% FINDENDSJUNCTIONS - find junctions and endings in a line/edge image%% Usage: [rj, cj, re, ce] = findendsjunctions(edgeim, disp)% % Arguments:  edgeim - A binary image marking lines/edges in an image.  It is%                      assumed that this is a thinned or skeleton image (or%                      nearly so).%             disp   - An optional flag 0/1 to indicate whether the edge%                      image should be plotted with the junctions and endings%                      marked.  This defaults to 0.%% Returns:    rj, cj - Row and column coordinates of junction points in the%                      image. %             re, ce - Row and column coordinates of end points in the%                      image.% Copyright (c) 2006 Peter Kovesi% School of Computer Science & Software Engineering% The University of Western Australia% pk at csse uwa edu au% http://www.csse.uwa.edu.au/% % Permission is hereby granted, free of charge, to any person obtaining a copy% of this software and associated documentation files (the "Software"), to deal% in the Software without restriction, subject to the following conditions:% % The above copyright notice and this permission notice shall be included in % all copies or substantial portions of the Software.%% The Software is provided "as is", without warranty of any kind.% November 2006function [rj, cj, re, ce] = findendsjunctions(edgeim, disp)    if nargin == 1	disp = 0;    end        % Ensure edge/line image really is thinnned otherwise tests for junctions    % and endings may fail.    b = bwmorph(edgeim,'skel',Inf);        % Set up look up table to find junctions.  To do this we use the function    % defined at the end of this file to test that the centre pixel within a 3x3    % neighbourhood is a junction.    lut = makelut(@junction, 3);    junctions = applylut(b, lut);    [rj,cj] = find(junctions);        % Set up a look up table to find endings.      lut = makelut(@ending, 3);    ends = applylut(b, lut);    [re,ce] = find(ends);        if disp    	show(edgeim,1), hold on	plot(cj,rj,'r+')	plot(ce,re,'g+')        end%----------------------------------------------------------------------% Function to test whether the centre pixel within a 3x3 neighbourhood is a% junction. The centre pixel must be set and the number of transitions/crossings% between 0 and 1 as one traverses the perimeter of the 3x3 region must be 6 or% 8.%% Pixels in the 3x3 region are numbered as follows%%       1 4 7%       2 5 8%       3 6 9function b = junction(x)        a = [x(1) x(2) x(3) x(6) x(9) x(8) x(7) x(4)];    b = [x(2) x(3) x(6) x(9) x(8) x(7) x(4) x(1)];        crossings = sum(abs(a-b));        b = x(5) && crossings >= 6;    %----------------------------------------------------------------------% Function to test whether the centre pixel within a 3x3 neighbourhood is an% ending. The centre pixel must be set and the number of transitions/crossings% between 0 and 1 as one traverses the perimeter of the 3x3 region must be 2.%% Pixels in the 3x3 region are numbered as follows%%       1 4 7%       2 5 8%       3 6 9function b = ending(x)    a = [x(1) x(2) x(3) x(6) x(9) x(8) x(7) x(4)];    b = [x(2) x(3) x(6) x(9) x(8) x(7) x(4) x(1)];        crossings = sum(abs(a-b));        b = x(5) && crossings == 2;