# Temporal Subtraction Technique for Thoracic MDCT Based on Residual VoxelMorph
## 1 Introduction
It is important to develop highly efficient and accurate registration methods to reduce these image artifacts, as well as putting CAD systems to practical use in clinical settings as medical devices. There are rigid and nonrigid methods in image registration techniques. Rigid registration has a fast computation time, and it is ideal for aligning normally non-deformable objects such as bones. However, it is not suitable for matching objects with complicated deformation, such as organs, bronchial walls, and blood vessels. On the other hand, nonrigid registration allows for flexible matching of objects with these deformations. However, the limitations of attempting to achieve nonrigid registration are the high computational cost and the difficulty of accurate matching. Given these circumstances, we are currently investigating a nonrigid registration method that can perform fast, highly flexible, and rigorous matching. Although lots of methods for nonrigid image registration of medical images have been developed, there remain various problems, for instance, they are not yet sufficient to deal with local changes caused by temporal differences and the shooting device environment. Therefore, there is no established approach to registration methods that can be applied to a variety of images. Moreover, deep neural networks have been attracting attention in recent years. Deep neural networks are expected to achieve highly accurate analysis in a short time by intensively learning with a large training dataset of various images containing complex information. Among them is VoxelMorph, a registration method based on unsupervised deep learning [6] that integrates a fully convolutional U-net architecture and spatial transformer and simultaneously trains them to align images. Although VoxelMorph is a useful method, preparing large training datasets is difficult for medical image analysis, as in our study. Therefore, the possibilities of incorrect learning, gradient loss, and overlearning are concerns. However, the introduction of a residual block in image recognition is reportedly expected to be able to prevent the gradient loss problem as well as overlearning [7]. Residual blocks are realized by adding residual mappings and skip connections and can improve feature utilization when learning upper-layer features from lower-layer features in convolution. Hence, by introducing residual blocks to VoxelMorph, high learning efficiency can be expected even with a limited training set. In this research, we propose a method for generating temporal subtraction images of thoracic CT images based on ResidualVoxelMorph, which introduces a residual block to VoxelMorph to enable flexible positioning at a low computational cost. In other words, this technique contributes to the construction of a 3D temporal subtraction technique that can rapidly generate subtraction images that can more clearly detect early lesions that are difficult to detect with 2D X-ray images and that can be used for lung cancer screening with thoracic CT. This technique can improve reading performance for physicians and contribute to early case detection and lesions treatment for patients.