1. An image processing apparatus comprising: an image combining portion that generates a plurality of combined images, each of the plurality of combined images corresponding to one of a plurality of different depth positions in a specimen, by combining, for each of the depth positions, a plurality of fluorescence images captured with different exposure levels at the depth position, the plurality of fluorescence images being generated by capturing fluorescence coming from the specimen at each of the different depth positions; a smoothed-luminance calculating portion that calculates a representative luminance for each of the plurality of combined images generated by the image combining portion and that calculates a smoothed luminance for each of the plurality of combined images by smoothing the calculated representative luminance along the depth direction; a luminance correcting portion that generates a corrected image for each of the depth positions by correcting a luminance of a corresponding one of the plurality of combined images based on 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 corrected images each of which is generated for a respective one of the depth positions by the luminance correcting portion.