Analysis of 3D/2D Image Registration and a New Registration Approach Based on Residual Neural Networks

Image registration is an essential component of image processing with a wide range
of applications, particularly in the medical field. The goal of image registration is to
determine optimal deformations that align two or more images. Our contributions to
this field are twofold.
First, we analyze 3D/2D registration problems. A particular challenge with such registration problems is that a 3D deformation is sought based on 2D data. Since typically regularization is utilized to ensure the existence of reasonable solutions, the question arises of which regularization is appropriate for 3D/2D registration.
We address this question and prove the suitability of a class of second-order regularizers. We additionally prove that first-order regularizers are generally not appropriate. Furthermore, we show that our working assumptions apply for common settings of 3D/2D registration and we also extend our results to registration problems of other dimensions. Our analysis contributes to a more comprehensive understanding of image registration problems.
Second, we present the new residual neural network-based registration approach RNR. This method enables the registration of multiple consecutive images. Moreover, the method ensures diffeomorphic deformations under certain conditions. This is a desirable property in many applications, as diffeomorphisms are invertible and sustain image features.
We show that RNR is theoretically sound and provide a comprehensive validation. In
particular, we demonstrate that the method allows for larger deformations than comparative approaches and has competitive speed. Finally, we apply the method to build a breathing model, which in turn forms the basis for respiratory surface electromyography modeling. The latter is a highly relevant field that is used, for example, to improve mechanical ventilation for patients.