Sometimes (e.g. newspaper or compressing images) we have to reduce depth of our image to only 1 bit. We can do it simply by applying thresholding:

But the result is usually not satisfactory for us – it has large regions of the same color.
There is a better idea than thresholding when it comes to monochromatic images:

1. Take original image:

2. Apply gaussian noise:

3. Do thresholding:

After this procedure we have an image that creates illusion that it has more than 1 bit depth. It’s so called dithering.
I’ve found this idea in “Practical signal processing” written by Mark Owen.