# Urban Riverway Extraction from High-Resolution SAR Image Based on Blocking Segmentation and Discontinuity Connection

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Algorithm Description

**I**= {I

_{i}

_{, j}, (i, j) ∈

**Ω**} be a SAR intensity image defined on its spatial domain

**Ω**= {(i, j): i = 1, …, M, j = 1, …, N}, where (i, j) denotes the pixel lattice position, I

_{i}

_{, j}∈ {0, …, 255} is the intensity at (i, j), and M and N are the numbers of rows and columns of

**I**, respectively.

#### 2.1. Overlapping Block Partition and Classification

_{0}and h

_{0}) to obtain a set of sub-image blocks. The overlapping block partition process can be expressed as

**B**= {

**B**

_{l}, l = 1, …, h × v} and

**B**’ = {

**B**’

_{l}, l = 1, …, h × v} represent the partitioned non-overlapping and overlapping image block collections, l is the index of the image block, and v and h are the number of image blocks along the X- and Y-axes.

**B**’ can be classified into blocks covering riverways and blocks not covering riverways by visual interpretation. Suppose that the number of sub-image blocks

**B**’

_{${l}_{1}$}covering riverway and

**B**’

_{${l}_{2}$}not covering riverway in

**B**’ is n

_{1}and n

_{2}, where l

_{1}∈ {1, …, n

_{1}}, l

_{2}∈ {1, …, n

_{2}}. For

**B**’

_{${l}_{2}$}, which is processed as background, the result is denoted as

**J**

_{${l}_{2}$}= {J

_{i}

_{, j}, (i, j) ∈

**Ω**

_{${l}_{2}$}}, where J

_{i}

_{, j}= 0 means background, and

**Ω**

_{${l}_{2}$}is the spatial domain corresponding to

**B**’

_{${l}_{2}$}.

#### 2.2. SRAD Filtering Preprocessing

**B**’

_{${l}_{1}$}, the spatial domain is denoted as

**Ω**

_{${l}_{1}$}, l

_{1}∈ {1, …, n

_{1}}. Taking I

_{i}

_{, j}, (i, j) ∈

**Ω**

_{${l}_{1}$}, as input, SRAD uses the following update function for the iterative filtering,

^{2}represent the gradient and Laplacian operator, respectively, and c(q) is defined as

_{i}

_{, j}is the instantaneous diffusion coefficient, which can be calculated by the equation

_{0}(ξ), can be approximated by

_{0}≤ 1 is the initial diffusion coefficient.

**I**at (i, j), respectively.

**F**

_{${l}_{1}$}= {F

_{i}

_{, j}, (i, j) ∈

**Ω**

_{${l}_{1}$}} is obtained, where F

_{i}

_{, j}= ${I}_{i,j}^{t}$.

#### 2.3. Extraction of Riverway Segments

**F**

_{${l}_{1}$}is used to quickly obtain the average pixel intensity μ

_{i}

_{, j}and the standard deviation σ

_{i}

_{, j}in a w × w window centered on (i, j). To calculate the threshold T

_{i}

_{, j}at (i, j), the following equation is used,

**Ω**

_{${l}_{1}$}, κ ∈ [0.2, 0.5] is the empirical adjustable parameter. To facilitate the subsequent processing, the T

_{i}

_{, j}is used to binarize

**F**

_{${l}_{1}$}:

_{i}

_{, j}= 0 means background, and R

_{i}

_{, j}= 1 means riverway,

**R**

_{${l}_{1}$}= {R

_{i}

_{, j}, (i, j) ∈

**Ω**

_{${l}_{1}$}}.

**R**

_{${l}_{1}$}, and the false riverway fragments are removed by setting the area and aspect ratio thresholds of the connected component:

**R**

_{${l}_{1}$}; T

_{a}is the area threshold; and T

_{r}is the aspect ratio threshold. If Equation (12) is satisfied, the z-th connected component is considered as a true riverway segment. After traversing all connected components, the number of true riverway segments is denoted as Z’, and the extraction result is

**R**’

_{${l}_{1}$}= {R’

_{i}

_{, j}, (i, j) ∈

**Ω**

_{${l}_{1}$}}, where R’

_{i}

_{, j}∈ {0, 1}, R’

_{i}

_{, j}= 1 means riverway, R’

_{i}

_{, j}= 0 means background.

