Phase 1 of the SwissFEL Injector Test Facility consists of a 2.6-cell S-band RF gun, a spectrometer, and a series of transverse beam diagnostic systems such as YAG screens, slit and pepper-pot masks. Its primary purpose is the demonstration of a high-brightness electron beam meeting the specifications of the SwissFEL main linac. Phase space characterization at beam energies up to 7MeV, where space charge still dominates, is performed with YAG screens in combination with slit- and pinhole (pepper-pot) masks. Advanced image analysis is used to mitigate artefacts due to background, pixel readout noise, or dark current. We present our data analysis procedure for the slit scan method, with particular emphasis on image processing and its effect on the reconstructed emittance. Pepper-pot measurements using an independent analysis framework are used to cross-check the slit scan results.