A unified FEM-based framework for medical image registration and segmentation

Medical image registration and segmentation are challenging because, medical images are generally corrupted by noise, image artifacts and the various anatomical regions of interest in medical images often do not have distinct sharp boundaries. However, these anatomical regions frequently exhibit consistent shape and topological characteristics which is an advantage when compared to natural images. In our proposed work, we take into account the above mentioned aspects and devise automatic registration and segmentation methods using the popular energy minimization framework, with an application to medical images. In contrast to the widely used level set based segmentation approach, we follow the template-based segmentation approach, which is more suitable for medical images as it can easily handle multi-region segmentation and also has the desirable property of preserving the known topology of the anatomical structures. However, unlike the traditional template-based segmentation and registration methods that use uniform meshes along with the finite difference method (FDM) to solve the partial differential equations (PDEs) that arise in these methods, we use the finite element method (FEM) and solve the PDEs on a non-uniform mesh to obtain solutions whose accuracy is well adapted to the salient features in the image domain. In this work, we present a unified FEM-based registration and segmentation framework where the goal is to estimate a deformation field following the minimization of an energy that consists of a common diffusion-based regularization term and data term that depends on the appropriate segmentation or registration objective. Further, we extend this framework through the incorporation of an additional shape prior based regularization term that is learned from training data. Lastly, we propose a novel variational formulation for discrete deformable registration and show that interestingly it can be cast into our unified FEM-based registration and segmentation framework. We validated our proposed unified FEM-based segmentation and registration framework on real medical images including some of the popular benchmark datasets. We present a thorough evaluation of the various registration and segmentation algorithms developed in our work by comparing their performance with the other established methods in image registration and segmentation.