function [u_out,ef,s,tmbs,lambda_n] = signature_full_n(u_in,scale,l_0,l_n);

% input:
% u_in: 8 bit binary image
% scale: number of steps from lambda_0 to lambda_n (optional)
% l_0, l_n: normalized lambda ranges from l_0 to l_n (optional)
%
% output:
% u_out: list of scale images, one for each normalized lambda value
% ef: full signature
% s: S-signature
% tmbs: 1-d measure of T-\boundary(S) for each lambda
% lambda_n: list of normalized lambda values

if ~exist('scale','var');
    fprintf('[warn] Scale unset -- using scale == 50.\n');
    scale = 50;
end
if ~exist('l_0','var') || ~exist('l_n','var');
    fprintf('[warn] l_0 or l_n unset -- using 1 and 50.\n');
    l_0 = 1; l_n = 50;
end;    
 
area_n = sum(sum(u_in./max(max(u_in))));
lambda_n = l_n + (l_0 - l_n) * ((1:scale)./scale);
% from FNS paper, want area of (n_scale * object) = 1
n_scale = sqrt(1/area_n);
[N,M]       = size(u_in);     % u_in should be 8 bit binary image
u_out=zeros(scale,N,M);
%S          = max(N,M);       % use this to set scales
nNeighbors = 16;              % we use 16 neighbors

for i = 1:scale;
    u_out(i,:,:) = Graph_anisoTV_L1_v2(u_in,lambda_n(i)*n_scale,nNeighbors,2);   % do not change the last input argument
    [e,s,t] = energy_full(squeeze(u_out(i,:,:)),u_in,lambda_n(i)*n_scale);
    output(i,:) = [e,s,t]/255;
	 
end

ef  = output(:,1);
s  = output(:,2);
tmbs  = output(:,3);