1. An image processing device for performing edge-preserving smoothing, comprising: a reducing unit for reducing an input image; a reduced image smoothing unit for performing a smoothing processing on a reduced image generated by the reducing unit with edges preserved; and an edge-preserving enlarging unit for enlarging an image generated by the reduced image smoothing unit with the edges preserved, wherein the edge-preserving enlarging unit performs a filtering processing after enlargement, by determining a pixel value of a target pixel for the filtering processing based on weighted addition of pixel values of respective reference pixels; and the edge-preserving enlarging unit sets weighting coefficients for the pixel values of the respective reference pixels, based on differences between a pixel value of the input image corresponding to the target pixel and pixel values of the respective reference pixels and based on distances between the target pixel and the respective reference pixels.