# Fourier Domain Adaptation for the Identification of Grape Leaf Diseases
###### Abstract
In order to improve the generalization ability of the grape leaf disease recognition model in many different fields, this chapter adopts the field adaptive method to improve the generalization ability. The third model maps the distributed datasets of grape leaf diseases into a special feature space, which makes the same disease data close to each other and then trains the target function in the feature space. There is no limit to the number of source domains and target domains, so the domain adaptive method can improve the generalization ability of the recognition model. The shift between two distributions should be minimized through domain adaptation. Some classical methods minimize the distance between the transformed source domain and the target domain by finding a mapping function, such as transfer component analysis (TCA) [7], joint distribution adaptation (JDA) [8], and dynamic distribution adaptation (DDA) [9]. All of them are based on the common difference metric maximum mean difference (MMD). However, due to the limited expression ability of these metrics, even minimizing MMD cannot guarantee the alignment of the two domain datasets. Another popular method is generative adversarial network (GAN), which can enhance the generalization ability of the model by training the robustness of the model on adversarial samples. It minimizes domain differences by using trained discriminators to maximize confusion between source domain and target domain representations [10]. However, most of the target domains do not have manual labeling in reality. When the label distribution is inconsistent, adversarial training makes it very easy to close the features of different categories in different data domains, resulting in the negative effect of adversarial domain adaptation. Thus, a grape leaf disease identification method based on Fourier domain adaptation is proposed in this paper that does not require any training to perform the domain alignment with a small number of target domain labels. The method includes a simple Fourier transform and its inverse and three convolutional neural networks, namely Alexnet [11], Vgg13 [12], and Resnet101 [13]. Firstly, the low-order frequency of the target image is replaced by the low-order frequency of the source image by calculating the fast Fouriertransform (FFT) [14]; afterward, the transformed image is reconstructed by inverse FFT (iFFT) using the primitive annotation of the source domain. Then, the source domain images and generated images are constructed into a new dataset, which is then trained in three different networks. In order to reduce the trouble caused by the randomness of style transformation, this paper still uses the farthest point sampling method to select images with significant differences for transformation. In this paper, a grape leaf disease identification method based on Fourier domain adaptation is proposed to identify the types of grape diseases. The main contributions of this paper are as follows:  
1. A grape leaf disease identification method based on Fourier domain adaptation to identify three common types of grape diseases;
2. The (fast) Fourier transform (FFT) is used for the adaptive method of grape leaf disease identification from different domains;
3. Reducing the impact of randomness on experiments using the farthest point sampling method. The organizational structure of this paper is as follows. In the next section, we introduce the materials and methods. Section 3 includes experiments and gives the results of experiments. Section 4 is the discussion on Fourier domain adaptation for identification of grape leaf diseases. Section 5 provides the conclusion.