# Topology Adaptive Water Boundary Extraction Based on a Modified Balloon Snake: Using GF-1 Satellite Images as an Example

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. B-Snake Method

^{2}+ β(s)|v″(s)|

^{2}represents the internal energy; ${\mathrm{k}}_{1}\overrightarrow{\mathrm{N}(\mathrm{s})}-\mathrm{k}\frac{\nabla \mathrm{P}}{||\nabla \mathrm{P}||}$ is the external energy; v′(s) and v″(s) denote the first and second derivatives of the curve with respect to sand control the smoothness and continuity of the curve, respectively; $\overrightarrow{\mathrm{N}(\mathrm{s})}$ is the unit outward normal of the contour, and it acts as the inflation force; $\nabla \mathrm{P}$ is the gradient of the external energy; $\Vert \nabla \mathrm{P}\Vert $ is the norm of $\nabla \mathrm{P}$, and $\frac{\nabla \mathrm{P}}{||\nabla \mathrm{P}||}$ is the image force; α(s) and β(s) are the coefficients of the smoothing force and the continuity force, respectively, and both are non-negative quantities; and k

_{1}is the coefficient of the inflation force. When k

_{1}> 0, the curve expands outward, otherwise, it contracts inward; k is the weight of the image force, and it is non-negative.

^{n}and v

^{n−1}represent the N × 2 order matrix (N is the number of discrete control points of the contour) comprising the contour node coordinates of the nth and (n − 1)th iteration, respectively; A is the N × N matrix, and

## 3. Proposed MB-Snake Method

#### 3.1. Adaptive Image Preprocessing

_{i}= f(x

_{i}), where x

_{i}= 1, 2,…, 10, y

_{i}is the number of pixels the DN value of which fall in the value range of [(x

_{i}− 1) × 255 / 10, x

_{i}× 255 / 10) can be acquired from step (1). Here the DN value contrast is categorized into two types, including high and low, according to k

_{25}, the absolute value of the slope of the straight line determined by point P

_{2}(x

_{2}, y

_{2}) and point P

_{5}(x

_{5}, y

_{5}). The definition of k

_{25}is displayed in Figure 3b. The reason why the points P

_{2}and P

_{5}are selected is that different types of satellite images have distinctly different k

_{25}, and satellite images can be separated much more easily by using them. The images with k

_{25}> 0.01 are classified into images with low DN value contrast, otherwise are high. The threshold 0.01 is an empirical value determined by multiple trials. In fact, the values of k

_{25}are quite different for satellite images of varied DN value contrasts, thus the threshold is not that sensitive, with the values between 0.01 and 0.15 all competent for the separation.

#### 3.2. Topology Collision Detection and Handling

#### 3.2.1. Topology Collision Detection

_{i}= (x

_{i}, y

_{i}), V

_{i+1}= (x

_{i+1}, y

_{i+1}), V

_{i+2}= (x

_{i+2}, y

_{i+2}), if the vector $\overrightarrow{{\mathrm{V}}_{\mathrm{i}}{\mathrm{V}}_{\mathrm{i}+1}}$ and $\overrightarrow{{\mathrm{V}}_{\mathrm{i}+1}{\mathrm{V}}_{\mathrm{i}+2}}$ satisfy:

_{i}, V

_{i+1}, and V

_{i+2}, otherwise no topology collision exists.

_{i}V

_{i+1}(i ∈ N, 1 ≤ i ≤ n−3, n is the total node number of the curve S

_{0}), and V

_{k}V

_{k+1}(k ∈ N, i+1 ≤ k ≤ n−1) are demonstrated in Figure 5. Assuming V

_{i}= (a

_{1}, b

_{1}), V

_{i+1}= (a

_{2}, b

_{2}), V

_{k}= (c

_{1}, d

_{1}), V

_{k+1}= (c

_{2}, d

_{2}), and a

_{min}= min{a

_{1}, a

_{2}}, a

_{max}= max{a

_{1}, a

_{2}}, b

_{min}= min{b

_{1}, b

_{2}}, b

_{max}= max{b

_{1}, b

_{2}}, c

_{min}= min{c

_{1}, c

_{2}}, c

_{max}= max{c

_{1}, c

_{2}}, d

_{min}= min{d

_{1}, d

_{2}}, d

_{max}= max{d

_{1}, d

_{2}}, the two-dimensional plane is divided into nine regions, numbered 1 to 9, by the four lines x = a

_{min}, x = a

_{max}, y = b

_{min}, and y = b

_{max}, the situations in which the line segment V

_{i}V

_{i+1}will not intersect with V

_{k}V

_{k+1}are listed below.

