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Textural analysis might give new insights into the quantitative characterization of metabolically active tumors. More than thirty textural parameters have been investigated in former F18-FDG studies already. The purpose of the paper is to declare basic requirements as a selection strategy to identify the most appropriate heterogeneity parameters to measure textural features. Our predefined requirements were: a reliable heterogeneity parameter has to be volume independent, reproducible, and suitable for expressing quantitatively the degree of heterogeneity. Based on this criteria, we compared various suggested measures of homogeneity. A homogeneous cylindrical phantom was measured on three different PET/CT scanners using the commonly used protocol. In addition, a custom-made inhomogeneous tumor insert placed into the NEMA image quality phantom was imaged with a set of acquisition times and several different reconstruction protocols. PET data of 65 patients with proven lung lesions were retrospectively analyzed as well. Four heterogeneity parameters out of 27 were found as the most attractive ones to characterize the textural properties of metabolically active tumors in FDG PET images. These four parameters included Entropy, Contrast, Correlation, and Coefficient of Variation. These parameters were independent of delineated tumor volume (bigger than 25-30 ml), provided reproducible values (relative standard deviation< 10%), and showed high sensitivity to changes in heterogeneity. Phantom measurements are a viable way to test the reliability of heterogeneity parameters that would be of interest to nuclear imaging clinicians.