% EDGELINK - Link edge points in an image into lists
%
% Usage: [edgelist edgeim, etype] = edgelink(im, minlength, location)
%
% **Warning** 'minlength' is ignored at the moment because 'cleanedgelist'
% has some bugs and can be memory hungry
%
% Arguments: im - Binary edge image, it is assumed that edges
% have been thinned (or are nearly thin).
% minlength - Optional minimum edge length of interest, defaults
% to 1 if omitted or specified as []. Ignored at the
% moment.
% location - Optional complex valued image holding subpixel
% locations of edge points. For any pixel the
% real part holds the subpixel row coordinate of
% that edge point and the imaginary part holds
% the column coordinate. See NONMAXSUP. If
% this argument is supplied the edgelists will
% be formed from the subpixel coordinates,
% otherwise the the integer pixel coordinates of
% points in 'im' are used.
%
% Returns: edgelist - a cell array of edge lists in row,column coords in
% the form
% { [r1 c1 [r1 c1 etc }
% r2 c2 ...
% ...
% rN cN] ....]
%
% edgeim - Image with pixels labeled with edge number.
% Note that junctions in the labeled edge image will be
% labeled with the edge number of the last edge that was
% tracked through it. Note that this image also includes
% edges that do not meet the minimum length specification.
% If you want to see just the edges that meet the
% specification you should pass the edgelist to
% DRAWEDGELIST.
%
% etype - Array of values, one for each edge segment indicating
% its type
% 0 - Start free, end free
% 1 - Start free, end junction
% 2 - Start junction, end free (should not happen)
% 3 - Start junction, end junction
% 4 - Loop
%
% This function links edge points together into lists of coordinate pairs.
% Where an edge junction is encountered the list is terminated and a separate
% list is generated for each of the branches.
%
% Note I am not sure if using bwmorph's 'thin' or 'skel' is best for
% preprocessing the edge image prior to edgelinking. The main issue is the
% treatment of junctions. Skel can result in an image where multiple adjacent
% junctions are produced (maybe this is more a problem with my junction
% detection code). Thin, on the other hand, can produce different output when
% you rotate an image by 90 degrees. On balance I think using 'thin' is better.
% Note, however, the input image should be 'nearly thin' otherwise the thinning
% operation could shorten the ends of structures. Skeletonisation and thinning
% is surprisingly awkward.
%
% See also: DRAWEDGELIST, LINESEG, MAXLINEDEV, CLEANEDGELIST,
% FINDENDSJUNCTIONS, FILLEDGEGAPS
% Copyright (c) 1996-2013 Peter Kovesi
% Centre for Exploration Targeting
% The University of Western Australia
% peter.kovesi at 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.
% February 2001 - Original version
% September 2004 - Revised to allow subpixel edge data to be used
% November 2006 - Changed so that edgelists start and stop at every junction
% January 2007 - Trackedge modified to discard isolated pixels and the
% problems they cause (thanks to Jeff Copeland)
% January 2007 - Fixed so that closed loops are closed!
% May 2013 - Completely redesigned with a new linking strategy that
% hopefully handles adjacent junctions correctly. It runs
% about twice as fast too.
function [edgelist, edgeim, etype] = edgelink(im, minlength, location)
% Set up some global variables to avoid passing (and copying) of arguments,
% this improves speed.
global EDGEIM;
global ROWS;
global COLS;
global JUNCT;
if ~exist('minlength','var') || isempty(minlength), minlength = 0; end
EDGEIM = im ~= 0; % Make sure image is binary.
EDGEIM = bwmorph(EDGEIM,'clean'); % Remove isolated pixels
% Make sure edges are thinned. Use 'thin' rather than 'skel', see
% comments in header.
EDGEIM = bwmorph(EDGEIM,'thin',Inf);
[ROWS, COLS] = size(EDGEIM);
% Find endings and junctions in edge data
[RJ, CJ, re, ce] = findendsjunctions(EDGEIM);
Njunct = length(RJ);
Nends = length(re);
% Create a sparse matrix to mark junction locations. This makes junction
% testing much faster. A value of 1 indicates a junction, a value of 2
% indicates we have visited the junction.
