Partial Differential Equation-Constrained Diffeomorphic Registration from Sum of Squared Differences to Normalized...

Area of Science:

• Medical image analysis
• Computational anatomy
• Image registration

Background:

• Current Large Deformation Diffeomorphic Metric Mapping (LDDMM) methods primarily use Sum of Squared Differences (SSD) for image similarity.
• Extending PDE-constrained LDDMM to diverse similarity metrics is crucial for broader applicability.

Purpose of the Study:

• To develop a unifying framework for PDE-constrained LDDMM with multiple image similarity metrics beyond SSD.
• To evaluate the performance of different optimization strategies (gradient-descent, Gauss-Newton-Krylov) with novel metrics.

Main Methods:

• Derived optimization equations for gradient-descent and Gauss-Newton-Krylov (GNK) using Normalized Cross-Correlation (NCC), local NCC (lNCC), Normalized Gradient Fields (NGFs), and Mutual Information (MI).
• Implemented and evaluated PDE-LDDMM with spatial and band-limited parameterizations.
• Compared performance against benchmark deep learning-based methods and ANTS-lNCC.

Main Results:

• GNK optimization significantly improved registration with NCC and lNCC, outperforming gradient-descent.
• Band-limited PDE-LDDMM with NCC and lNCC demonstrated top-tier performance.
• The proposed methods matched or exceeded the accuracy of state-of-the-art deep learning models.

Conclusions:

• The extended PDE-LDDMM framework with various image similarity metrics offers robust and accurate deformable image registration.
• This work facilitates the use of physically meaningful diffeomorphisms in clinical applications.
• NGFs and MI show potential for multimodal registration despite underperforming in some evaluations.