Abstract : We present the principle, a possible implementation and performance estimates of a novel geometrical concept for a high resolution positron emission tomograph. The concept, which can for example be implemented in a brain PET device, promisses to lead to an essentially parallax free 3D image reconstruction with excellent spatial resolution and constrast, uniform over the complete field of view. The key components are matrices of long axially oriented scintillator crystals which are read out at both extremities by segmented Hybrid Photon Detectors. We discuss the relevant design considerations for a 3D axial PET camera module, motivate parameter and material choices, and estimate its performance in terms of spatial and energy resolution. We support these estimates by Monte Carlo simulations and in some cases by first experimental results. From the performance of a camera module, we extrapolate to the reconstruction resolution of a 3D axial PET scanner in a semi-analytical way and compare it to an existing state-of-the art brain PET device. We finally describe a dedicated data acquisition system, capable to fully exploit the advantages of the proposed concept. We conclude that the proposed 3D Axial concept and the discussed implementation is a competitive approach for high resolution brain PET. Excellent energy resolution and Compton enhanced sensitivity are expected to lead to high quality reconstruction and reduced scanning times.