1. An image processing device, comprising: a transformation ratio calculation unit which calculates a transformation ratio of an image after transformation, the image after transformation being obtained by transforming an original image based on a predetermined rule; a filter coefficient calculation unit which calculates filter coefficients based on the transformation ratio; and a pixel value calculation unit which calculates a pixel value of each pixel in the image after transformation based on the filter coefficients and outputs the pixel value of the pixel in the image after transformation as image data after transformation.