You have yourself what is not necessarily an easy problem. If the contour was guaranteed to be convex it would be greatly simplified, but level-sets don't obey this.
Here is one possibility:
%%Sample image:
I = imread('cameraman.tif');
sz = size(I);
M = I<50; %map
E = bwperim(M); %edges
E = bwareaopen(E,100); %edges of big things (for example)
amp = 4; %amplification factor
bounds = bwboundaries(E); %get the boundaries
szAmp = sz*amp; %amplification size
E2 = false(szAmp); %preallocate
for ii = 1:numel(bounds)
E2 = E2 | poly2mask(bounds{ii}(:,2)*amp,bounds{ii}(:,1)*amp,szAmp(1),szAmp(2));
%Make mask out of each bounded polygon
end
E2 = bwperim(E2); %get the edge again
imtool(E2) %inspect it
