1. A fluorescence observation apparatus comprising: a light source unit that radiates, onto an observation target site, illumination light in a wavelength band absorbed by a blood vessel, a first excitation light that includes the wavelength band of the illumination light and that excites an autofluorescent substance in the blood vessel to generate autofluorescence, and a second excitation light that excites fluorescent dye that distinguishably stains normal tissue or abnormal tissue, generating agent fluorescence, and that has a different wavelength band from the first excitation light; an image-acquisition unit that obtains images by respectively capturing reflected light obtained by radiating the illumination light, and autofluorescence and agent-fluorescence obtained by radiating the first and second excitation light onto the observation target site; and an image processing unit that extracts a blood-vessel image from a reflected-light image obtained by the image-acquisition unit, that obtains a reference image by applying interpolation to the area in an autofluorescence image that corresponds to the extracted blood-vessel image, and that corrects an agent-fluorescence image obtained by the image-acquisition unit based on the obtained reference image, wherein the image processing unit comprises a blood-vessel image-extraction unit that extracts a blood-vessel image based on brightness information of the reflected-light image obtained by the image-acquisition unit, a reference-image generating unit that generates a reference image by applying interpolation, using the brightness of the surrounding area, to the area corresponding to the blood-vessel image in an autofluorescence image obtained by the image-acquisition unit, and a fluorescence-image correcting unit that performs correction by dividing the brightness of the agent-fluorescence image obtained by the image-acquisition unit by the brightness of the reference image.