1. An image processing apparatus, comprising: an image reading unit that scans a document to detect pixel values of a plurality of color components of each pixel; a pixel color determining unit that determines whether or not a color of each pixel is a specific color based on the pixel values of the plurality of color components of each pixel detected by the image reading unit; an isolated point determining unit that determines whether or not each pixel is an isolated point based on the pixel values of the plurality of color components of each pixel detected by the image reading unit; and a document discriminating unit that discriminates whether the document is a color document or a black-and-white document based on the pixel values of the plurality of color components of each pixel detected by the image reading unit while treating the pixels, the color of which has been determined to be the specific color by the pixel color determining unit and which have been determined to be isolated points by the isolated point determining unit, as black-and-white pixels.