- (1)
- c
_{min}> a_{max}, as the line segment V_{k}V_{k+1}shown in regions 3, 4, and 5; - (2)
- c
_{max}< a_{min}, as the line segment V_{k}V_{k+1}shown in regions 1, 7, and 8; - (3)
- d
_{min}> b_{max}, as the line segment V_{k}V_{k+1}shown in regions 5, 6, and 7; - (4)
- d
_{max}< b_{min}, as the line segment V_{k}V_{k+1}shown in regions 1, 2, and 3; - (5)
- V
_{k}and V_{k+1}lie in the same side of the line determined by V_{i}and V_{i+1}, as the line segment V_{k}V_{k+1}shown in the L_{1}location of region 9; and - (6)
- V
_{i}and V_{i+1}lie in the same side of the line determined by V_{k}and V_{k+1}, as the line segment V_{k}V_{k+1}shown in the L_{2}location of region 9.

_{i}V

_{i+1}= V

_{n}V

_{1}and the line segment V

_{k}V

_{k+1}= V

_{1}V

_{2}, and the topology collision detection conditions and processes are the same as abovementioned. If the line segments V

_{i}V

_{i+1}and V

_{k}V

_{k+1}satisfy one of the abovementioned six conditions, there is no topology collision in the curve, otherwise topology collision exists.

#### 3.2.2. Topology Collision Handling

_{0}are arranged clockwise, and that the topology collision detection procedure has detected that the line segment V

_{i}V

_{i+1}intersects with V

_{k}V

_{k+1}, and the line segment V

_{j}V

_{j+1}intersects with V

_{m}V

_{m+1}, as the topology collision situation shown in Figure 6a, the topology collision handling of the MB-Snake method will be implemented via the following three steps:

_{i}V

_{i+1}and V

_{k}V

_{k+1}and reconnect head node V

_{i}of line segment V

_{i}V

_{i+1}with tail node V

_{k+1}of line segment V

_{k}V

_{k+1}. Then, reconnect tail node V

_{i+1}of line segment V

_{i}V

_{i+1}with head node V

_{k}of line segment V

_{k}V

_{k+1}. Through the first interruption and reconnection, the curve splits into an exterior curve S

_{1}= {V

_{1}, V

_{2}, …., V

_{i}, V

_{k+1}, V

_{k+2}, …, V

_{n}} and an interior curve S′

_{2}= {V

_{i+1}, V

_{i+2}, …, V

_{k}}. However, as demonstrated in Figure 6b, self-intersection still exists for S′

_{2}.

_{2}into a new curve S

_{2}= {V

_{m+1}, V

_{m+2}, …, V

_{j}}, without self-intersections, and an extra closed loop S

_{3}= {V

_{i+1}, V

_{i+2}, …, V

_{m}, V

_{j+1}, V

_{j+2}, …, V

_{k}}, as displayed in Figure 6c.

_{2}may be speckle noise or true islands, but given that the node number of speckle noise is usually much smaller than that of true islands, whether curve S

_{2}is kept depends on whether the node number of it is larger than the threshold in this paper. Counting the node number of S

_{2}and recording it as N, if N < T (T is the empirical threshold of the node number of speckle noise, and T = 50 via multiple trials), curve S

_{2}will be viewed as speckle noise and deleted; otherwise, it will be kept. Curve S

_{3}is an extra curve produced during topology collision processing. It is deleted, as shown in Figure 6d.

