## 2 Related Work  
An image-based (not DEM-based) registration method is expected to match multimodal images based on the similarities of their edges and corners. Thus, template-based methods with traditional metrics, such as normalized cross-correlation (NCC) or mutual information between two images, have been proposed for image registration [12; 13]. Meanwhile, other suitable metrics have been proposed for more accurate template-matching of SAR and optical images [14; 15; 16; 17]. However, these methods use image features of a relatively wide area. The template-matching accuracy decreases with small template size, whereas its robustness for occlusions and partial difference (e.g., between pre- and post-disaster) decreases with large template size. Although machine-learning-based (especially deep-learning-based) SAR and optical image-matching methods have been proposed [18; 19; 20], the range of pixels considered in these methods are whole image correspondences or some of them have a limitation in rotation robustness. The identification of local correspondence is not possible with these methods; hence, a new technique that can perform image registration with local features when applied to disaster sites is required since landform responses may be partially or fully changed after a disaster event. Local image features are often employed to achieve the image-based registration of satellite data. Particularly, keypoint-based methods [21; 22; 23] can estimate the correspondence between two images using uncorrelated local features, similar to template-based  
Figure 2: An optical image generated by a conditional GAN ([11], **left**) and an optical image (**right**). Note the loss of local features due to blurring. methods. Methods that adopt a keypoint detector and a feature descriptor [24; 25; 26; 27] are frequently used to match (i.e., estimate the correspondence of) two images. These methods describe features that are robust to geometric fluctuation (e.g., rotation, scaling) and changes in environmental (e.g., lighting) conditions. They find keypoint pairs that have similar features as corresponding points, thereby achieving image matching. Since these methods use local features, they can achieve partial correspondence, even when a part of the captured area has collapsed due to disaster. Meanwhile, machine learning methods based on deep neural networks (DNNs) have been widely used for image modal translation [28; 29; 30; 31; 32]. In this work, we mainly focus on GANs. A GAN trains a generator that generates data and a discriminator that determines the authenticity of the data to produce a generator that can generate data similar to the original features through comparison. The loss function of a GAN, \(\mathcal{L}_{\text{GAN}}\), is given as follows:  
\[\mathcal{L}_{\text{GAN}}(G,D)=\mathbb{E}_{\mathbf{y}}[logD(\mathbf{y})]+\mathbb{E}_{ \mathbf{z}}[log(1-D(G(\mathbf{z})))], \tag{1}\]  
where \(G()\) indicates the generated data based on the input data by the generator (\(G\)), \(D()\) indicates the probability that a discriminator (\(D\)) can correctly discriminate between a real input and a fake (artificial) input, \(\mathbf{y}\) and \(\mathbf{z}\) indicate the answer and a random value, respectively. The purpose of training a GAN is to obtain a well-trained generator that can produce sufficient fake data to deceive the discriminator. The generator \(G^{*}\) is given as follows:  
\[G^{*}=arg\underset{G}{min}\underset{D}{max}\mathcal{L}_{\text{GAN}}(G,D). \tag{2}\]  
An application of a GAN is a conditional GAN (cGAN), whose generator obtains inputs rather than random values. It is a common multipurpose image interpretation method, and its loss function \(\mathcal{L}_{\text{cGAN}}\) is given as follows:  
\[\mathcal{L}_{\text{cGAN}}(G,D)=\mathbb{E}_{\mathbf{y}}[logD(\mathbf{y})]+\mathbb{E}_{ \mathbf{x},\mathbf{z}}[log(1-D(\mathbf{x},\ G(\mathbf{x},\mathbf{z})))], \tag{3}\]  
where \(\mathbf{x}\) indicates the input. A well-trained generator for the cGAN can be obtained in the same way as Equation (2).