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Combining the Band-Limited Parameterization and Semi-Lagrangian Runge–Kutta Integration for Efficient PDE-Constrained LDDMM
Journal of Mathematical Imaging and Vision ( IF 2 ) Pub Date : 2021-02-05 , DOI: 10.1007/s10851-021-01016-4
Monica Hernandez

The family of PDE-constrained Large Deformation Diffeomorphic Metric Mapping (LDDMM) methods is emerging as a particularly interesting approach for physically meaningful diffeomorphic transformations. The original combination of Gauss–Newton–Krylov optimization and Runge–Kutta integration shows excellent numerical accuracy and fast convergence rate. However, its most significant limitation is the huge computational complexity, hindering its extensive use in Computational Anatomy applied studies. This limitation has been treated independently by the problem formulation in the space of band-limited vector fields and semi-Lagrangian integration. The purpose of this work is to combine both in three variants of band-limited PDE-constrained LDDMM for further increasing their computational efficiency. The accuracy of the resulting methods is evaluated extensively. For all the variants, the proposed combined approach shows a significant increment of the computational efficiency. In addition, the variant based on the deformation state equation is positioned consistently as the best performing method across all the evaluation frameworks in terms of accuracy and efficiency.



中文翻译:

结合带限参数化和半拉格朗日Runge-Kutta积分,实现有效的PDE约束LDDMM

PDE约束的大变形微形度量映射(LDDMM)方法家族正在成为一种对物理有意义的微形变换特别有趣的方法。Gauss-Newton-Krylov优化和Runge-Kutta积分的原始组合显示出极好的数值精度和快速的收敛速度。但是,其最大的局限性是巨大的计算复杂性,从而阻碍了其在计算解剖学应用研究中的广泛使用。该限制已通过在带限制矢量场和半拉格朗日积分中的问题公式独立处理。这项工作的目的是将带限PDE约束的LDDMM的三个变体结合起来,以进一步提高其计算效率。广泛评估了所得方法的准确性。对于所有变体,所提出的组合方法显示出计算效率的显着提高。此外,基于变形状态方程的变量在准确性和效率方面始终是所有评估框架中性能最佳的方法。

更新日期:2021-02-05
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