Know which branchpoints are connected to other branchpoints?

If I get a skeleton of a binary image and return the branchpoints I want to know which ones are connected to which. eg if I have 5 branchpoints and branchpoint 2 is connected to branchpoint 4, how would I know this?

Answer 1

[DGM]

There are probably smarter ways to do it, but:

% a logical image
inpict = imread('hands1-mask.png');

% the skeleton
sk = bwskel(inpict);
imshow(sk)

% i'm just going to consider all nodes
% i.e. both branchpoints and endpoints
bp = bwmorph(sk,'branchpoints');
ep = bwmorph(sk,'endpoints');
N = bp | ep; 
% dilate to make sure 8-connectivity is broken
N = bwmorph(N,'dilate');

% the edges alone
E = sk & ~N;

% form label arrays
[Le numedges] = bwlabel(E,8); % for addressing
[Ln numnodes] = bwlabel(N,8); % for sampling

% find connectivity list
connectednodes = zeros(numedges,2);
for ke = 1:numedges
    % create a mask and sample the node label array
    thismk = bwareafilt((Le == ke) | N,1);
    connectednodes(ke,:) = nonzeros(unique(Ln(thismk)));
end

% summarize
edgelist = (1:numedges).';
nodelist = (1:numnodes).';
table(edgelist,connectednodes)

ans = 9x2 table
    edgelist    connectednodes
    ________    ______________

       1           1     7    
       2           2     5    
       3           3     5    
       4           4     6    
       5           5     6    
       6           6     7    
       7           7     8    
       8           8    10    
       9           8     9    

I'm sure any other information can be figured out from there.

% we can still figure out what the neighbors are
neighbornodes = cell(numnodes,1);
for k = 1:numnodes
    mk = connectednodes == k;
    mk = any(mk,2) & ~mk; % exclude self-connection
    neighbornodes{k} = connectednodes(mk).';
end
table(nodelist,neighbornodes)

ans = 10x2 table
    nodelist    neighbornodes
    ________    _____________

        1        {[     7]}  
        2        {[     5]}  
        3        {[     5]}  
        4        {[     6]}  
        5        {[ 2 3 6]}  
        6        {[ 4 5 7]}  
        7        {[ 1 6 8]}  
        8        {[7 10 9]}  
        9        {[     8]}  
       10        {[     8]}  

This can probably be broken if nodes are too close to each other (<3px or so). At that point, the dilation eliminates the interconnecting edge.