Joint Shape Reconstruction and Registration via a Shared Hybrid Diffeomorphic Flow

Area of Science:

• Medical Imaging
• Computational Geometry
• Machine Learning

Background:

• Deep implicit functions (DIFs) represent shapes but struggle with inter-shape correspondence for medical image registration.
• Existing deformation field methods decouple template and deformation field optimization, leading to suboptimal results.

Purpose of the Study:

• To propose a novel framework, Shared Hybrid Diffeomorphic Flow (SHDF), for unified optimization of shape representation and correspondence.
• To enhance the accuracy of shape representation and medical image registration.

Main Methods:

• Formulated signed distance functions (SDFs) as 1D integrals for seamless integration with ordinary differential equation (ODE) based deformation field learning.
• Employed a recurrent learning strategy to solve initial value problems for shape representations and deformations using the same ODE.
• Introduced global smoothness regularization to mitigate local optima from limited external data.

Main Results:

• The proposed SHDF framework achieves shared optimization for deformation and template fields.
• Experiments on medical datasets demonstrate superior performance of SHDF compared to state-of-the-art methods in shape representation and registration.

Conclusions:

• SHDF offers a unified approach to learning implicit shape representations and establishing correspondences.
• The method significantly improves accuracy in medical image registration tasks.