According to one embodiment, an image processing apparatus includes an ε filter that compares the difference between a pixel value of a target pixel to be processed and that of a surrounding pixel neighboring the target pixel in each pixel block of an input image with a predetermined threshold. When the difference exceeds the predetermined threshold, the ε filter performs the replacement of the pixel value of the surrounding pixel. The predetermined threshold includes at least two different thresholds, a first threshold and a second threshold larger than the first threshold. When the difference exceeds the second threshold, the ε filter performs the replacement of the pixel value of the surrounding pixel in stages such that the pixel value of the surrounding pixel approaches that of the target pixel.