1. A method for converting halftone images into continuous-tone images, comprising: obtaining a halftone image; defining a two-stage filter, wherein a first stage is a smoothing filter and a second stage is a sigma filter connected to the smoothing filter; defining parameters for the smoothing filter and the sigma filter; inputting a halftone image into a smoothing filter to derive an intermediate image; inputting the intermediate image into the sigma filter to selectively smooth pixels (which lie within 2 standard deviations from the center pixel in each window); and outputting from said sigma filter a continuous-tone image which is piecewise-smooth and has preserved edges.