# A Lightweight and High-Accuracy Model for Pavement Crack Segmentation
## 3 Methods
### Haar Wavelet Down-Sampling  
Semantic segmentation models often employ strided convolution or pooling methods for down-sampling feature maps. While these approaches reduce spatial resolution, they inevitably cause the loss of critical information, particularly spatial details such as edges and textures. This issue is especially pronounced in crack segmentation tasks, where cracks are typically thin, irregular, and have low contrast with the background. The loss of fine details significantly impacts segmentation performance.  
To address this challenge, we propose a down-sampling module based on Haar wavelet transform (Haar Wavelet Down-sampling, HWD). This module enables resolution reduction while preserving spatial information effectively. Haar wavelet transform is a simple yet efficient discrete wavelet transform that is well suited for image processing. Specifically, for a 2D feature map of size H \(\times\) W, Haar wavelet transform decomposes it into four sub-components of size H/2 \(\times\) W/2: one low-frequency component \(H_{1}\) and three high-frequency components corresponding to horizontal \(H_{2}\), vertical \(H_{3}\), and diagonal directions \(H_{4}\). These sub-components collectively retain comprehensive spatial information about the input feature map.  
Figure 3 illustrates the workflow of the HWD module. First, the input feature map undergoes Haar wavelet transform, which decomposes it into four sub-components: one low-frequency approximation and three high-frequency details corresponding to horizontal, vertical, and diagonal directions. These sub-components are then concatenated along the channel dimension, effectively reducing the spatial resolution by half while increasing the number of channels to four times the original count. Subsequently, a \(1\times 1\) convolution is applied to compress the channel dimension to match the specific requirements of downstream tasks. This design not only reduces the feature map resolution while preserving critical spatial information but also enhances the feature extraction capability of subsequent convolutional layers through the reorganization of information across the channel dimension. The mathematical expression of the process is as follows:  
\[\begin{array}{l}(H_{1},H_{2},H_{3},H_{4})=\text{HWT}(x)\\ x^{\prime}=\text{Conv}(\text{Concat}(H_{1},H_{2},H_{3},H_{4}))\end{array} \tag{1}\]  
The fundamental distinction between the down-sampling method based on Haar wavelet transform and traditional approaches such as strided convolution or pooling lies in its ability to preserve more detailed information during down-sampling. Haar wavelet transform maps spatial information into the channel dimension instead of discarding it outright. This characteristic enables the model to extract richer contextual information from these lossless features, significantly enhancing its ability to capture fine details such as crack edges and textures. Moreover, Haar wavelet transform is computationally effi-cient, with a low complexity that aligns well with the design requirements of lightweight semantic segmentation networks. Consequently, the introduction of the HWD module not only improves the segmentation performance of the model but also enhances its adaptability to complex details in crack images, making it particularly suitable for challenging real-world applications.