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Purpose: Accurate tumor delineation in positron emission tomography (PET) images is crucial in oncology. Although recent methods achieved good results, there is still room for improvement regarding tumors with complex shapes, low signal-to-noise ratio, and high levels of uptake heterogeneity., Methods: The authors developed and evaluated an original clustering-based method called spatial positron emission quantification of tumor-Automatic Lp-norm estimation (SPEQTACLE), based on the fuzzy C-means (FCM) algorithm with a generalization exploiting a Hilbertian norm to more accurately account for the fuzzy and non-Gaussian distributions of PET images. An automatic and reproducible estimation scheme of the norm on an image-by-image basis was developed. Robustness was assessed by studying the consistency of results obtained on multiple acquisitions of the NEMA phantom on three different scanners with varying acquisition parameters. Accuracy was evaluated using classification errors (CEs) on simulated and clinical images. SPEQTACLE was compared to another FCM implementation, fuzzy local information C-means (FLICM) and fuzzy locally adaptive Bayesian (FLAB)., Results: SPEQTACLE demonstrated a level of robustness similar to FLAB (variability of 14% ± 9% vs 14% ± 7%, p = 0.15) and higher than FLICM (45% ± 18%, p < 0.0001), and improved accuracy with lower CE (14% ± 11%) over both FLICM (29% ± 29%) and FLAB (22% ± 20%) on simulated images. Improvement was significant for the more challenging cases with CE of 17% ± 11% for SPEQTACLE vs 28% ± 22% for FLAB (p = 0.009) and 40% ± 35% for FLICM (p < 0.0001). For the clinical cases, SPEQTACLE outperformed FLAB and FLICM (15% ± 6% vs 37% ± 14% and 30% ± 17%, p < 0.004)., Conclusions: SPEQTACLE benefitted from the fully automatic estimation of the norm on a case-by-case basis. This promising approach will be extended to multimodal images and multiclass estimation in future developments.