# When Deep Learning Meets Data Alignment:
## 4 Review of Learning-Based Approaches for Registration
### Transformation Level
The network takes a pair of volumes and predicts the displacement fields needed to register source to target. According to the authors, it improves the results compared to U-net [98] and VoxelMorph [97]. This method produces deformations with fewer regions of non-invertibility where the surface folds over itself. To achieve this, they employed an explicit anti-folding regularization to penalize _foldings_, which are the spatial locations where the deformation is non-invertible and is indicated by a negative determinant of the Jacobian matrix. With convolutional networks, [PERSON] et al. [65] performed the 3D reconstruction from a single 2D image by learning to apply large deformations and compelling mesh reconstructions by inferring Free Form Deformation (FFD) parameters. They employed a lightweight CNN based on the MobileNet architecture [99] to infer FDD parameters to deform a template and infer a 3D mesh of the given image. As a result, the network learns how to deform a given template to match features present in a 2D image with finer geometry than other methods working with voxel grids and point clouds, because there is no discretization. [PERSON] et al. [64] proposed a multi-channel CNN (MCNN) for deformable registration of CT scans with digital subtraction angiography (DSA) images of the cardiovascular system. The network is composed of several sub-networks that converge before the fully connected layers. They named this architecture as a multi-channel convolutional neural network. They employed a CNN model based on the VGG network combined with a vascular diameter variation model to directly regress and predict transformation parameters. With this architecture, each channel of the MCNN process a different phase of the vascular deformation cycle, comparing the results of each to choose the best result. [PERSON] and [PERSON] [17] employed Fully Convolutional Networks (FCNs) to optimize and learn spatial transformations between pairs of images to be non-rigidly registered. Their method works with medical images at the voxel level and, according to the authors, it improves the results of STNs, which cannot manage small transformations. The spatial transformation between pairs of images is obtained directly by maximizing an image-wise similarity metric, similar to traditional approaches. The use of FCNs facilitates the voxel-to-voxel prediction of deformation fields, which also allows learning small transformations. [PERSON] et al. [36] proposed a method for 3D garment fitting on bodies. To extract global features of the body model, they employed a PointNet [90] but with leaky ReLUs with a slope of 0.1. After that, a second stream, composed by six residual blocks, is used to extract features from the garment mesh and also take as input the previous global body features. Thirdly, the features provided by both networks are merged employing four Multi Layer Perceptron (MLP) blocks shared by all points. The final MLP block outputs a vector with the 3D translation information. With this method, the authors achieved results nearly as accurate as a Physics-Based Simulation (PBS), but less time-consuming. Similarly, PointNetLK [62] is a method for 3D rigid registration which modifies the Lucas and Kanade (LK) [100] algorithm integrated with PointNet. The process is mainly divided into two steps: initially, two 3D point sets are passed through a shared Multi Layer Perceptron of the two inputs and a symmetric pooling function. Second, the transformation is obtained and applied to the moving point cloud. The whole procedure is iteratively repeated until a minimum quality threshold is reached. According to the authors, this method exhibits remarkable generalization of unseen objects and shape variation due to the encoding of the alignment process in the network architecture that only needs to learn the PointNet representation. [PERSON] et al. [76] proposed a deterministic PointNetLK method to improve the generalization by using analytical gradients.