It's just a bit of algebra. You need to find the perpendicular lines at the endpoints. The slope is -1 over the slope of the main line. Then you can use point slope formula like you learned in 10th grade. Do that for each endpoint. I think you can do this because you're a talented engineer. Then use the 4 line segment endpoints and plug into poly2mask(). Then dilate and multiply by the mask to "chop off" the ends.
mask = poly2mask(x,y,rows,columns);
fatLineImage = imdilate(binaryImage, true(30));
finalImage = fatLineImage .* uint8(mask);
