We present our study on the reconstruction of photoelectron tracks in gas pixel detectors used for astrophysical X-ray polarimetry. Our work aims to maximize the performance of convolutional neural networks (CNNs) to predict the impact point of incoming X-rays from the image of the photoelectron track. A very high precision in the reconstruction of the impact point position is achieved thanks to the introduction of an artificial sharpening process of the images. We find that providing the CNN-predicted impact point as input to the state-of-the-art analytic analysis improves the modulation factor (~1% at 3 keV and ~6% at 6 keV) and naturally mitigates a subtle effect appearing in polarization measurements of bright extended sources known as “polarization leakage”.