1. An information processing device comprising: a detector configured to detect a pointed-to position, pointed to by a pointing object, on a projection object onto which light including information of an input image is projected; and processing circuitry configured to when the pointed-to position belongs to a first region, perform control for executing first processing corresponding to an operation on the first region based on the pointed-to position, the first region being a part of a projection region of the projection object, the projection region being a region onto which the light including the information of the input image is projected, and when the pointed-to position belongs to a second region, perform control for executing second processing corresponding to an operation on the second region based on the pointed-to position, the second region being in the projection region and being less bright than the first region, wherein the first processing comprises processing for displaying a projection image formed by projecting, onto the projection object, light including information of an image that is different from the input image, and the second processing comprises processing for changing a shape of the projection image formed by projecting, onto the projection object, the light including the information of the input image.