#### 2.4. Discontinuity Connection between Riverway Segments

#### 2.4.1. Construction of the Convex Hull

_{0}, E

_{1}, …, E

_{8}) as example. E

_{0}, the point with the smallest Y-coordinate value, is taken as the reference point. The other points E

_{1}–E

_{8}are connected to E

_{0}and sorted according to their angles with the X-coordinate, as shown in Figure 2a. The coordinates of three adjacent edge points form a third-order square matrix, where the determinant can be calculated. For example, given E

_{0}(x

_{0}, y

_{0}), E

_{1}(x

_{1}, y

_{1}), and E

_{2}(x

_{2}, y

_{2}), the determinant of the square matrix formed by these points can be calculated as

_{1}is determined as a convex hull point. As shown in Figure 2, all the edge points are processed (the green lines indicate the intermediate process, and the red lines are determined convex hull borders) to obtain the convex hull of the riverway segment.

**R**’

_{${l}_{1}$}, the results are denoted as

**P**

_{${l}_{1}$}= {

**P**

_{${l}_{1}$}(z), z = 1, …, Z’}, where l

_{1}∈ {1, …, n

_{1}},

**P**

_{${l}_{1}$}(z) is the convex hull of the z-th riverway segment in

**R**’

_{${l}_{1}$}.

#### 2.4.2. Pyramid Representation of Convex Hull Image

**P**

_{${l}_{1}$}as input, a Gaussian Pyramid (GP) is constructed by Gaussian smoothing and sub-sampling

**P**

_{${l}_{1}$}.

**G**

_{k}is the k-th layer of GP; k ∈ {1, …, K}, K is the total number of layers;

**H**

_{r}is the 2-D Gaussian low-pass filter for reducing resolution; ⊗ is the convolution operation; and S is the step size, such that (↓S)[·] means downsampling with step size S.

**G**

_{k}and superimposing it with the

**G**

_{k}

_{-1}, k ∈ {1, …, K}. When k = K,

**C**

_{k}represents the k-th layer of CP; ${\mathit{C}}_{k}^{\prime}$ is the extension of

**C**

_{k}to match the size of

**G**

_{k}

_{-1},

**H**

_{e}is the 2-D Gaussian high-pass filter for resolution expansion, and (↑S)[·] means upsampling with step size S.

#### 2.4.3. Multi-Layer Region Growth

**C**

_{k}of CP, three kinds of pixel intensity values can be obtained based on its construction process. For

**C**

_{k}(i, j) = 0,

**G**

_{k}(i, j) =

**C**’

_{k}

_{+1}(i, j) = 0, such that k- and (k+1)-th layers are both background at (i, j). For

**C**

_{k}(i, j) = 2,

**G**

_{k}(i, j) =

**C**’

_{k}

_{+1}(i, j) = 1, such that k- and (k+1)-th layers are both riverway at (i, j). For

**C**

_{k}(i, j) = 1,

**G**

_{k}(i, j) = 0 and

**C**’

_{k}

_{+1}(i, j) =1, indicating that the position (i, j) may belong to the discontinuity between riverway segments. Therefore, the search strategy for the seeds in

**C**

_{k}, k ∈ {1, …, K} is to select the points with

**C**

_{k}(i, j) = 1 as the seeds.

**C**

_{k}, k ∈ {1, …, K}, the seed can grow in four directions along in eight angles with its position as the center, as shown in Figure 3. The four directions are horizontal (1↔5), right diagonal (2↔6), vertical (3↔7), and left diagonal (4↔8). The seed’s growth strategy is to expand along each growth angle from seed until the pixel with intensity value 2 is found in its maximum growth range and there is no pixel with intensity 0 on the growth path. On each growth angle, the length of the growth path in pixels is denoted as ${r}_{k}^{\mathrm{o}}$, where o ∈ {1, …, 8} is the growth angle index.

_{k}, the seed can be determined to belong to the discontinuity between riverway segments. The connection process is employed to change the seed into a riverway segment, such that

**C**

_{k}(i, j) = 1 →

**C**

_{k}(i, j) = 2.

**C**

_{K}, the determined seeds are used for region growth, and the growth results are passed to the next layer to connect the discontinuities, layer by layer. When k = 1,

**C**

_{0}is obtained, which is the connection result of

**P**

_{${l}_{1}$}. For the final riverway extraction image

**J**

_{${l}_{1}$}=

**C**

_{0}−

**P**

_{${l}_{1}$}+

**R**’

_{${l}_{1}$}= {J

_{i}

_{, j}, (i, j) ∈

**Ω**

_{${l}_{1}$}}, where J

_{i}

_{, j}∈ {0, 1}, J

_{i}

_{, j}= 1 means riverway, and J

_{i}

_{, j}= 0 means background. If there is a little background noise inside the riverway extracted in

**J**

_{${l}_{1}$}, the connected component method of Section 2.3 can be used to optimize it.

