Accurate and robust tumor delineation in PET/CT images is crucial in oncology and radiotherapy and is still challenging for tumors with complex shapes, low signal-to-noise ratio and high uptake heterogeneity. We have developed a method called SPEQTACLE, based on a generalization of the Fuzzy C-Means (FCM) algorithm using a Hilbertian norm, estimated for each modality through an automatic scheme on each image. Robustness of the algorithm was assessed on multiple phantom acquisitions. Accuracy was evaluated on simulated and clinical images. On PET images, SPEQTACLE demonstrated high performance with significant improvement over the state-of-the-art for the most complex cases. For PET/CT cases, SPEQTACLE provided results in high agreement with manual delineations, outperforming other FCM implementation.