In this study, we propose and evaluate new methods for automatic extraction of the brain surface and the mid-sagittal plane from functional positron emission tomography (PET) images. Designing methods for these segmentation tasks is challenging because the spatial distribution of intensity values in a PET image depends on the applied radiopharmaceutical and the contrast to noise ratio in a PET image is typically low. We extracted the brain surface with a deformable model which is based on a global optimization algorithm. The global optimization allows reliable automation of the extraction task. Based on the extracted brain surface, the mid-sagittal plane was determined. The method was tested with the image of the Hoffman brain phantom (FDG) and the images from the brain studies with the FDG (17 images) and the C11-Raclopride tracers (4 images). In addition to the brain surfaces, we applied the deformable model for extraction of the coarse cortical structure based on the tracer uptake from FDG-PET brain images. The proposed segmentation methods provide a promising direction for automatic processing and analysis of PET brain images.