Finding the center of luminance or tone of a picture?

I need a script that will take a picture convert it to  La*b* coordinates and give the values x and y below where m is  255- L.  This is the tonal center of mass. of the picture.. The equations are described below except in stead of colorimetric barycenter substitute tonal center.  This is needed for a paper of the aesthetics of pictorial composition. You would get credit in the paper.