Before revision:  This paper will demonstrate an unprecedented idea of making use of both robustness of CNNs and rigorousness of mathematical model to obtain meaningful registration maps between 2D images under the aforementioned strict constraints for the sake of well-posedness .
After revision:  This paper will demonstrate an unprecedented idea of making use of both robustness of CNNs and rigorousness of mathematical model to obtain meaningful registration results without prescribing any landmarks. Moreover, unlike other learning-based 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 .