Energetic neutral atom (ENA) images are computed from an empirical solar wind proton model and recent models of the Martian exosphere. The proton model describes the proton bulk velocity in the interaction region and the neutral model the profiles of H, H2 and O (hot) and O (thermal). We assume a Maxwellian proton velocity distribution. The ENA production model is analytical; thus an ENA image can be constructed for any vantage point by line of sight integration, and we present examples of such images. In this work we study the influence of different parameters in the input models on the generated images and examine the relative importance of the different parameters on the global ENA production rate as well as on image morphology for particular vantage points. All together our parameter set includes 14 variables for solar wind conditions, flow geometry, and the exosphere model. Changing the parameters also makes it possible to mimic various features of the solar wind-Mars interaction, such as some of the effects caused by the recently observed magnetic anomalies. It is found that the exobase temperature of atomic hydrogen is the parameter that affects the ENA production and images most. We also investigate the backscattering of ENAs that precipitate on the Martian atmosphere. It is found to be an important effect for views of Mars in the antisunward direction. The outflux of ENAs from the near Mars region is studied, and two maxima are found. One at an angle of approximately 115¿ to the Mars-Sun line corresponding to ENAs produced downstream of the bow shock and one at approximately 150¿ corresponding to ENAs produced upstream of the bow shock in the solar wind.