JUNCT = spalloc(ROWS,COLS, Njunct);
for n = 1:Njunct
JUNCT(RJ(n),CJ(n)) = 1;
end
% ? Think about using labels >= 2 so that EDGEIM can be uint16, say. %
EDGEIM = double(EDGEIM); % Cast to double to allow the use of -ve labelings
edgeNo = 0;
% Summary of strategy:
% 1) From every end point track until we encounter an end point or
% junction. As we track points along an edge image pixels are labeled with
% the -ve of their edge No.
% 2) From every junction track out on any edges that have not been
% labeled yet.
% 3) Scan through the image looking for any unlabeled pixels. These
% correspond to isolated loops that have no junctions.
%% 1) Form tracks from each unlabeled endpoint until we encounter another
% endpoint or junction.
for n = 1:Nends
if EDGEIM(re(n),ce(n)) == 1 % Endpoint is unlabeled
edgeNo = edgeNo + 1;
[edgelist{edgeNo} endType] = trackedge(re(n), ce(n), edgeNo);
etype(edgeNo) = endType;
end
end
%% 2) Handle junctions.
% Junctions are awkward when they are adjacent to other junctions. We
% start by looking at all the neighbours of a junction.
% If there is an adjacent junction we first create a 2-element edgetrack
% that links the two junctions together. We then look to see if there are
% any non-junction edge pixels that are adjacent to both junctions. We then
% test to see which of the two junctions is closest to this common pixel and
% initiate an edge track from the closest of the two junctions through this
% pixel. When we do this we set the 'avoidJunction' flag in the call to
% trackedge so that the edge track does not immediately loop back and
% terminate on the other adjacent junction.
% Having checked all the common neighbours of both junctions we then
% track out on any remaining untracked neighbours of the junction
for j = 1:Njunct
if JUNCT(RJ(j),CJ(j)) ~= 2; % We have not visited this junction
JUNCT(RJ(j),CJ(j)) = 2;
% Call availablepixels with edgeNo = 0 so that we get a list of
% available neighbouring pixels that can be linked to and a list of
% all neighbouring pixels that are also junctions.
[ra, ca, rj, cj] = availablepixels(RJ(j), CJ(j), 0);
for k = 1:length(rj) % For all adjacent junctions...
% Create a 2-element edgetrack to each adjacent junction
edgeNo = edgeNo + 1;
edgelist{edgeNo} = [RJ(j) CJ(j); rj(k) cj(k)];
etype(edgeNo) = 3; % Edge segment is junction-junction
EDGEIM(RJ(j), CJ(j)) = -edgeNo;
EDGEIM(rj(k), cj(k)) = -edgeNo;
% Check if the adjacent junction has some untracked pixels that
% are also adjacent to the initial junction. Thus we need to
% get available pixels adjacent to junction (rj(k) cj(k))
[rak, cak] = availablepixels(rj(k), cj(k));
% If both junctions have untracked neighbours that need checking...
if ~isempty(ra) && ~isempty(rak)
% Find untracked neighbours common to both junctions.
commonrc = intersect([ra ca], [rak cak], 'rows');
for n = 1:size(commonrc, 1);
% If one of the junctions j or k is closer to this common
% neighbour use that as the start of the edge track and the
% common neighbour as the 2nd element. When we call
% trackedge we set the avoidJunction flag to prevent the
% track immediately connecting back to the other junction.
distj = norm(commonrc(n,:) - [RJ(j) CJ(j)]);
distk = norm(commonrc(n,:) - [rj(k) cj(k)]);
edgeNo = edgeNo + 1;
if distj < distk
edgelist{edgeNo} = trackedge(RJ(j), CJ(j), edgeNo, ...
commonrc(n,1), commonrc(n,2), 1);
else
edgelist{edgeNo} = trackedge(rj(k), cj(k), edgeNo, ...
commonrc(n,1), commonrc(n,2), 1);
end
etype(edgeNo) = 3; % Edge segment is junction-junction
end
end
% Track any remaining unlabeled pixels adjacent to this junction k
for m = 1:length(rak)
if EDGEIM(rak(m), cak(m)) == 1
edgeNo = edgeNo + 1;
edgelist{edgeNo} = trackedge(rj(k), cj(k), edgeNo, rak(m), cak(m));
etype(edgeNo) = 3; % Edge segment is junction-junction
end
end
% Mark that we have visited junction (rj(k) cj(k))
JUNCT(rj(k), cj(k)) = 2;
end % for all adjacent junctions
% Finally track any remaining unlabeled pixels adjacent to original junction j
for m = 1:length(ra)
if EDGEIM(ra(m), ca(m)) == 1
edgeNo = edgeNo + 1;
edgelist{edgeNo} = trackedge(RJ(j), CJ(j), edgeNo, ra(m), ca(m));
etype(edgeNo) = 3; % Edge segment is junction-junction
end
end
end % If we have not visited this junction
end % For each junction
%% 3) Scan through the image looking for any unlabeled pixels. These
% should correspond to isolated loops that have no junctions or endpoints.
