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, coordinates of pixels in the original image being obtained by coordinate transformation of coordinates of pixels in the image after transformation, the transformation ratio being calculated based on a distance between adjoining ones of the coordinates of pixels in the original image; 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, wherein the filter coefficient calculation unit calculates the filter coefficients for each pixel of the image after transformation based on the transformation ratio for each pixel of the image after transformation.