1. An object information acquiring apparatus, comprising: a receiver that receives acoustic waves propagating through an object at a plurality of measurement positions; and a processor that acquires projection image data obtained by projecting on a two-dimensional flat surface a distribution of property information relating to a measurement target within the object, wherein the processor acquires intensity-dependent three-dimensional image data within the object and non-intensity-dependent three-dimensional image data within the object, based on the acoustic waves, determines voxel coordinates projected onto the two-dimensional flat surface, based on the intensity-dependent three-dimensional image data, and acquires the projection image data, based on values of the non-intensity-dependent three-dimensional image data corresponding to the voxel coordinates.