1. An image processing apparatus for improving the definition of an input image, the input image consisting of a plurality of pixels, the pixels being divided into an edge portion and a background portion, the image processing apparatus comprising: a compound operating unit for generating a noise-eliminated image by subjecting the input image to an open-close process and a close-open process; a sharpness processing unit for generating an enhanced image by subjecting the input image to a sharpness process; and an edge detecting unit for receiving the noise-eliminated image and the enhanced image and determining that each pixel of the input image belongs to the edge portion or the background portion; wherein when one pixel belongs to the edge portion, the edge detecting unit outputs the gray level of the pixel of the enhanced image, and when one pixel belongs to the background portion, the edge detecting unit outputs the gray level of the pixel of the noise-eliminated image.