1. An image processing device comprising: an original reception unit that receives an original image; a dot image generation unit that generates, on the basis of additive information to be added to the original image, a dot image in which a plurality of dots each formed by one or more pixels are arranged; a state alteration unit that, when any of the dots in the dot image is determined to be not extractable, alters a state of the non-extractable dot on the basis of a relationship between a position on the dot image generated by the dot image generation unit and a corresponding position on the original image; and a composite image generation unit that generates a composite image by superimposing, on the original image, the dot image having the state of the non-extractable dot altered by the state alteration unit.