Ok, this is a good start, try the following, assuming that your image is a
b = edge(a,'Canny',,3);
So what you showed was b. Then do
c = bwlabel(b);
d = regionprops(c,'area');
That should label all the edges and then get their length. Then you should be able to discard all the small edges by using ismember based on the regionprops.
Once you have only one or two, which are the boundary of the bone, then you can use cumsum along the horizontal dimension so that each line will be something like this
0 0 0 0 0 ... 1 1 1 1 1 1 ... 2 2 2 2
where 0 is the left side before the first edge, the 1 is the central region and the 2 is the right side after the second edge. Then select the region == 1 and you should have the bone region.