#### 2.5. Riverway Extraction Result Output

_{0}and v

_{0}pixels are removed along the X- and Y-axes of the image space. The non-overlapping riverway extraction results are then stitched to form the output image. The process of riverway extraction can be expressed as

**J**

_{l}and

**J**’

_{l}are the l-th overlapping and non-overlapping image blocks, respectively, and l ∈ {1, …, h × v},

**J**= {J

_{i}

_{, j}, (i, j) ∈

**Ω**} is the final riverway extraction output image, where J

_{i}

_{, j}∈ {0, 1}, J

_{i}

_{, j}= 1 means riverway and J

_{i}

_{, j}= 0 means background.

## 3. Experiment and Analysis

#### 3.1. Data

#### 3.2. Experiment and Results

_{0}= h

_{0}= 5), Figure 4 is partitioned into 16 sub-image blocks, denoted as

**B**’

_{1,1}–

**B**’

_{4,4}, as shown in Figure 5. According to whether there is riverway cover, the partitioned sub-image blocks can be classified as

**B**’

_{${l}_{1}$}= {

**B**’

_{1,1},

**B**’

_{1,2},

**B**’

_{1,3},

**B**’

_{1,4},

**B**’

_{2,3},

**B’**

_{2,4},

**B**’

_{3,2},

**B**’

_{3,3},

**B**’

_{3,4},

**B**’

_{4,1},

**B**’

_{4,2}} and

**B**’

_{${l}_{2}$}= {

**B**’

_{2,1},

**B**’

_{2,2},

**B**’

_{3,1},

**B**’

_{4,3},

**B**’

_{4,4}} by visual interpretation. As the sub-image blocks in

**B**’

_{${l}_{2}$}were regarded as background (i.e., blocks were converted into binary images with all pixel intensity values of 0), the results are not shown here. Three sub-image blocks—

**B’**

_{1,3},

**B**’

_{1,4}, and

**B**’

_{3,4}in

**B**’

_{${l}_{1}$}—with different riverway morphology were selected to display the results of each processing step.

**B**’

_{${l}_{1}$}were set as ξ = 0.5, ξ = 1, ρ = 0.1, and q

_{0}= 0.5. The filtering results of the selected three sub-image blocks are shown in Figure 6a1–c1. The speckle noise was effectively filtered out, and the water and land boundaries had been well preserved. Figure 6a2–c2 are the results of segmenting the filtered outputs using the Sauvola algorithm, where w = 50 and κ = 0.3. From the segmentation results, there were some false riverway fragments. The false riverway fragments can be removed by taking the thresholds T

_{a}= 400 and T

_{r}= 1.5 of the connected components to obtain the extraction results of the riverway segments, as shown in Figure 6a3–c3.

**J**

_{g}is the corresponding ground truth of

**J**, | ∙ | denotes the number of elements in the set, dice(

**J**,

**J**

_{g}) ∈ [0, 1], the higher the value, the better the extraction result. The Jaccard similarity has a relation with the Sorensen–Dice similarity as follows,

**J**,

**J**

_{g}) ∈ [0, 1]; the higher the value, the better the extraction result.

**buf**

_{λ}is the evaluation region with radius λ,

**bor**is the riverway boundary obtained from the experiment when λ = 0,

**buf**is the standard riverway boundary line, and A

^{λ}is the cumulative percentage of overlap within λ. The accuracy evaluation results are presented in Table 1.

## 4. Discussion

#### 4.1. Block Processing Strategy

^{2}. The image was processed using the proposed blocking strategy, and the study area was partitioned into 16 sub-image blocks (see Figure 5). The computational complexity of the SRAD filter was less than 16(2 × M/4 × N/4)

^{2}, as the sub-image blocks that do not cover riverways are only used as background and not for filtering. The results were then graphed and compared using the number of pixels as abscissa and the computational complexity as ordinate. As shown in Figure 9, the number of calculations can be significantly reduced using the proposed blocking procedure.

**B**

_{1,2}and

**B**

_{1,3}) in the non-overlapping partition and the adjacent sub-image blocks (

**B**’

_{1,2}and

**B**’

_{1,3}) in the corresponding overlapping partition are selected as an example, as shown in Figure 11a1–d1, where

**B**’

_{1,2}and

**B**’

_{1,3}share a region of 10 pixels wide at the adjacent boundary relative to

**B**

_{1,2}and

**B**

_{1,3}. After SRAD filtering, riverway segments extraction and discontinuity connection, the extraction results are stitched, as shown in Figure 11a2,b2, and the stitched boundary parts are marked by a red rectangle box. To make it clearer, enlarge the red rectangle as shown in Figure 11a3,b3.

