# When Deep Learning Meets Data Alignment:
## 4 Review of Learning-Based Approaches for Registration
### Transformation Level  
Some works have been successfully employed neural networks for learning and applying geometric transformations. Some of these achievements have been done using GAN architectures or variants of them. For instance, [PERSON] et al. [47] demonstrated good results using neural networks for finding realistic geometric transformations for 2D image compositing. Image compositing refers to overlap images coming from different scenes; thus, achieving a good realism implies a good transformation to minimize the appearance and geometric differences. For this purpose, they propose a GAN architecture using Spatial Transform Networks (STNs) [95], named ST-GAN. According to the authors of ST-GAN, this idea could be extended to other image alignment tasks. STNs have shown good results resolving geometric variations; thus, with this architecture, the network learns to perform realistic geometric warps, demonstrating potential 3D capabilities. [PERSON] et al. [60] also used GANs to carry out the registration of magnetic resonance (MR) and transrectal ultrasound (TRUS) images as well as evaluate the provided result. The generator network provides the transformation parameters to align both inputs, while the discriminator performs a quality evaluation of that alignment. [PERSON] et al. [54] used GANs for deformable multimodal medical image registration in 2D. The network outputs a transformed image and also a deformation field. Similarly, in three-dimensional space, [PERSON] and [PERSON] [39], as referenced above, performed the reconstruction of incomplete archaeological models also using GANs, in which the generator network provides a reconstructed model. [PERSON] et al. [79] also proposed a registration method based on a GAN architecture with a gradient loss which can manage local structure information across modalities. This makes it more robust against large deformations, noise, and blur. [PERSON] and [PERSON] [27] managed multiple point clouds registration using DNNs. They approached this problem by including two networks, a localization network named L-Net, and an occupancy map network, M-Net. The L-Net estimates the sensor pose for a given point cloud, sharing some optimization parameters between the input point clouds. The goal of this network is to estimate the sensor pose in a global frame. To do that, the L-Net network is divided into a feature extraction module followed by an MLP that outputs the sensor pose. The feature extraction module employed depends on the input format of the point cloud. If it is an organized point cloud, a CNN is employed for that purpose. If not, the features are extracted using PointNet [90]. Later, the M-Net receives those location coordinates in the global space and retrieves the discrete occupancy map. Besides, the L-Net network locates each input point cloud in a global space; there is no target for the alignment. With a similar architecture, [PERSON] et al. [71] presented 3 DN, a combination of PointNet and MLPs that deforms 3D meshes to resemble a target, given in the form of a 2D image or point cloud, as close as possible preserving the properties of the source. The proposal extracts global features from both source and target inputs using CNN/PointNet. Next, those features are used to estimate the per-vertex displacement with an 'offset decoder'. To overcome the problem of tessellation differences, an intermediate sampled point cloud is calculated from both source and target. They employed a combination of four different loss functions, measuring the similarity between the deformed source and the target, symmetry, local geometric details, and self-intersections. This work proposes an end-to-end network architecture for mesh deformation. Using autoencoders, [PERSON] et al. [29], with their SDNs introduced before, replicated the shape of a body previously encoded in a given template. For 3D medical image non-rigid registration, [PERSON] and [PERSON] [45] employed an architecture inspired by STNs extending the works of [PERSON] et al. [96] and [PERSON] et al. [97].