Graph cut-based method for segmenting the left ventricle from MRI or echocardiographic images

In this paper, we present a fast and interactive graph cut method for 3D segmentation of the endocardial wall of the left ventricle (LV) adapted to work on two of the most widely used modalities: magnetic resonance imaging (MRI) and echocardiography. Our method accounts for the fundamentally different nature of both modalities: 3D echocardiographic images have a low contrast, a poor signal-to-noise ratio and frequent signal drop, while MR images are more detailed but also cluttered and contain highly anisotropic voxels. The main characteristic of our method is to work in a 3D Bezier coordinate system instead of the original Euclidean space. This comes with several advantages, including an implicit shape prior and a result guarantied not to have any holes in it. The proposed method is made of 4 steps. First, a 3D sampling of the LV cavity is made based on a Bezier coordinate system. This allows to warp the input 3D image to a Bezier space in which a plane corresponds to an anatomically plausible 3D Euclidean bullet shape. Second, a 3D graph is built and an energy term (which is based on the image gradient and a 3D probability map) is assigned to each edge of the graph, some of which being given an infinite energy to ensure the resulting 3D structure passes through key anatomical points. Third, a max-flow min-cut procedure is executed on the energy graph to delineate the endocardial surface. And fourth, the resulting surface is projected back to the Euclidean space where a post-processing convex hull algorithm is applied on every short axis slice to remove local concavities. Results obtained on two datasets reveal that our method takes between 2 and 5s to segment a 3D volume, it has better results overall than most state-of-the-art methods on the CETUS echocardiographic dataset and is statistically as good as a human operator on MR images.