 | 0.0552 | 0.0340 | 0.0440 | |

$\mathrm{m}=30$ | SLIC | 0.5014 | 0.5500 | 0.6046 | 0.6470 | 0.6793 |

BSLIC | 0.6257 | 0.6613 | 0.6786 | 0.7042 | 0.7222 | |

Improving Rate | 0.1243 | 0.1113 | 0.0740 | 0.0572 | 0.0430 |

${\mathit{k}}^{\prime}$ | 500 | 1000 | 1500 | 2000 | 2500 | |
---|---|---|---|---|---|---|

$\mathrm{m}=5$ | SLIC | 0.2146 | 0.1540 | 0.1455 | 0.1247 | 0.1170 |

BSLIC | 0.2348 | 0.1395 | 0.1334 | 0.1204 | 0.1113 | |

Improving Rate | −0.0202 | 0.0146 | 0.0121 | 0.0043 | 0.0057 | |

$\mathrm{m}=15$ | SLIC | 0.1731 | 0.1505 | 0.1242 | 0.1140 | 0.1064 |

BSLIC | 0.1415 | 0.1369 | 0.1172 | 0.1078 | 0.1012 | |

Improving Rate | 0.0277 | 0.0136 | 0.0071 | 0.0062 | 0.0051 | |

$\mathrm{m}=30$ | SLIC | 0.1936 | 0.1572 | 0.1307 | 0.1193 | 0.1090 |

BSLIC | 0.1585 | 0.1346 | 0.1176 | 0.1067 | 0.1036 | |

Improving Rate | 0.0351 | 0.0227 | 0.0130 | 0.0126 | 0.0053 |

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**MDPI and ACS Style**

Wang, H.; Peng, X.; Xiao, X.; Liu, Y.
BSLIC: SLIC Superpixels Based on Boundary Term. *Symmetry* **2017**, *9*, 31.
https://doi.org/10.3390/sym9030031

**AMA Style**

Wang H, Peng X, Xiao X, Liu Y.
BSLIC: SLIC Superpixels Based on Boundary Term. *Symmetry*. 2017; 9(3):31.
https://doi.org/10.3390/sym9030031

**Chicago/Turabian Style**

Wang, Hai, Xiongyou Peng, Xue Xiao, and Yan Liu.
2017. "BSLIC: SLIC Superpixels Based on Boundary Term" *Symmetry* 9, no. 3: 31.
https://doi.org/10.3390/sym9030031