# Texture and Materials Image Classification Based on Wavelet Pooling Layer in CNN
## 2 Related Work  
This section highlights some applications that have used the wavelet pooling layer to improve their performance. A new architecture called WaveCNN was proposed in [12]. They note that the pooling layer (Max-Pooling) in a conventional CNN does not consider the feature structure of the previous layer. Then, Max-Pooling may lose some features. Therefore, they replace the pooling layer with wavelet decomposition. They succeed in more adequately representing the features for MNIST handwritten digit classification. A novel method that combined classical CNN layers with squeeze-and-excitation modules and the Haar wavelet as a pooling layer was proposed by [13]. The main objective is the real-time classification of vehicle types. The development of the method improves the classifier's performance by highlighting essential feature maps and decreasing the network entropy. Moreover, they propose a cross-entropy cost function and the use of DWT instead of Max-Pooling to improve the recognition rate. According to this layer, their model is named Wavelet Deep Neural Network (WDNN). Another alternative is the application of a multilevel analysis [14]. The method merges multiple wavelets transforms, as they function similarly to filters within convolutional neural networks. They show that some neighborhood methods introduce edge halos, aliasing, and blurring effects in specific datasets. Choosing the correct pooling method is key to obtaining good results. Thus, they explore the use of wavelet bases such as Haar, Coiflet, and Daubechies to perform pooling. In semantic segmentation tasks, encoder-decoder-type networks have been used [15]. This type of CNNs usually uses pooling to reduce computational costs and improve invariances relative to certain distortions and expands the receptive field. However, pooling can result in information loss, which disruptive to later operations, such as feature extraction and analysis. Moreover, each image pixel is assigned a specific class in semantic segmentation tasks by dividing it into regions of interest. Therefore, a pooling method based on wavelet operations has been proposed to divide it into regions of interest. In [16], the authors presented an approach called 3D WaveUNet, based on wavelets and deep learning for 3D neuron segmentation. The encoder-decoder network is integrated with a 3D wavelet to segment the nerve fibers into cubes; the wavelets help the deep networks remove noise from the data and connect the broken fibers. At the end of the method, the segmented nerve fibers into cubes are assembled to generate the entire neuron. In this case, the neuron segmentation method can completely extract the target neuron in noisy neuron images. A U-Net architecture based on wavelet transform pooling is proposed in [17]. This work aims to segment multiple sclerosis (MS) lesions in magnetic resonance images (MR). One characteristic is that the first stage of the network uses the wavelet transform, and in the second stage, its inverse is used. In both stages, it highlights abrupt changes in the image and better describes the features. An advantage is its multiresolution analysis; thus, its use improves the detection of lesions of different sizes and in segmentation. In the area of image restoration, a multilevel wavelet CNN (MWCNN) method was proposed to balance the size of the receptive area and computational efficiency [18]. The main idea is to integrate the wavelet transform within the CNN architecture to reduce feature maps. The MWCNTs method is also based on a U-Net architecture and the inverse wavelet transform (IWT) for the reconstruction stage with a high resolution. In [9], they proposed another alternative called wavelet pooling as a layer inside the CNN architecture. This method decomposes the image into two sub-bands, discarding the first level to reduce the size of the feature map. The approach allows a structured compression of the data, reducing the creation of denoised edges and other defects in the image.