What you want is referred to as "threshold" in image processing. Basically, it takes an image as an input and outputs an image that has all pixels with a value below a given threshold set to black, and all pixels the value of which is above the threshold set to white. This results in a black-and-white image from an arbitrary input image.
Generally, you want to convert to grayscale first for more predictable results, but it is possible to threshold a full-color image as well.
You can use a graphical tool such as GIMP to do this interactively (you'll find the tool through the main menu -> Colors -> Threshold), or you can use ImageMagick something like this:
convert colored.png -threshold 75% thres_colored.png Running the above command on the example image produces the result shown below.
Since thresholding is often somewhat of a trial-and-error process to get a result you're happy with, particularly if the source image is not very close to black-and-white already, I recommend the GUI approach if possible, but if that is not an option for whatever reason you can do it through the command line as well.