1. An apparatus that maintains the average density of an input image while converting the input image having image signals with K density levels that are ordered in successive scanlines to an output image with L density levels, where L is less than K, for output to a device capable of rendering images having L density levels, the apparatus comprising: a first memory for storing the input image signals; means for adding to each input image signal i(m,n) stored in said memory error correction signals .epsilon.(m,n) to provide corrected image signals i'(m,n) with adjusted density levels that reflect the average density level of the input image; means for comparing each corrected image signal of the input image to a predefined threshold value T to determine an output image signal b(m,n) defined by L density levels for each image signal of the output image, said comparing means comparing each corrected image signal on each of the successive scanlines in a first process direction; a second memory for storing said output image signal to be rendered on the output device that is limited to images having L density levels; means for deriving a first quantization error e.sub.f (m,n) and a second quantization error e.sub.b (m,n) for each output image signal determined by said comparing means; means for propagating the first quantization error of each image signal to a predetermined neighborhood of input image signals, said propagating means forming error correction signals to be directed to each input image signal using a fraction of the first quantization error; and means for reversing the direction said propagating means distributes the second quantization error to the predetermined neighborhood of input image signals, said reversing means directing said propagating means in a second process direction opposite to the first process direction, the second quantization error being propagated in the second process direction without modifying each output image signal determined in the first process direction, whereby said propagating means reduces correlated patterns formed in the output image.