Graph-based Mumford-Shah segmentation of dynamic PET with application to input function estimation

A graph-theoretic three-dimensional (3-D) segmentation algorithm based on Mumford-Shah energy minimization is applied to the segmentation of brain ¹⁸F-fluoro-deoxyglucose (FDG) dynamic positron emission tomography data for the automated extraction of tissues with distinct time activity curves (TACs), and, in particular, extraction of the internal carotid arteries and venous sinuses for the noninvasive estimation of the input arterial TAC. Preprocessing by principal component analysis (PCA) and a Mahalanobis distance metric provide segmentation based on distinct TAC shape rather than simply activity levels. Evaluations on simulation and clinical FDG brain positron emission tomography (PET) studies demonstrate that differing tissue types can be accurately demarcated with superior performance to k-means clustering approaches, and, in particular, the internal carotids and venous sinuses can be robustly segmented in clinical brain dynamic PET datasets, allowing for the fully automatic noninvasive estimation of the arterial input curve.