Building a 4D statistical model of the left ventricle from cardiac MR images using Kernel PCA

In this paper, we construct a 4D statistical model of the left ventricle using human cardiac short-axis MR images. 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. Kernel PCA is utilized to explore the nonlinear variation of landmarks. The distribution of the landmarks is divided into the inter- and intra-subject subspaces. The results of kernel PCA are compared to linear PCA for each of these subspaces 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 PCA is more compact. For a constant number of modes the reconstruction error is approximately equal for both models. KPCA produces a statistical model with substantially better specificity.