Deformable Image Registration Using Functions of Bounded Deformation.

Area of Science:

• Computer Vision
• Medical Image Processing
• Computational Mechanics

Background:

• Deformable image registration is crucial for comparing images, but existing models assume smooth displacement fields.
• Discontinuities in displacement fields are common in medical images due to noise or pathologies.
• The space of functions of bounded deformation (BD) offers a framework for discontinuous fields.

Purpose of the Study:

• To propose a novel deformable registration model, the BD model, capable of handling discontinuous displacement fields.
• To establish the mathematical foundation and prove the existence of solutions for the BD model.
• To evaluate the performance of the BD model against established and state-of-the-art registration methods.

Main Methods:

• Formulating a variational model based on the space of functions of bounded deformation (BD).
• Proving the existence of solutions for the proposed BD model.
• Conducting numerical experiments on 2D and 3D datasets, comparing against Demons, diffeomorphic Demons, and vectorial total variation models.

Main Results:

• The BD model successfully handles discontinuous displacement fields.
• On 2D images, the BD model outperformed classical Demons, log-domain diffeomorphic Demons, and vectorial total variation models.
• On 3D databases, the BD model achieved competitive target registration error compared to over ten other models.

Conclusions:

• The BD model provides a robust framework for deformable image registration, particularly when displacement fields are discontinuous.
• The proposed model offers a competitive alternative to existing methods, showing significant improvements in accuracy and robustness.
• This work extends the applicability of deformable registration to challenging medical imaging scenarios.