1. A projection system comprising: a plurality of projection units configured to collectively project an image as a whole on a projection area; a generation unit configured to generate corrected images including respective correction points which are used for detecting distortions of projection images, which are projected by the respective projection units, based on designated relationships between the projection images of the projection units and the projection area; and a compensation coefficient calculation unit configured to calculate compensation coefficients, which correspond to the projection units, based on one or more correction captured images that are acquired by capturing the corrected images projected on the projection area, wherein the generation unit is configured to further generate margin parts in the corrected images, which correspond to the projection units that project the projection images in outer areas of the projection area, in a manner so that parts defining the correction points in the corrected images are projected within the projection area while the parts defining correction points in the corrected images corresponding to the projection units that are next to each other are overlapped.