Combined fuzzy logic and random walker algorithm for PET image tumor delineation

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The random walk (RW) technique serves as a powerful tool for PET tumor delineation, which typically involves significant noise and/or blurring. One challenging step is hard decision-making in pixel labeling. Fuzzy logic techniques have achieved increasing application in edge detection. We aimed to combine the advantages of fuzzy edge detection with the RW technique to improve PET tumor delineation.


A fuzzy inference system was designed for tumor edge detection from RW probabilities. Three clinical PET/computed tomography datasets containing 12 liver, 13 lung, and 18 abdomen tumors were analyzed, with manual expert tumor contouring as ground truth. The standard RW and proposed combined method were compared quantitatively using the dice similarity coefficient, the Hausdorff distance, and the mean standard uptake value.


The dice similarity coefficient of the proposed method versus standard RW showed significant mean improvements of 21.0±7.2, 12.3±5.8, and 18.4%±6.1% for liver, lung, and abdominal tumors, respectively, whereas the mean improvements in the Hausdorff distance were 3.6±1.4, 1.3±0.4, 1.8±0.8 mm, and the mean improvements in SUVmean error were 15.5±6.3, 11.7±8.6, and 14.1±6.8% (all P’s<0.001). For all tumor sizes, the proposed method outperformed the RW algorithm. Furthermore, tumor edge analysis demonstrated further enhancement of the performance of the algorithm, relative to the RW method, with decreasing edge gradients.


The proposed technique improves PET lesion delineation at different tumor sites. It depicts greater effectiveness in tumors with smaller size and/or low edge gradients, wherein most PET segmentation algorithms encounter serious challenges. Favorable execution time and accurate performance of the algorithm make it a great tool for clinical applications.

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