Level set segmentation with shape prior knowledge using intrinsic rotation, translation and scaling alignment

Level set-based algorithms have been extensively used for medical image segmentation. Despite their relative success, standard level set segmentations tend to fail when images are severely corrupted or in poorly defined regions. This problem has been tackled incorporating shape prior knowledge, i.e. restricting the evolving curve to a distribution of shapes pre-defined during a training process. Such shape restriction needs to incorporate invariance to translation, rotations and scaling. The common approach for this is to solve a registration problem during the curve evolution, i.e. finding optimal registration parameters. This procedure is slow and produces variable results depending on the order in which the registration parameters were optimized. To overcome this issue Cremers et al. (2006) proposed an intrinsic alignment formulation, which is a normalized coordinate system for each shape, thus avoiding the optimization step to account for the registration. Nevertheless, their proposed solution considered only scaling and translation, but not rotations which are critical for medical imaging applications. We added rotations to this intrinsic alignment, using eigenvalues and eigenvector matrices of the covariance matrix of each shape, and we incorporated them into the evolution equation, allowing us to use shape priors in complex segmentation problems. We tested our algorithm combined with a Chan-Vese functional in synthetic images and in 2D right ventricle MRI.