Improving Instance Optimization in Deformable Image Registration with Gradient Projection

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Abstract
Deformable image registration is inherently a multi-objective optimization (MOO) problem, requiring a delicate balance between image similarity and deformation regularity. These conflicting objectives often lead to poor optimization outcomes, such as being trapped in unsatisfactory local minima or experiencing slow convergence. Deep learning methods have recently gained popularity in this domain due to their efficiency in processing large datasets and achieving high accuracy. However, they often underperform during test time compared to traditional optimization techniques, which further explore iterative, instance-specific gradient-based optimization. This performance gap is more pronounced when a distribution shift between training and test data exists. To address this issue, we focus on the instance optimization (IO) paradigm, which involves additional optimization for test-time instances based on a pre-trained model. IO effectively combines the generalization capabilities of deep learning with the fine-tuning advantages of instance-specific optimization. Within this framework, we emphasize the use of gradient projection to mitigate conflicting updates in MOO. This technique projects conflicting gradients into a common space, better aligning the dual objectives and enhancing optimization stability. We validate our method using a state-of-the-art foundation model on the 3D Brain inter-subject registration task (LUMIR) from the Learn2Reg 2024 Challenge. Our results show significant improvements over standard gradient descent, leading to more accurate and reliable registration results.

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