Deterministic spectral clustering for segmentation of dynamic PET images

Objectives Quantification of PET images usually requires the identification of regions of interest (ROI). Clustering methods can be used to identify functional regions where voxels have the same temporal behavior. Yet, they are usually either sensitive to initialization or favor convex-shaped clusters. To address these limitations, we propose a deterministic spectral clustering (DSC) that can handle arbitrary shaped clusters.

Methods In DSC, eigenvectors of a kernel matrix based on voxel time activity curves is used as a high-dimensional representation of the data. Then data are clustered in a lower dimensional space with global k-means (GKM) to avoid any random step in the method. We performed Gate Monte Carlo simulations of Gemini GXL PET 4D acquisitions. The Zubal brain phantom was used with TAC based on a 3-compartment model. 12 PET images were reconstructed with 2.2x2.2x2.8 mm3 voxels and 20 frames of 1 minute each, using fully 3D OSEM (5 iterations, 8 subsets). To assess the accuracy of ROI identification, we calculated Pratt’s figure of merit (FOM) and Adjusted Rand Index (AR). Cluster separation was evaluated using the unsupervised Normalized Minimum Distance (NMD) criterion. Results were compared to those obtained by a GKM approach [Likas et al 2003]. The variability of the results of spectral clustering with (DSC) and without (SC) deterministic step was studied over 100 replicated runs on the same image and compared with GKM and k-means (KM).

Results Compared to GKM, DSC increased the AR score by a factor of 1.61±0.82 and the FOM score by a factor of 2.04±1.04. NMD scores were also increased by a factor of 1.51±0.53 when using DSC, compared to GKM. The NMD scores for replicated runs were 0.28±0.00 with DSC, 0.24±0.06 with SC, 0.14±0.00 with GKM and 0.13±0.01 with KM.

Conclusions The deterministic property and accuracy improvements in ROI definition offered by DSC might have a significant impact for dynamic PET image segmentation