1. An image processing apparatus comprising: a bit extender that receives n-bit image data, carries out an α-bit bit extension, and outputs resultant basic (n+α)-bit image data, n and α being positive integers; and an edge-preserving smoothing filter for smoothing the basic (n+α)-bit image data by using additional gray levels provided by the bit extension, wherein the edge-preserving smoothing filter is an epsilon filter having a threshold value ε equal to 2 α .