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. However, most learning-based methods cannot ensure the bijectivity of the registration, which makes it difficult to establish a 1-1 correspondence between the images. In this paper, we develop a novel method for large deformation image registration by a fusion of convolutional neural network (CNN) and quasiconformal theory. More specifically, we propose a new fidelity term for incorporating the CNN features in our quasiconformal energy minimization model, which enables us 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.

中文翻译：

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大变形图像配准的CNN驱动准同形模型

在过去的几十年中，图像配准已得到广泛研究，并在科学，工程和医学中得到了众多应用。用于大变形图像配准的大多数常规数学模型都依赖于规定的界标，这些界标通常需要乏味的手动标记并且容易出错。近年来，对使用机器学习进行图像配准的兴趣激增。但是，大多数基于学习的方法不能确保配准的双射性，这使得很难在图像之间建立1-1对应关系。在本文中，我们通过融合卷积神经网络（CNN）和拟保形理论，开发了一种用于大变形图像配准的新方法。进一步来说，我们提出了一个新的保真度术语，将CNN功能纳入我们的准保形能量最小化模型中，这使我们能够获得有意义的注册结果而无需规定任何标志。而且，与其他基于学习的方法不同，我们的方法的双射性由准保形理论保证。实验结果表明该方法的有效性。更广泛地讲，我们的工作揭示了如何将严格的数学理论和实用的机器学习方法集成在一起，以开发具有改进性能的计算方法。实验结果表明该方法的有效性。更广泛地讲，我们的工作揭示了如何将严格的数学理论和实用的机器学习方法集成在一起，以开发具有改进性能的计算方法。实验结果表明该方法的有效性。更广泛地讲，我们的工作揭示了如何将严格的数学理论和实用的机器学习方法集成在一起，以开发具有改进性能的计算方法。