1. A fluorescence endoscope device comprising: a light source configured to emit excitation light and illumination light for irradiating a subject; a fluorescence-image acquisition sensor configured to capture image information of fluorescence generated at the subject due to the irradiation with the excitation light from the light source; a reference-image acquisition sensor configured to capture image information of return light returning from the subject due to the irradiation with the illumination light from the light source; and a processor comprising hardware, the processor implementing: an image generating portion configured to generate a fluorescence image based on the image information of the fluorescence, and to generate a reference image based on the image information of return light; a divided-fluorescence-image generating portion configured to divide the fluorescence image by the reference image to generate a divided fluorescence image, wherein effects of one or both of an observation distance and observation angle on intensity value is reduced in the divided fluorescence image as compared to the fluorescence image; a first-region extracting portion configured to extract a first region or first regions of the fluorescence image, the first region or first regions having a gradation value higher than a first threshold gradation value, wherein the first threshold gradation value is set to distinguish between: pixels in the fluorescence image having gradation values representing a first background site; and pixels in the first region or first regions of the fluorescence image having gradation values representing a target site and pixels in the first region or first regions of the fluorescence image having gradation values representing the effects of one or both of observation distance and observation angle; a second-region extracting portion configured to extract a second region or second regions of the divided fluorescence image, the second region or second regions having a gradation value higher than a second threshold gradation value different from the first threshold gradation value, wherein the second threshold gradation value is set to distinguish between: pixels in the divided fluorescence image having gradation values representing a second background site; and pixels in the second region or second regions of the divided fluorescence image having gradation values representing the target site; and a corrected-fluorescence-image generating portion configured to: extract, from the fluorescence image, an overlap region where the first region or first regions of the fluorescence image overlaps the second region or second regions of the divided fluorescence image; and generate a corrected fluorescence image in which the overlap region is identified.