Delineation of tumours in Positron Emission Tomography (PET) plays a crucial role in accurate diagnosis and radiotherapy treatment planning. In this context, it is of outmost importance to devise efficient and operator-independent segmentation algorithms capable of reconstructing the tumour three-dimensional (3D) shape. In previous work, we proposed a system for 3D tumour delineation on PET data (expressed in terms of Standardized Uptake Value - SUV), based on a two-step approach. Step 1 identified the slice enclosing the maximum SUV and generated a rough contour surrounding it. Such contour was then used to initialize step 2, where the 3D shape of the tumour was obtained by separately segmenting 2D PET slices, leveraging the slice-by-slice marching approach. Additionally, we combined active contours and machine learning components to improve performance. Despite its success, the slice marching approach poses unnecessary limitations that are naturally removed by performing the segmentation directly in 3D. In this paper, we migrate our system into 3D. In particular, the segmentation in step 2 is now performed by evolving an active surface directly in the 3D space. The key points of such an advancement are that it performs the shape reconstruction on the whole stack of slices simultaneously, naturally leveraging cross-slice information that could not be exploited before. Additionally, it does not require any specific stopping condition, as the active surface naturally reaches a stable topology once convergence is achieved.Performance of this fully 3D approach is evaluated on the same dataset discussed in our previous work, which comprises fifty PET scans of lung, head and neck, and brain tumours. The results have confirmed that a benefit is indeed achieved in practice for all investigated anatomical districts, both quantitatively, through a set of commonly used quality indicators (dice similarity coefficient >87.66%, Hausdorff distance < 1.48 voxel and Mahalanobis distance < 0.82 voxel), and qualitatively in terms of Likert score (>3 in 54% of the tumours).
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