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.
翻译:在过去几十年里,对图像登记进行了广泛的研究,在科学、工程和医学方面应用了无数。用于大规模变形图像登记的常规数学模型大多依赖于指定标志,通常需要烦琐的手工标签,容易出错。近年来,人们对于使用机器学习进行图像登记的兴趣激增。在本文中,我们开发了一种新型方法,通过将准正统理论和进化神经网络(CNN)结合起来,对图像进行大规模变形登记。更具体地说,我们提出了一种半正规能源模型,其中含有一种新颖的忠实术语,它包含使用预先培训过的CNN所提取的特征,从而使我们能够在不对指定标志进行任何指导的情况下获得有意义的登记结果。此外,与许多先前的图像登记方法不同,我们的方法的双轨性得到了准形式理论的保证。实验结果展示了拟议方法的有效性。更广泛地说,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结合起来,以发展计算方法,改进性能。