_{0}can be split into exterior curve S

_{1}and interior contour S

_{2}, and topology collisions existing in the water images with islands can be managed. Then, continuing the iterative evolution of curve S

_{1}, setting k

_{1}= −k

_{1}, and continuing the evolution of curve S

_{2}, the correct object boundaries can be finally acquired. If there are p islands in an image, this topology collision detection and handling mechanism will be repeated p times to address all the topology collisions.

#### 3.3. Definite Termination of Contour Evolution

## 4. Experiments and Results

#### 4.1. Experimental Data

_{25}, those with k

_{25}< 0.01 are images with high DN value contrast, otherwise are images with low DN value contrast.

#### 4.2. Extraction Results

_{1}= 0.2, and k = 2.0. Figure 8b,e,h,k,n,q shows the MB-Snake method extraction results based on Figure 7a–f, respectively. The yellow circles in these figures are the initial contours, and the red boundaries are the borders acquired by the MB-Snake method.

^{−7}, and r = 1. The parameters were q = 38, λ = 2.28, ε = 1.0 × 10

^{−7}, and r = 1 in Figure 8f; q = 20, λ = 1, ε = 1.0 × 10

^{−2}, and r = 1 in Figure 8i; q = 27, λ = 2.28, ε = 1.0 × 10

^{−7}, and r = 1 in Figure 8l; q = 21, λ = 2.28, ε = 1.0 × 10

^{−7}, and r = 1 in Figure 8o; and q = 30, λ = 3, ε = 1.0 × 10

^{−7}, and r = 1 in Figure 8r.

## 5. Performance Measure

#### 5.1. Correctness

#### 5.2. Completeness

#### 5.3. AOM

_{1}and R

_{2}refer to the regions enclosed by the algorithm-extracted boundaries and the reference boundaries, respectively. R

_{1}∩ R

_{2}represents the region contained in both R

_{1}and R

_{2}, and R

_{1}∪ R

_{2}refers to the region contained in either R

_{1}or R

_{2}.

## 6. Discussion

#### 6.1. Analysis of Results

#### 6.1.1. Comparison with the B-Snake Method

#### 6.1.2. Comparison with the OT-Snake Method

#### 6.2. Reliability Evaluation

#### 6.2.1. Positioning Accuracy

_{1}of the reference boundary was set as one pixel, and the correctness comparison of the B-Snake, the MB-Snake, and the OT-Snake method results using the six experimental images are shown in Figure 11. Generally, Figure 11 shows that the MB-Snake method proposed in this paper has higher positioning accuracy when compared with the accuracies of the B-Snake and OT-Snake methods. Specifically, in comparison with the B-Snake method, the MB-Snake method improves the extracted results and positioning accuracy, on one hand, by enhancing the boundary and avoiding weak boundary overflows, and on the other hand, by avoiding redundant boundary lines via the topology collision detection and handling mechanism. When compared to the OT-Snake method, the MB-Snake method exhibits distinctly higher positioning accuracies for all the six satellite images in spite of the fact that all six MB-Snake method results are acquired under the same set of model parameters, while none of the six OT-Snake method results are obtained with the same set of parameters and all the OT-Snake method results are the best results obtained by trying 30 sets of parameters. The correctness of the OT-Snake method is also lower than that of the B-Snake method, and the reason accounting for which is the OT-Snake method could not be able to extract shapes smaller than the grid size under the constraints of curve node locations.

#### 6.2.2. Integrity Level

_{2}of the extracted boundary was set as one pixel, and the completeness comparison of the B-Snake, the MB-Snake, and the OT-Snake method results for the six experimental images are shown in Figure 12. Generally, Figure 12 shows that the MB-Snake method proposed in this paper has a higher integrity level when compared to those of the B-Snake and OT-Snake methods. Specifically, the severe weak boundary overflows in the B-Snake method results reduced its integrity when compared with the MB-Snake method. However, compared with its correctness, the B-Snake method has higher completeness because that the redundant boundaries expanded the areas of buffer regions, and made TN larger. Despite the fact that the OT-Snake method results are the best results obtained by trying 30 sets of parameters, the completeness of the OT-Snake method is still low because the limitation of curve node locations.

