# Abstract:

This work presents new application of the random field theory in medical imaging. Results from both integral geometry and random field theory can be used to detect locations with significantly increased radiotracer uptake in images from positron emission tomography (PET). The assumptions needed to use these results are verified on a set of real and simulated phantom images. The proposed method of detecting activation (locations with increased radiotracer concentration) is used to quantify the quality of simulated PET images. Dependence of the quality on the injection dose (amount of applied radiotracer) and patient's body parameters is estimated. It is used to derive curves of constant quality determining the injection dose needed to achieve desired quality of the resulting images. The curves are compared with the formula currently used in medical practice.

# Keywords:

random field theory, Euler characteristic, PET imaging, PET image quality

60G35, 60G60

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