Small satellites have limited payload and their attitudes are sometimes difficult to determine from the limited onboard sensors alone. Wrong attitudes lead to inaccurate map projections and measurements that require post-processing correction. In this study, we propose an automated and robust scheme that derives the satellite attitude from its observation images and known satellite position by matching land features from an observed image and from well-registered base-map images. The scheme combines computer vision algorithms (i.e., feature detection, and robust optimization) and geometrical constraints of the satellite observation. Applying the proposed method to UNIFORM-1 observations, which is a 50 kg class small satellite, satellite attitudes were determined with an accuracy of 0.02 degrees, comparable to that of star trackers, if the satellite position is accurately determined. Map-projected images can be generated based on the accurate attitudes. Errors in the satellite position can add systematic errors to derived attitudes. The proposed scheme focuses on determining satellite attitude with feature detection algorithms applying to raw satellite images, unlike image registration studies which register already map-projected images. By delivering accurate attitude determination and map projection, the proposed method can improve the image geometries of small satellites, and thus reveal fine-scale information about the Earth.