Background based Gaussian mixture model lesion segmentation in PET

Purpose: Quantitative ¹⁸F-fluorodeoxyglucose positron emission tomography is limited by the uncertainty in lesion delineation due to poor SNR, low resolution, and partial volume effects, subsequently impacting oncological assessment, treatment planning, and follow-up. The present work develops and validates a segmentation algorithm based on statistical clustering. The introduction of constraints based on background features and contiguity priors is expected to improve robustness vs clinical image characteristics such as lesion dimension, noise, and contrast level. Methods: An eight-class Gaussian mixture model (GMM) clustering algorithm was modified by constraining the mean and variance parameters of four background classes according to the previous analysis of a lesion-free background volume of interest (background modeling). Hence, expectation maximization operated only on the four classes dedicated to lesion detection. To favor the segmentation of connected objects, a further variant was introduced by inserting priors relevant to the classification of neighbors. The algorithm was applied to simulated datasets and acquired phantom data. Feasibility and robustness toward initialization were assessed on a clinical dataset manually contoured by two expert clinicians. Comparisons were performed with respect to a standard eight-class GMM algorithm and to four different state-of-the-art methods in terms of volume error (VE), Dice index, classification error (CE), and Hausdorff distance (HD). Results: The proposed GMM segmentation with background modeling outperformed standard GMM and all the other tested methods. Medians of accuracy indexes were VE <3%, Dice >0.88, CE <0.25, and HD <1.2 in simulations; VE <23%, Dice >0.74, CE <0.43, and HD <1.77 in phantom data. Robustness toward image statistic changes (±15%) was shown by the low index changes: <26% for VE, <17% for Dice, and <15% for CE. Finally, robustness toward the user-dependent volume initialization was demonstrated. The inclusion of the spatial prior improved segmentation accuracy only for lesions surrounded by heterogeneous background: in the relevant simulation subset, the median VE significantly decreased from 13% to 7%. Results on clinical data were found in accordance with simulations, with absolute VE <7%, Dice >0.85, CE <0.30, and HD <0.81. Conclusions: The sole introduction of constraints based on background modeling outperformed standard GMM and the other tested algorithms. Insertion of a spatial prior improved the accuracy for realistic cases of objects in heterogeneous backgrounds. Moreover, robustness against initialization supports the applicability in a clinical setting. In conclusion, application-driven constraints can generally improve the capabilities of GMM and statistical clustering algorithms.