1. An image processing device comprising: a low-pass input image generation unit which generates a low-pass input image obtained by applying a first low-pass filter to an input image; a low-pass halftone image generation unit which generates a low-pass halftone image obtained by applying a second low-pass filter to a halftone image corresponding to the input image; a dot displacing unit which performs the dot displacement processing to displace a dot in the halftone image to make a difference between the low-pass input image and the low-pass halftone image smaller, and updates a dot arrangement of the halftone image; an input-reflected low-pass halftone image generation unit which generates an input-reflected low-pass halftone image representing a difference between the low-pass input image and the low-pass halftone image; a focused dot setting unit which sets a focused dot in the halftone image; and a dot placement pixel determination unit which determines a dot placement pixel by comparing pixel values to each other in the input-reflected low-pass halftone image, the dot placement pixel being a location where a dot is placed in the halftone image when dot displacement processing is performed to improve uniformity of gradation distribution in the input-reflected low-pass halftone image, thereby reducing error between the low-pass input image and the low-pass halftone image, wherein the dot displacing unit performs the dot displacement processing to displace the focused dot in the halftone image to a position of the dot placement pixel in the halftone image, and updates a dot arrangement of the halftone image.