**B**’

_{1,2}and

**B**’

_{1,3}during stitching, so that the object can naturally transition at the stitching line.

_{0}and h

_{0}, selecting a larger value can ensure smooth connection, but it will increase the amount of calculation. As the sub-image block extraction result is a binary image, it will not involve the color difference of different categories, so we select an overlap of 5 to 10 pixels that can meet the stitching requirements. The overlap degree can also be adjusted adaptively according to the size of the block, such as setting it to 5% of the block size.

**B**’

_{${l}_{2}$}= {

**B**’

_{2,1},

**B**’

_{2,2},

**B**’

_{3,1},

**B**’

_{4,3},

**B**’

_{4,4}} is processed by the extraction procedure of this paper, and the results are shown in Figure 12a1–e1. As can be seen from Figure 12a1–e1, there are regions identified as riverways in each sub-image block. This is because the extraction is based on the regions with low overall brightness and continuous distribution, while there are always some regions with relatively low brightness in the sub-image blocks. It can be seen from the comparison with the original image in Figure 4 that these mis-extractions are low brightness object regions in the sub-image blocks, such as asphalt road, shadow, urban artificial lake, sewage pool and so on. All the extraction results are stitched together, as shown in Figure 12a2. It can be seen from the figure that these mis-extractions are not connected to the real riverway, while those originally interrupted riverway segments are connected together after the treatment of the discontinuity connection measures proposed in this paper. In the last step of this method, the connected component processing of Figure 12a2 can remove the mis-extractions, and the result is shown in Figure 12b2.

#### 4.2. Sub-Image Block Filtering

_{i}and σ

_{i}are the mean and standard deviation of the i-th ROI, respectively. Larger ENL values mean that the image is smoothed well. CNR, which measures image contrast by dividing the intensity difference between the selected object and the background regions by the sum of standard deviations, can be calculated as

#### 4.3. Discontinuity Connection

**B**’

_{4,1}as an example to illustrate the limitation of the convex hull processing mechanism, as shown in Figure 14.

**B**’

_{1,1}and

**B**’

_{1,2}—with different size discontinuities are selected as an example to illustrate the limitations of parameter adjustment, as shown in Figure 15.

**B**’

_{1,1}is small, when the 3-layer search is set, the discontinuity connection can be completed, while the discontinuity of

**B**’

_{1,2}is only partially connected.

**B**’

_{1,2}can complete the discontinuity connection when the 5-layer search is set, while

**B**’

_{1,1}has stopped the connection.

#### 4.4. Feasibility and Robustness Analysis

_{0}= v

_{0}= 5; and the partition results are displayed as red rectangular boxes in the figures. It can be seen from the partition that some sub-image blocks do not cover riverway and can be directly processed as the background, while the background of the sub-image blocks covering the riverway is relatively simple, which is beneficial to the extraction of the riverway. Each image is processed by the proposed method, and the riverway extraction result is represented as red and superimposed on the original image, as shown in Figure 17.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 6.**Results of each step. (

