I assume you have the x,y coordinates of the perimeter of the circle. Then you can just use improfile() and call diff() and look for changes of +1.
values = improfile(binaryImage, xCircle, yCircle);
dv = diff(values);
numTransitions = sum(dv==1);
Of course you'll have to take special care at the ends of the array, like if the white part started exactly at element #1 and was zero at the very last element.
