grey of three bands
More clarification needed, but the question seems easy, if I undestood it properly. As RGB have three bands (Levels) and Gray has one level only (with qualtizations levels).
Above mentioned is direct conversion to binary image. For improve the image quality, you can do it in number of ways, like local thresholding, global thresholding, you can use the Otshu's thresholding also. All depends on targeted applications.
Please refer the chapter of Image Segmentation, Book Digital Image Processing using Matlab Author: Golzalez (McGraw Hill), you will get numerous solution.