Purpose:In clinical practice, positron emission tomography (PET) images are mostly analysed visually, but the sensitivity and specificity of this approach greatly depends on the observer's experience. Quantitative analysis of PET images would alleviate this problem by helping define an objective limit between normal and pathological findings. We present an anomaly detection framework for the individual analysis of PET images. Approach: We created subject-specific abnormality maps that summarise the pathology's topographical distribution in the brain by comparing the subject's PET image to a model of healthy PET appearance that is specific to the subject under investigation. This model was generated from demographically and morphologically-matched PET scans from a control dataset.Results: We generated abnormality maps for healthy controls, patients at different stages of Alzheimer's disease and with different frontotemporal dementia syndromes. We showed that no anomalies were detected for the healthy controls and that the anomalies detected from the patients with dementia coincided with the regions where abnormal uptake was expected. We also validated the proposed framework using the abnormality maps as inputs of a classifier and obtained higher classification accuracies than when using the PET images themselves as inputs. Conclusions: The proposed method was able to automatically locate and characterise the areas characteristic of dementia from PET images. The abnormality maps are expected to i) help clinicians in their diagnosis by highlighting, in a data-driven fashion, the pathological areas, and ii) improve the interpretability of subsequent analyses, such as computer-aided diagnosis or spatio-temporal modelling.