# Research on Crack Width Measurement Based on Binocular Vision and Improved DeeplabV3+
## 2 Crack Region Segmentation Algorithm
### Idam  
The ASPP structure of the original DeeplabV3+ model uses the dilated convolution with expansion rates of 3, 6, 18, and 24 in parallel to extract the feature relationships of images under different receptive fields. However, when the dilated rate is greater than 24, the dilated convolution will gradually lose the feature extraction ability. Therefore, [PERSON] et al. adopted dilated convolution with expansion rates of 3, 6, 12, 18, and 24 to replace the parallel feature extraction structure of ASPP by dense connection, and proposed a DenseASPP model [28], which obtained more and larger receptive fields. However, this method still has the problem of the checkerboard effect, that is, it is assumed that the dilated convolution with convolution kernel size 3 and expansion rate 2 is used to perform three consecutive  
Figure 1: Improved DeeplabV3+ model.  
operations on the image, and the covering points are marked with blue. The extracted pixels are shown in Figure 3. As can be seen from the white squares in the figure, the correlation between local information is destroyed and the information is seriously lost.  
To this end, the HDC strategy is adopted in this paper, that is, dilated convolutions with different expansion rates are used alternately and continuously to reduce the influence of the checkerboard effect [29]. Suppose that when there are \(N\) dilated convolutional layers with kernel size _ksize_, the dilation rate is {\(d_{1}\),..., \(d_{i}\),..., \(d_{n}\)}, define the maximum distance between two non-zero points as follows.  
\[M_{i}=MAX[M_{i+1}-2d_{i},M_{i+1}-2(M_{i+1}-d_{i}),d_{i}] \tag{2}\]  
where \(M_{n}=d_{n}\), HDC strategy requires \(M_{2}\leq\)_ksize_. When _ksize_ = 3 and \(d\) = {1,2,5}, \(M_{2}=MAX\) [1,-1,2] = \(2\leq 3\), HDC strategy is satisfied. The convolution extraction result is shown in Figure 4, which shows that this connection strategy can effectively use image information and weaken the checkerboard effect.  
Figure 3: The checkerboard effect. (**a**) The first; (**b**) the second; (**c**) the third.  
Figure 2: Schematic diagram of the bottleneck residual block.  
To obtain enough and large enough receptive fields, the convolution kernel with an expansion rate of {1,2,5} is designed to be used twice in this paper. The IDAM model structure is shown in Figure 5:  
Bring the current structure into the receptive field calculation formula:  
\[\left\{\begin{array}{l}RF=(d-1)\times(ksize-1)+ksize\\ RF_{n}=RF_{n-1}+k_{n}-1\end{array}\right. \tag{3}\]  
In the formula, \(RF_{n}\) represents the receptive field of the n-layer dilated convolution, \(k_{n}\) is the size of the \(n\)-layer dilated convolution, and the maximum receptive field size of IDAM is [\(2\times 2\times(1+2+5)+1\)] = 33. It is sufficient to process the \(1/16\) (\(80\times 80\) pixels) depth feature map input in the trunk network. Compared with the four receptive field combinations of ASPP structure, according to the permutation combination, the number of extracted feature combinations of IDAM can be calculated as follows:  
\[N_{IDAM}=\sum_{m=1}^{n=6}C_{n}^{m}=63 \tag{4}\]  
It can be seen that the IDAM model structure obtains more combined high-level semantic features.