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Purpose Image texture is increasingly used to discriminate tissues and lesions in PET/CT. For quantification or in computer-aided diagnosis, textural feature analysis must produce robust and comparable values. Because statistical feature values depend on image count statistics, we investigated in depth the stability of Haralick features values as functions of acquisition duration, and for common image resolutions and reconstructions. Methods A homogeneous cylindrical phantom containing 9.6 kBq/ml Ge-68 was repeatedly imaged on a Siemens Biograph mCT, with acquisition durations ranging from three seconds to three hours. Images with 1.5, 2, and 4 mm isometrically spaced voxels were reconstructed with filtered back-projection (FBP), ordered subset expectation maximization (OSEM), and the Siemens TrueX algorithm. We analysed Haralick features derived from differently quantized (3 to 8-bit) grey level co-occurrence matrices (GLCMs) as functions of exposure E, which we defined as the product of activity concentration in a volume of interest (VOI) and acquisition duration. The VOI was a 50 mm wide cube at the centre of the phantom. Feature stability was defined for df/dE → 0. Results The most stable feature values occurred in low resolution FBPs, whereas some feature values from 1.5 mm TrueX reconstructions ranged over two orders of magnitude. Within the same reconstructions, most feature value-exposure curves reached stable plateaus at similar exposures, regardless of GLCM quantization. With 8-bit GLCM, median time to stability was 16 s and 22 s for FBPs, 18 s and 125 s for OSEM, and 23 s, 45 s, and 76 s for PSF reconstructions, with longer durations for higher resolutions. Stable exposures coincided in OSEM and TrueX reconstructions with image noise distributions converging to a Gaussian. In FBP, the occurrence of stable values coincided the disappearance of negatives image values in the VOI. Conclusions Haralick feature values depend strongly on exposure, but invariance exists within defined domains of exposure. Here, we present an easily replicable procedure to identify said stable exposure domains, where image noise does not substantially add to textural feature values. Only by imaging at predetermined feature-invariant exposure levels and by adjusting exposure to expected activity concentrations, can textural features have a quantitative use in PET/CT. The necessary exposure levels are attainable by modern PET/CT systems in clinical routine.