Primal-dual convex optimization in large deformation diffeomorphic metric mapping: LDDMM meets robust regularizers

Area of Science:

• Medical image analysis
• Computational anatomy
• Optimization algorithms

Background:

• Large deformation diffeomorphic metric mapping (LDDMM) is crucial for analyzing anatomical changes.
• Existing LDDMM methods can struggle with preserving sharp boundaries and discontinuities.
• Robust regularizers are needed to improve the accuracy and stability of registration.

Purpose of the Study:

• To develop and evaluate a primal-dual convex optimization method for LDDMM.
• To incorporate robust regularizers (Huber, V-Huber, total generalized variation) into LDDMM.
• To assess the method's performance in preserving object boundary discontinuities.

Main Methods:

• Chambolle and Pock primal-dual algorithm for convex optimization.
• Diagonal preconditioning for guaranteed convergence to the global minimum.
• Implementation on Graphics Processing Units (GPUs) for computational efficiency.

Main Results:

• The proposed method successfully converges to diffeomorphic solutions across all tested robust regularizers.
• It demonstrates superior preservation of discontinuities at object boundaries compared to baseline methods.
• Robust regularizers achieved competitive registration performance, comparable to standard LDDMM.

Conclusions:

• The primal-dual optimization framework with robust regularizers offers an effective approach for LDDMM.
• GPU acceleration enables efficient computation and evaluation on large datasets.
• This method enhances the accuracy of anatomical registration, particularly for structures with sharp boundaries.