for ru = 1:ROWS
for cu = 1:COLS
if EDGEIM(ru,cu) == 1 % We have an unlabeled edge
edgeNo = edgeNo + 1;
[edgelist{edgeNo} endType] = trackedge(ru, cu, edgeNo);
etype(edgeNo) = endType;
end
end
end
edgeim = -EDGEIM; % Finally negate image to make edge encodings +ve.
% Eliminate isolated edges and spurs that are below the minimum length
% ** DISABLED for the time being **
% if nargin >= 2 && ~isempty(minlength)
% edgelist = cleanedgelist2(edgelist, minlength);
% end
% If subpixel edge locations are supplied upgrade the integer precision
% edgelists that were constructed with data from 'location'.
if nargin == 3
for I = 1:length(edgelist)
ind = sub2ind(size(im),edgelist{I}(:,1),edgelist{I}(:,2));
edgelist{I}(:,1) = real(location(ind))';
edgelist{I}(:,2) = imag(location(ind))';
end
end
clear global EDGEIM;
clear global ROWS;
clear global COLS;
clear global JUNCT;
%----------------------------------------------------------------------
% TRACKEDGE
%
% Function to track all the edge points starting from an end point or junction.
% As it tracks it stores the coords of the edge points in an array and labels the
% pixels in the edge image with the -ve of their edge number. This continues
% until no more connected points are found, or a junction point is encountered.
%
% Usage: edgepoints = trackedge(rstart, cstart, edgeNo, r2, c2, avoidJunction)
%
% Arguments: rstart, cstart - Row and column No of starting point.
% edgeNo - The current edge number.
% r2, c2 - Optional row and column coords of 2nd point.
% avoidJunction - Optional flag indicating that (r2,c2)
% should not be immediately connected to a
% junction (if possible).
%
% Returns: edgepoints - Nx2 array of row and col values for
% each edge point.
% endType - 0 for a free end
% 1 for a junction
% 5 for a loop
function [edgepoints endType] = trackedge(rstart, cstart, edgeNo, r2, c2, avoidJunction)
global EDGEIM;
global JUNCT;
if ~exist('avoidJunction', 'var'), avoidJunction = 0; end
edgepoints = [rstart cstart]; % Start a new list for this edge.
EDGEIM(rstart,cstart) = -edgeNo; % Edge points in the image are
% encoded by -ve of their edgeNo.
preferredDirection = 0; % Flag indicating we have/not a
% preferred direction.
% If the second point has been supplied add it to the track and set the
% path direction
if exist('r2', 'var') && exist('c2', 'var')
edgepoints = [edgepoints
r2 c2 ];
EDGEIM(r2, c2) = -edgeNo;
% Initialise direction vector of path and set the current point on
% the path
dirn = unitvector([r2-rstart c2-cstart]);
r = r2;
c = c2;
preferredDirection = 1;
else
dirn = [0 0];
r = rstart;
c = cstart;
end
% Find all the pixels we could link to
[ra, ca, rj, cj] = availablepixels(r, c, edgeNo);
while ~isempty(ra) || ~isempty(rj)
% First see if we can link to a junction. Choose the junction that
% results in a move that is as close as possible to dirn. If we have no
% preferred direction, and there is a choice, link to the closest
% junction
% We enter this block:
% IF there are junction points and we are not trying to avoid a junction
% OR there are junction points and no non-junction points, ie we have
% to enter it even if we are trying to avoid a junction
if (~isempty(rj) && ~avoidJunction) || (~isempty(rj) && isempty(ra))
% If we have a prefered direction choose the junction that results
% in a move that is as close as possible to dirn.
if preferredDirection
dotp = -inf;
for n = 1:length(rj)
dirna = unitvector([rj(n)-r cj(n)-c]);
dp = dirn*dirna';
if dp > dotp
dotp = dp;
rbest = rj(n); cbest = cj(n);
dirnbest = dirna;
end
end
% Otherwise if we have no established direction, we should pick a
% 4-connected junction if possible as it will be closest. This only
% affects tracks of length 1 (Why do I worry about this...?!).