**a1**)–(

**c1**) Filtering result. (

**a2**)–(

**c2**) Sauvola algorithm segmentation results. (

**a3**)–(

**c3**) Extraction results of riverway segments.

**Figure 7.**Results and evaluation. (

**a1**)–(

**c1**) Constructed convex hull. (

**a2**)–(

**c2**) Riverway extraction results. (

**a3**)–(

**c3**) Qualitative evaluation.

**Figure 9.**Computational complexity of speckle reduction anisotropic diffusion (SRAD) before and after blocking.

**Figure 11.**Example of stitching non-overlapping and overlapping sub-image block extraction results. (

**a1**)–(

**d1**) Original sub-image blocks. (

**a2**)–(

**b2**) Stitching of extraction results of non-overlapping and overlapping partition. (

**a3**)–(

**b3**) Comparison of partial enlargement near the stitching line.

**Figure 12.**Example of riverway extraction from unclassified sub-image blocks. (

**a1**)–(

**e1**) Processing results of sub-image blocks without riverway cover. (

**a2**)–(

**b2**) Intermediate and final results of riverway extraction.

**Figure 14.**Example of the limitation of the minimum convex hull. (

**a**) Original image. (

**b**) Extracted riverway segments. (

**c**) Constructed convex hulls. (

**d**) Regions of growth. (

**e**) Riverway with discontinuity connection. (

**f**) Optimization of riverway extraction.

**Figure 15.**Example of multi-layer region growth. Left: (

**a**) and (

**d**) Riverway segments extraction results of

**B**’

_{1,1}and

**B**’

_{1,2}. Middle: (

**b**) and (

**e**) Region growth results of 3-layer search. Right: (

**c**) and (

**f**) Region growth results of 5-layer search.

**Figure 16.**SAR test images covering urban riverways. (

**a**) 1100 × 1800; (

**b**) 3000 × 1950; (

**c**) 1400 × 1000, and (

**d**) 1550 × 2950 pixels.

**Figure 17.**Riverway extraction results and its qualitative evaluation. (

**a**) 1100 × 1800; (

**b**) 3000 × 1950; (

**c**) 1400 × 1000, and (

**d**) 1550 × 2950 pixels.

Sub-Image Block | dice | jaccard | Radius of the Evaluation Region | ||||
---|---|---|---|---|---|---|---|

Overlap | 1 Pixel | 2 Pixels | 3 Pixels | 4 Pixels | |||

B’_{1,3} | 96.93 | 94.04 | 45.28 | 74.26 | 94.63 | 98.37 | 99.34 |

B’_{1,4} | 95.46 | 91.31 | 43.96 | 73.99 | 92.11 | 94.00 | 96.55 |

B’_{3,4} | 94.86 | 90.22 | 40.51 | 71.57 | 91.06 | 93.81 | 94.72 |

Method | dice | jaccard | Radius of the Evaluation Region | ||||
---|---|---|---|---|---|---|---|

Overlap | 1 Pixel | 2 Pixels | 3 Pixels | 4 Pixels | |||

Proposed method | 93.97 | 88.63 | 44.65 | 72.07 | 94.23 | 97.82 | 98.69 |

1-D Otsu in [12] | 72.52 | 56.89 | 32.47 | 58.27 | 72.60 | 75.26 | 76.65 |

2-D Otsu in [13] | 84.47 | 73.12 | 37.51 | 63.47 | 77.78 | 81.01 | 81.89 |

FCM in [16] | 87.08 | 77.12 | 39.85 | 65.41 | 80.13 | 83.28 | 83. 96 |

**Table 3.**Comparison between Equivalent Numbers of Looks (ENL) and Contrast Noise Ratio (CNR) evaluation of different filter results.

Image | Index | Lee | Kuan | Frost | SRAD |
---|---|---|---|---|---|

B’_{1,3} | ENL | 9.76 | 10.45 | 11.20 | 12.51 |

CNR | 16.94 | 17.82 | 17.35 | 18.55 | |

B’_{1,4} | ENL | 5.33 | 7.07 | 8.76 | 8.89 |

CNR | 8.91 | 11.02 | 11.27 | 11.74 | |

B’_{3,4} | ENL | 7.38 | 7.95 | 7.81 | 8.41 |

CNR | 12.79 | 13.56 | 13.87 | 15.19 |

Image | dice | jaccard | Radius of the Evaluation Region | ||||
---|---|---|---|---|---|---|---|

Overlap | 1 Pixel | 2 Pixels | 3 Pixels | 4 Pixels | |||

Figure 15a | 92.45 | 85.96 | 45.51 | 79.43 | 84.23 | 91.89 | 92.59 |

Figure 15b | 93.84 | 88.39 | 45.23 | 80.74 | 86.37 | 92.74 | 93.25 |

Figure 15c | 90.89 | 83.30 | 43.78 | 78.26 | 83.64 | 91.27 | 92.10 |

Figure 15d | 95.04 | 90.55 | 46.03 | 82.72 | 87.46 | 94.28 | 94.89 |

Average: | 93.06 | 87.05 | 45.14 | 80.29 | 85.42 | 92.55 | 93.21 |

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## Share and Cite

**MDPI and ACS Style**

Li, Y.; Yang, Y.; Zhao, Q.
Urban Riverway Extraction from High-Resolution SAR Image Based on Blocking Segmentation and Discontinuity Connection. *Remote Sens.* **2020**, *12*, 4014.
https://doi.org/10.3390/rs12244014

**AMA Style**

Li Y, Yang Y, Zhao Q.
Urban Riverway Extraction from High-Resolution SAR Image Based on Blocking Segmentation and Discontinuity Connection. *Remote Sensing*. 2020; 12(24):4014.
https://doi.org/10.3390/rs12244014

**Chicago/Turabian Style**

Li, Yu, Yun Yang, and Quanhua Zhao.
2020. "Urban Riverway Extraction from High-Resolution SAR Image Based on Blocking Segmentation and Discontinuity Connection" *Remote Sensing* 12, no. 24: 4014.
https://doi.org/10.3390/rs12244014