We investigate the usage of a schlieren imaging setup to measure the geometrical dimensions of a plasma channel in atomic vapor. Near resonant probe light is used to image the plasma channel in the tenuous vapor and machine learning techniques are tested for extracting quantitative information from the images. We build a database of simulated signals with a range of plasma parameters for training Deep Neural Networks, and demonstrate that they can estimate, from the schlieren images, reliably and with high accuracy the location, the radius and the maximum ionization fraction of the plasma channel as well as the width of the transition region between the core of the plasma channel and the unionized vapor. We test several different neural network architectures with supervised learning and show that the parameter estimations supplied by the networks are resilient with respect to slight changes of the experimental parameters that may occur in the course of a measurement.