Is your deformable image registration truly diffeomorphic? This research challenges the conventional use of finite difference approximations in assessing the diffeomorphism of spatial transformations, proposing a more accurate criterion for digital images. Spatial transformations are important in deformable image registration. This paper investigates the geometric meaning of different finite difference approximations of the Jacobian determinant. It demonstrates that using a central difference alone is insufficient to determine diffeomorphism for digital images. The authors propose a novel “digital diffeomorphism” criteria, requiring four unique finite difference approximations to be positive for 2D transformations and ten for 3D transformations. This method accurately detects non-diffeomorphic digital transformations, solving errors present in the central difference approximation. Access the source code on GitHub to explore this enhanced approach to deformable image registration, ensuring greater accuracy and reliability in your digital image analysis.
As a contribution to the International Journal of Computer Vision, this paper addresses a fundamental challenge in deformable image registration, a core area in computer vision. By proposing a more robust method for assessing diffeomorphism, the article advances the field's ability to produce accurate and reliable spatial transformations, aligning with the journal's focus on innovative computer vision techniques.