1. An image processing apparatus, comprising: an edge amount calculating device configured to calculate edge amounts of an image in a plurality of directions for each of a plurality of frequency bands of the image; a character edge area determination device configured to determine, based on the calculated edge amounts, whether or not a selected picture element of the image is of a character edge area; and a sharpness control device configured to correct a frequency characteristic of the image by performing a first connection to the edge amounts in the respective plurality of directions when the selected picture element is determined to be of a character edge area by the character edge area determining device, and by performing a second correction to the edge amounts when the selected picture element is determined not to be of a character edge area by the character edge area determining device.