1. An image processing apparatus, comprising: an image inputting part inputting an image in which a first pixel group and a second pixel group indicating mutually different color components are included and at least pixels of the second pixel group are arranged in discrete positions; a color estimating part estimating first color component data at the discrete pixel positions of the second pixel group based on first color component data belong to pixels of the first pixel group; a calculating part calculating color-difference data at the discrete pixel positions of the second pixel group based on the first color component data being estimated at the discrete pixel positions of the second pixel group and second color component data belong to the pixels of the second pixel group; a smoothing part performing smoothing processing on a discrete color-difference image formed of the color-difference data being calculated at the discrete pixel positions of the second pixel group; and a color-difference estimating part estimating color-difference data at pixel positions of pixel group other than the second pixel group on the image input by the image inputting part based on the discrete color-difference image after being smoothed.