4D statistical shape modeling of the left ventricle in cardiac MR images

Statistical shape models have shown improved reliability and consistency in cardiac image segmentation. They incorporate a sufficient amount of a priori knowledge from the training datasets and solve some major problems such as noise and image artifacts or partial volume effect. In this paper, we construct a 4D statistical model of the left ventricle using human cardiac short-axis MR images. Kernel PCA is utilized to explore the nonlinear variation of a population. The distribution of the landmarks is divided into the inter- and intra-subject subspaces. We compare the result of Kernel PCA with linear PCA and ICA for each of these subspaces. The initial atlas in natural coordinate system is built for the end-diastolic frame. The landmarks extracted from it are propagated to all frames of all datasets. We apply the 4D KPCA-based ASM for segmentation of all phases of a cardiac cycle and compare it with the conventional ASM. The proposed statistical model is evaluated by calculating the compactness capacity, specificity and generalization ability measures. We investigate the behavior of the nonlinear model for different values of the kernel parameter. The results show that the model built by KPCA is less compact than PCA but more compact than ICA. Although for a constant number of modes the reconstruction error is a little higher for the KPCA-based statistical model, it produces a statistical model with substantially better specificity than PCA- and ICA-based models. Quantitative analysis of the results demonstrates that our method improves the segmentation accuracy.