1. An image processing apparatus comprising: an image combining portion that generates combined images by combining, for each depth position in a specimen, a plurality of fluorescence images captured with differing exposure levels at each depth position, which are fluorescence images generated by capturing fluorescence coming from the specimen at different depth positions in the specimen; a smoothed-luminance calculating portion that calculates a representative luminance from the individual combined images generated by the image combining portion and that calculates a smoothed luminance for the individual combined images by smoothing the calculated representative luminance in the depth direction; a luminance correcting portion that generates corrected images by correcting the luminance of the individual combined images on the basis of differences between the smoothed luminance and the representative luminance calculated by the smoothed-luminance calculating portion; and a three-dimensional image generating portion that generates a three-dimensional image of the specimen from the plurality of corrected images generated by the luminance correcting portion.