EigenU-Net: integrating eigenvalue decomposition of the Hessian into U-Net for 3D coronary artery segmentation

<i>Objective</i>. Coronary artery segmentation is critical in medical imaging for the diagnosis and treatment of cardiovascular disease. However, manual segmentation of the coronary arteries is time-consuming and requires a high level of training and expertise.<i>Approach</i>. Our model, EigenU-Net, presents a novel approach to coronary artery segmentation of cardiac computed tomography angiography (CCTA) images that seeks to directly embed the geometrical properties of tubular structures, i.e. arteries, into the model. To examine the local structure of objects in the image we have integrated a closed-form solution of the eigenvalues of the Hessian matrix of each voxel for input into an U-Net based architecture.<i>Main results</i>. We demonstrate the feasibility and potential of our approach on the public IMAGECAS dataset consisting of 1000 CCTAs. The best performing model at 87% centerline Dice was EigenU-Net with Gaussian pre-filtering of the images.<i>Significance</i>. We were able to directly integrate the calculation of eigenvalues into our model EigenU-Net, to capture more information about the structure of the coronary vessels. EigenU-Net was able to segment regions that were overlooked by other models.