﻿ 多尺度空间下的隧道裂缝与渗水区域检测
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 同济大学学报(自然科学版)  2019, Vol. 47 Issue (12): 1825-1830.  DOI: 10.11908/j.issn.0253-374x.2019.12.019 0

### 引用本文

JIA Dongfeng, ZHANG Weiping, LIU Yanping. Tunnel Crack and Seepage Detection in Multi-scale Space[J]. Journal of Tongji University (Natural Science), 2019, 47(12): 1825-1830.   DOI: 10.11908/j.issn.0253-374x.2019.12.019

### 文章历史

1. 同济大学 土木工程学院，上海 200092;
2. 同济大学浙江学院，浙江 嘉兴 314051

Tunnel Crack and Seepage Detection in Multi-scale Space
JIA Dongfeng 1, ZHANG Weiping 1, LIU Yanping 2
1. College of Civil Engineering, Tongji University, Shanghai 200092, China;
2. Tongji Zhejiang College, Jiaxing 314051, China
Abstract: Based on the image of point cloud, a detection algorithm for cracks and water seepage area identification in multi-scale space is proposed. According to the physical features of tunnel cracks in different scale, meanwhile, with the definition of scale space, a fusion image detection operator is developed to maintain the stability of ribbon like cracks detection, at the same time, to restore the sensitivity to the small cracks in high gray value for obtaining more edge pixels. Therefore, the identification and detection of multi-scale cracks and seepage are achieved with the application of proposed algorithm. It is proved by an example that the algorithm can effectively eliminate the interference of fake cracks, and accurately identify and locate cracks in different scales.
Key words: point cloud image    multi-scale space    crack detection    seepage area

1 隧道裂缝的物理特点

2 本文裂缝提取算法

(1) 尺度空间构建

 $L(x, y, \sigma)=G(x, y, \sigma) * I(x, y)$ (1)

 $G(x, y, \sigma)=\frac{1}{2 \pi \sigma^{2}} \mathrm{e}^{-\left(x^{2}+y^{2}\right) / 2 \sigma^{2}}$ (2)

(2) 裂缝检测算子定义

 $r_{i j}: r_{j i}=1-\min \left(\mu_{i} / \mu_{j}, \mu_{j} / \mu_{i}\right)$ (3)

 $D_{1}=\min \left(r_{i k}, r_{i j}\right)$ (4)

 图 1 θ角的定义 Fig.1 The defination of θ

 $D_{2}=\left[\frac{\left(\sigma_{i j}^{2}\right)^{\left|R_{i j}\right|}}{\left(\sigma_{i}^{2}\right)^{\left|R_{i}\right|}\left(\sigma_{j}^{2}\right)^{\left|R_{j}\right|}}\right]$ (5)

 $f(D)=\frac{D_{1} D_{2}}{1-D_{1}-D_{2}-2 D_{1} D_{2}}$ (6)

 $D(\boldsymbol{X})=D+\frac{\partial \boldsymbol{D}^{\mathrm{T}}}{\partial \boldsymbol{X}} \boldsymbol{X}+\frac{1}{2} \boldsymbol{X}^{\mathrm{T}} \frac{\partial^{2} \boldsymbol{D}}{\partial \boldsymbol{X}^{2}} \boldsymbol{X}$ (7)

 $\hat{X}=-\frac{\partial^{2} \boldsymbol{D}^{-1}}{\partial \boldsymbol{X}^{2}} \frac{\partial \boldsymbol{D}}{\partial \boldsymbol{X}}$ (8)

 $D(\hat{X})=D+\frac{1}{2} \frac{\partial \boldsymbol{D}^{\mathrm{T}}}{\partial \boldsymbol{X}} \hat{X}$ (9)

3 实例分析 3.1 裂缝提取精度分析

 图 2 裂缝提取 Fig.2 Crack extraction

 图 3 不同尺度的裂缝提取 Fig.3 Crack extraction in different scale

3.2 渗水区域检测

 图 4 渗水图像直方图 Fig.4 Histogram of water seepage

 图 5 对比度拉伸 Fig.5 Constrastive stetching

 图 6 算法比较 Fig.6 Algorithm comparison
4 结语

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