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

Abstract

Level set segmentation has been successfully used in several image applications. However, they perform poorly when applied to severely corrupted images or when the object’s boundaries are blurred or occluded. Poor performance can be improved by introducing shape prior knowledge into the segmentation process by considering additional shape information from training examples. This can be achieved by adding a regularization term that penalizes shapes that differ from those learned from a training database. This regularizer must be invariant under translation, rotation and scaling transformations. Previous works have proposed coupling the curve evolution to a registration problem through an optimization procedure. This approach is slow and its results depend on how this optimization is implemented. An alternative approach introduced an intrinsic alignment, which normalizes each shape to be compared on a common coordinate system, avoiding the registration process. Nevertheless, the proposed intrinsic alignment considered only scaling and translation but not rotation, which is critical in several image applications. In this paper we present a new method to incorporate shape prior knowledge based on the intrinsic alignment approach, but extending it for scaling, translation and rotation invariance. Our approach uses a regularization term based on the eigenvalues and eigenvectors of the covariance matrix of each training shape, and this eigendecomposition dependency leads to a new set of evolution equations. We tested our regularizer, combined with Chan–Vese, in 2D and 3D synthetic and medical images, demonstrating the effectiveness of using shape priors with intrinsic scaling, translation and rotation alignment in different segmentation problems.