1. An information processing device comprising: a detector to detect a pointed position pointed by a pointing object on a projection plane onto which light including information of an input image is projected; and a controller to, when the pointed position belongs to a first region on the projection plane, perform control for executing first processing corresponding to an operation on the first region based on the pointed position, the first region indicating a region including at least a part of a projection image formed by projecting the light including the information of the input image onto the projection plane, whereas when the pointed position belongs to a second region on the projection plane, perform control for executing second processing corresponding to an operation on the second region based on the pointed position, the second region indicating a region including a smaller part of the projection image than the part of the projection image included in the first region.