  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 ($\sim 1 \%$
at 3 keV and $\sim 6 \%$ at 6 keV) and naturally mitigates a subtle effect
appearing in polarization measurements of bright extended sources known as
"polarization leakage".
