  Image registration has been widely studied over the past several decades,
with numerous applications in science, engineering and medicine. Most of the
conventional mathematical models for large deformation image registration rely
on prescribed landmarks, which usually require tedious manual labeling and are
prone to error. In recent years, there has been a surge of interest in the use
of machine learning for image registration. In this paper, we develop a novel
method for large deformation image registration by a fusion of quasiconformal
theory and convolutional neural network (CNN). More specifically, we propose a
quasiconformal energy model with a novel fidelity term that incorporates the
features extracted using a pre-trained CNN, thereby allowing us to obtain
meaningful registration results without any guidance of prescribed landmarks.
Moreover, unlike many prior image registration methods, the bijectivity of our
method is guaranteed by quasiconformal theory. Experimental results are
presented to demonstrate the effectiveness of the proposed method. More
broadly, our work sheds light on how rigorous mathematical theories and
practical machine learning approaches can be integrated for developing
computational methods with improved performance.
