1. An image processing apparatus comprising: an achromatization determination portion configured to determine whether to achromatize a target pixel in an image; an achromatization processing portion configured: to achromatize the target pixel that is determined to achromatize by the achromatization determination portion; and not to achromatize the target pixel that is determined not to achromatize by the achromatization determination portion; and a line designation portion configured: to permit achromatization by the achromatization determination portion and the achromatization processing portion for a line within a predetermined partial range in a sub-scanning direction in the image; and not to permit achromatization by the achromatization determination portion and the achromatization processing portion for a line that is out of the partial range in the sub-scanning direction in the image, wherein if a black pixel is present within a predetermined peripheral range from the target pixel in the sub-scanning direction, the achromatization determination portion determines whether to achromatize the target pixel, on the basis of an attribute of a background determination pixel that is present in an opposite direction from the target pixel with respect to the black pixel and within a range of a predetermined number of pixels from the black pixel, and if no black pixel is present within the predetermined peripheral range from the target pixel in the sub-scanning direction, the achromatization determination portion determines not to achromatize the target pixel.