1. An image processing device comprising: an image data input unit that receives image data; a pixel extracting unit that extracts a pixel area including a pixel of interest to be processed and peripheral pixels located around the pixel of interest from the image data; a pixel group generator that generates a plurality of pixel groups by dividing pixels in the pixel area in accordance with a pixel value distribution in the pixel area; a pixel group similarity calculator that calculates a similarity between a pixel group and a pixel group including the pixel of interest for each pixel group as a pixel group similarity to be defined for pixels belonging to the pixel group in the pixel area; a pixel value similarity calculator that calculates a pixel value similarity of each pixel in the pixel area on the basis of a pixel value of the pixel of interest; a filter coefficient calculator that calculates filter coefficients to be applied to pixels in the pixel area on the basis of the pixel group similarity and the pixel value similarity; and a smoothing processing unit that performs a smoothing process on the pixel value of the pixel of interest on the basis of pixel values in the pixel area and the filter coefficients.