else
distbest = inf;
for n = 1:length(rj)
dist = sum([rj(n)-r; cj(n)-c]);
if dist < distbest
rbest = rj(n); cbest = cj(n);
distbest = dist;
dirnbest = unitvector([rj(n)-r cj(n)-c]);
end
end
preferredDirection = 1;
end
% If there were no junctions to link to choose the available
% non-junction pixel that results in a move that is as close as possible
% to dirn
else
dotp = -inf;
for n = 1:length(ra)
dirna = unitvector([ra(n)-r ca(n)-c]);
dp = dirn*dirna';
if dp > dotp
dotp = dp;
rbest = ra(n); cbest = ca(n);
dirnbest = dirna;
end
end
avoidJunction = 0; % Clear the avoidJunction flag if it had been set
end
% Append the best pixel to the edgelist and update the direction and EDGEIM
r = rbest; c = cbest;
edgepoints = [edgepoints
r c ];
dirn = dirnbest;
EDGEIM(r, c) = -edgeNo;
% If this point is a junction exit here
if JUNCT(r, c);
endType = 1; % Mark end as being a junction
return;
else
% Get the next set of available pixels to link.
[ra, ca, rj, cj] = availablepixels(r, c, edgeNo);
end
end
% If we get here we are at an endpoint or our sequence of pixels form a
% loop. If it is a loop the edgelist should have start and end points
% matched to form a loop. If the number of points in the list is four or
% more (the minimum number that could form a loop), and the endpoints are
% within a pixel of each other, append a copy of the first point to the end
% to complete the loop
endType = 0; % Mark end as being free, unless it is reset below
if length(edgepoints) >= 4
if abs(edgepoints(1,1) - edgepoints(end,1)) <= 1 && ...
abs(edgepoints(1,2) - edgepoints(end,2)) <= 1
edgepoints = [edgepoints
edgepoints(1,:)];
endType = 5; % Mark end as being a loop
end
end
%----------------------------------------------------------------------
% AVAILABLEPIXELS
%
% Find all the pixels that could be linked to point r, c
%
% Arguments: rp, cp - Row, col coordinates of pixel of interest.
% edgeNo - The edge number of the edge we are seeking to
% track. If not supplied its value defaults to 0
% resulting in all adjacent junctions being returned,
% (see note below)
%
% Returns: ra, ca - Row and column coordinates of available non-junction
% pixels.
% rj, cj - Row and column coordinates of available junction
% pixels.
%
% A pixel is avalable for linking if it is:
% 1) Adjacent, that is it is 8-connected.
% 2) Its value is 1 indicating it has not already been assigned to an edge
% 3) or it is a junction that has not been labeled -edgeNo indicating we have
% not already assigned it to the current edge being tracked. If edgeNo is
% 0 all adjacent junctions will be returned
function [ra, ca, rj, cj] = availablepixels(rp, cp, edgeNo)
global EDGEIM;
global JUNCT;
global ROWS;
global COLS;
% If edgeNo not supplied set to 0 to allow all adjacent junctions to be returned
if ~exist('edgeNo', 'var'), edgeNo = 0; end
ra = []; ca = [];
rj = []; cj = [];
% row and column offsets for the eight neighbours of a point
roff = [-1 0 1 1 1 0 -1 -1];
coff = [-1 -1 -1 0 1 1 1 0];
r = rp+roff;
c = cp+coff;
% Find indices of arrays of r and c that are within the image bounds
ind = find((r>=1 & r<=ROWS) & (c>=1 & c<=COLS));
% A pixel is avalable for linking if its value is 1 or it is a junction
% that has not been labeled -edgeNo
for i = ind
if EDGEIM(r(i),c(i)) == 1 && ~JUNCT(r(i), c(i));
ra = [ra; r(i)];
ca = [ca; c(i)];
elseif (EDGEIM(r(i),c(i)) ~= -edgeNo) && JUNCT(r(i), c(i));
rj = [rj; r(i)];
cj = [cj; c(i)];
end
end
%---------------------------------------------------------------------
% UNITVECTOR Normalises a vector to unit magnitude
%
function nv = unitvector(v)
nv = v./sqrt(v(:)'*v(:));