Unsupervised Spectral Clustering for Segmentation of Dynamic PET Images

Segmentation of dynamic PET images is needed to extract the time activity curves (TAC) of regions of interest (ROI). These TAC can be used in compartmental models for in vivo quantification of the radiotracer target. While unsupervised clustering methods have been proposed to segment PET sequences, they are often sensitive to initial conditions or favour convex shaped clusters. Kinetic spectral clustering (KSC) of dynamic PET images was recently proposed to handle arbitrary shaped clusters in the space in which they are identified. While improved results were obtained with KSC compared to three state of art methods, its use for clinical applications is still hindered by the manual setting of several parameters. In this paper, we develop an extension of KSC to automatically estimate the parameters involved in the method and to make it deterministic. First, a global search procedure is used to locate the optimal cluster centroids from the projected data. Then an unsupervised clustering criterion is tailored and used in a global optimization scheme to automatically estimate the scale parameter and the weighting factors involved in the proposed Automatic and Deterministic Kinetic Spectral Clustering (AD-KSC). We validate the method using GATE Monte Carlo simulations of dynamic numerical phantoms and present results on real dynamic images. The deterministic results obtained with AD-KSC agree well with those obtained with optimal manual parameterization of KSC, and improve the ROI identification compared to three other clustering methods. The proposed approach could have significant impact for quantification of dynamic PET images in molecular imaging studies.