#### 6.2.3. Overall Accuracy

#### 6.3. Stability Assessment

#### 6.3.1. Sensitivity to Initial Contours

_{1}= 0.2, and k = 2.0, and the corresponding extracted results were shown in Figure 14a–r, respectively. The results suggest that when the locations of the initial contours are different and other settings are the same, the extracted results remain unchanged, i.e., the MB-Snake method proposed in this paper is insensitive to the locations of initial contours.

#### 6.3.2. Effects of Model Parameters

_{1}, and k in the energy function of the MB-Snake method are the same as those of the B-Snake method: (1) the coefficient of the first derivative α controls the smoothness of the curve; (2) the weight of the second derivative β affects the continuity of the curve; (3) the coefficient of the inflation force k

_{1}only influences the time consumption of the algorithm when the image force is large enough to balance the inflation force, further impacting the extracted results, resulting in boundary overflow when the image force is too small; and (4) the weight of the image force k determines whether the curve can exactly stop at true boundaries. The model parameters used in the experiment are α = 0.05, β = 0.0, k

_{1}= 0.2, and k = 2.0. This optimal parameter set was acquired, respectively, by keeping three of the parameters staying the same while changing the fourth one at a time, until the correctness of the extraction results achieve steady and optimal. Fifty GF-1 WFV satellite images containing water bodies of different types, inner land numbers, areas, boundary and background complexities, and digital number value contrasts were tested under this set of model parameters, and all the object boundaries were successfully extracted, demonstrating that the MB-Snake algorithm proposed in this paper is stable for model parameters.

#### 6.3.3. Effects of Spatial Resolution

#### 6.4. Image Demands

## 7. Conclusions and Outlook

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A

**Table A1.**Calculation efficiency of the B-Snake, the MB-Snake, and the OT-Snake methods for the six experimental images.

Method | Efficiency(s) | |||
---|---|---|---|---|

Image | B-Snake | MB-Snake | OT-Snake | |

Figure 7a | 66.1 | 89.4 | 21.2 | |

Figure 7b | 73.3 | 96.4 | 75.6 | |

Figure 7c | 2665.8 | 3427.8 | 1217.2 | |

Figure 7d | 62.8 | 85.7 | 54.6 | |

Figure 7e | 49.2 | 75.6 | 14.2 | |

Figure 7f | 1667.0 | 2049.8 | 85.7 |

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**Figure 3.**Distinction of satellite images with different DN value constrasts: (

**a**) sample DN value distribution diagram; and (

**b**) definition of k

_{25}.

**Figure 4.**Curves with or without topology collisions: (

**a**) adjacent line segment without topology collisions; (

**b**) adjacent line segment with topology collisions; (

**c**) non-adjacent line segment without topology collisions; (

**d**) non-adjacent line segment with topology collisions.

**Figure 6.**Topology collision handling mechanism of the MB-Snake method: (

**a**) self-intersection situations; (

**b**) 1st interruption and reconnection; (

**c**) 2nd interruption and reconnection; and (

**d**) extra curve deletion.

**Figure 7.**Six GF-1 WFV satellite experimental images: (

**a**) image of a lake without an island; (

**b**) image of a lake with a single island; (

**c**) image of a lake with multiple islands; (

**d**) image of a river without an island; (

**e**) image of a river with a single island; and (

**f**) image of a river with multiple islands.

**Figure 8.**The B-Snake, the MB-Snake, and the OT-Snake method extracted results using six GF-1 WFV satellite experimental images. The yellow circles/points represent the initial contours, and the red boundaries are the borders acquired by algorithms. (

**a**–

**c**) The B-Snake, the MB-Snake, and the OT-Snake method results for the image of the lake without an island; (

**d**–

**f**) the lake with a single island; (

**g**–

**i**) the lake with multiple islands; (

**j**–

**l**) the river without an island; (

**m**–

**o**) the river with a single island; and (

**p**–

**r**) the river with multiple islands.

**Figure 9.**Definitions of TP and FP. TP = True Positive, FP = False Positive, and r

_{1}refers to the buffer zone radium of the reference boundary.

