1. An image input-and-output apparatus, comprising: an imaging unit that takes an image of an object to be photographed to obtain imaging data; a three-dimensional-shape detection unit that projects pattern light to the object, takes an image of the object by the imaging unit, and detects the three-dimensional shape of the object; a recognizing unit that recognizes object information from the imaging data obtained by the imaging unit, the object information is written information on the object detected by the three-dimensional-shape detection unit; and a light source that emits light; a spatial modulation unit that performs spatial modulation of light emitted from the light source and outputs image signal light; a reference-information acquisition unit that obtains reference information of the object to be photographed by the imaging unit; a comparison-result-information acquisition unit that compares the reference information obtained by the reference-information acquisition unit and the written information recognized by the recognizing unit, and obtains the result of the comparison between the reference information and the written information as comparison result information; a projection optical system that projects the image signal light output from the spatial modulation unit in a projection direction; and a projecting unit that projects related information related to the object information recognized by the recognizing unit, the projecting unit comprising: a reference-information projecting unit that outputs image signal light based on the reference information obtained by the reference-information acquisition unit, through the spatial modulation unit, and projects the output image signal light onto the object or onto an image-projectable plane in the projection direction through the projection optical system, and a comparison-result-information projecting unit that outputs image signal light based on the comparison result information obtained by the comparison-result-information acquisition unit, through the spatial modulation unit and projects the output image signal light onto the object or onto an image-projectable plane in the projection direction through the projection optical system.