1. An image processing apparatus comprising: a first converting unit that performs a gradation conversion on an input image to generate a conversion image; a smoothed image generating unit that performs a smoothing process on the conversion image generated by the first converting unit or a first generation image generated from the conversion image to generate a plurality of level-value-limited conversion images, the smoothing process smoothing pixels within different ranges of level values with a filter having a same filter size; a synthesis processing unit that selects at least one of the level-value-limited conversion images generated by the smoothed image generating unit and synthesizes the at least one of the level-value-limited conversion images to generate a synthesis image; and a second converting unit that performs a gradation conversion on the synthesis image generated by the synthesis processing unit to generate a smoothed image that is converted to have a same gradation as that of the input image.