The simplest answer is to try using the edge function in the Image Processing Toolbox. Here is the doc. I tried it on your image to get an ok result. You might have to play with the algorithm/parameters to get a thicker/more defined edge:
img = imread('binary_image.png');
I = rgb2gray(img);
BW1 = edge(I,'sobel');
BW2 = edge(I,'canny');
figure;
imshowpair(BW1,BW2,'montage')
title('Sobel Filter Canny Filter');
(right click open image in a new tab/window for better resolution)
