Provided are an image processing apparatus, method and medium, more particularly, an image processing apparatus, method and medium which perform interpolation such that a pixel value in each pixel region included in a digital image and an average value of interpolation data extracted using a predetermined interpolation method in the pixel region are equal. The image processing apparatus includes an accumulative addition unit to sequentially integrate values of pixels included in an image, an interpolation unit to interpolate the integrated pixel values, and an accumulative subtraction unit to perform differentiation at a predetermined position of the interpolated pixel values.