1. An image processing apparatus comprising: a surrounding-pixels selecting unit that selects surrounding pixels that surround a correction pixel in an input image based on a low-pass filter; a reference-pixels selecting unit that selects reference pixels from the surrounding pixels based on pixel values of the correction pixel and the surrounding pixels; a smoothed-image creating unit that applies the low-pass filter to the reference pixels to create a smoothed image of the reference pixels; and an output image creating unit that creates an output image based on the smoothed image, and a difference image between the smoothed image and the input image.