**Figure 10.**Definitions of TN and FN. TN = True Negative, FN = False Negative, and r

_{2}refers to the buffer zone radium of the extracted boundary.

**Figure 11.**Correctness comparison of the B-Snake, the MB-Snake, and the OT-Snake method results using the six experimental images. Lake0 refers to the image of Figure 7a; Lake1 refers to the image of Figure 7b; LakeN refers to the image of Figure 7c; River0 refers to the image of Figure 7d; River1 refers to the image of Figure 7e; and RiverN refers to the image of Figure 7f. The symbols used below are all of the same meanings.

**Figure 12.**Completeness comparison of the B-Snake, the MB-Snake, and the OT-Snake method results using the six experimental images.

**Figure 13.**AOM comparison of the B-Snake, MB-Snake, and OT-Snake method results using the six experimental images.

**Figure 14.**The MB-Snake-extracted results with different initial contour locations: (

**a**–

**c**) the MB-Snake-extracted results for the image of a lake without an island under three different initial contour locations; (

**d**–

**f**) the MB-Snake-extracted results for the image of a lake with a single island under three different initial contour locations; (

**g**–

**i**) the MB-Snake-extracted results for the image of a lake with multiple islands under three different initial contour locations; (

**j**–

**l**) the MB-Snake-extracted results for the image of a river without an island under three different initial contour locations; (

**m**–

**o**) the MB-Snake-extracted results for the image of a river with a single island under three different initial contour locations; and (

**p**–

**r**) the MB-Snake-extracted results for the image of a river with multiple islands under three different initial contour locations.

**Figure 15.**Partially enlarged view of the extracted results of GF-1 WFV and Landsat 8 OLI for Figure 7c:

**left**(

**a**,

**c**) the results of GF-1 WFV; and

**right**(

**b**,

**d**) the results of Landsat 8 OLI.

**Table 1.**Summary of the six GF-1 WFV experimental images. GL: geo-location; AD: acquisition date; IS: image size (units: pixels); WT: water type; IIN: inner island number; BDCP: boundary complexity; BGCP: background complexity; BDCL: boundary clarity.

Image | GL | AD | IS | WT | IIN | BDCP | BGCP | BDCL |
---|---|---|---|---|---|---|---|---|

Figure 4a | Xiaogan, Hubei | 8 October 2014 | 220 × 299 | Lake | 0 | High | Low | Low |

Figure 4b | Xuancheng, Anhui | 6 August 2015 | 291 × 299 | Lake | 1 | High | Low | High |

Figure 4c | Arli, Tibet | 13 October 2015 | 994 × 1215 | Lake | N | High | Low | Low |

Figure 4d | Chongqing | 21 October 2015 | 367 × 273 | River | 0 | Low | Low | Low |

Figure 4e | Chongqing | 21 October 2015 | 293 × 235 | River | 1 | Low | Low | Low |

Figure 4f | Maanshan, Anhui | 3 December 2015 | 369 × 414 | River | N | Low | High | Low |

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**MDPI and ACS Style**

Du, W.; Chen, N.; Liu, D. Topology Adaptive Water Boundary Extraction Based on a Modified Balloon Snake: Using GF-1 Satellite Images as an Example. *Remote Sens.* **2017**, *9*, 140.
https://doi.org/10.3390/rs9020140

**AMA Style**

Du W, Chen N, Liu D. Topology Adaptive Water Boundary Extraction Based on a Modified Balloon Snake: Using GF-1 Satellite Images as an Example. *Remote Sensing*. 2017; 9(2):140.
https://doi.org/10.3390/rs9020140

**Chicago/Turabian Style**

Du, Wenying, Nengcheng Chen, and Dandan Liu. 2017. "Topology Adaptive Water Boundary Extraction Based on a Modified Balloon Snake: Using GF-1 Satellite Images as an Example" *Remote Sensing* 9, no. 2: 140.
https://doi.org/10.3390/rs9020140