| Resumen | Keywords: Medical Image Registration, Symmetry, Deep-Learning, Neurodegenerative Diseases
Non-rigid registration is a fundamental task in image processing and computer vision, involving the alignment of images that may undergo complex non-linear deformations. Non-rigid registration enables the comparison of anatomical structures, facilitates longitudinal studies, and supports surgical planning by allowing accurate alignment of images with significant deformations. However, ensuring that these transformations are smooth, physically plausible, and consistent is a major challenge.
A key challenge in non-rigid registration is the design of regularizers that constrain the transformations to avoid unrealistic or implausible deformations. One important aspect of regularization in this context is symmetry. Symmetry regularizers ensure that the transformation from one image to another is consistent when the process is reversed. Symmetry is especially important in applications like bi-directional image registration (e.g., in longitudinal medical studies, where changes in the anatomy over time must be tracked accurately in both directions), biomechanical modeling, and 3D reconstruction, where the accuracy and consistency of transformations are crucial. Without symmetry, the registration process may introduce biases or artifacts, particularly when dealing with data that involves dynamic or temporal changes. For instance, in medical imaging, ensuring that both forward and backward transformations between baseline and follow-up scans are consistent can lead to more reliable clinical interpretations.
Several approaches have been proposed to incorporate symmetry into non-rigid registration models, mainly in the Large Deformation Diffeomorphic Metric Mapping (LDDMM) paradigm and deep-learning based analogies such as VoxelMorph:
1) Direct symmetry regularization is imposed by adding energy based regularizers of symmetry to the loss function.
2) Indirect symmetry regularization is imposed by constraining the problem to the deformation state equation, which is derived from the inverse consistency composition constraint.
The primary objective of this research is to study and develop symmetry regularizers for nearly diffeomorphic registration methods and conduct a fair comparison of the performance of the different approaches in terms of accuracy, plausibility, consistency and computational complexity. The methods will be tested in datasets related to neurodegenerative disease applications, such as Alzheimer’s disease or Parkinson’s disease. |
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