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Multiscale Approach for Three
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SIAM Journal on Imaging Sciences, Volume 15, Issue 3, Page 1431-1468, September 2022. Image registration, especially for three-dimensional (3D) image registration, is widely used in clinical medicine. Many 3D image registration models have been proposed during the last decades. All these models achieve the minimum of the cost functional with some prior regularization. In addition, the physical mesh folding phenomenon is not taken into consideration in most models. This raises a question of whether one can achieve/approach the infimum of the cost functional without a regularization term and ensure no mesh folding. To give an answer to this question, a multiscale approach for 3D conformal image registration is presented in this paper. This approach ensures no mesh folding and gets close to the infimum of the cost functional without any regularization on the 3D conformal set. The 3D multiscale approach contains a series of deformation composition processes and the convergence of the process is presented. Furthermore, a numerical algorithm for this multiscale approach is proposed and the convergence of the numerical algorithm is proved. Moreover, several numerical tests are also listed to show the good performance of the proposed algorithm.
中文翻译：
SIAM 影像科学杂志，第 15 卷，第 3 期，第 1431-1468 页，2022 年 9 月。图像配准，尤其是三维（3D）图像配准，广泛应用于临床医学。在过去的几十年中，已经提出了许多 3D 图像配准模型。所有这些模型都通过一些先验正则化实现了成本函数的最小值。此外，大多数模型没有考虑物理网格折叠现象。这就提出了一个问题，即是否可以在没有正则化项的情况下实现/接近成本泛函的下确界并确保没有网格折叠。为了回答这个问题，本文提出了一种用于 3D 共形图像配准的多尺度方法。这种方法确保没有网格折叠，并接近成本泛函的下确界，而无需对 3D 保形集进行任何正则化。3D多尺度方法包含一系列变形合成过程，并提出了该过程的收敛性。此外，提出了这种多尺度方法的数值算法，并证明了数值算法的收敛性。此外，还列出了几个数值测试，以显示所提出算法的良好性能。 |
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