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## Copyright (C) 2024 David Legland
## All rights reserved.
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are met:
##
## 1 Redistributions of source code must retain the above copyright notice,
## this list of conditions and the following disclaimer.
## 2 Redistributions in binary form must reproduce the above copyright
## notice, this list of conditions and the following disclaimer in the
## documentation and/or other materials provided with the distribution.
##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
##
## The views and conclusions contained in the software and documentation are
## those of the authors and should not be interpreted as representing official
## policies, either expressed or implied, of the copyright holders.
function varargout = imageGraph(img, varargin)
%IMAGEGRAPH Create equivalent graph of a binary image.
%
% [N E] = imageGraph(IMG);
% or
% [N E F] = imageGraph(IMG);
% create graph representing adjacencies in image. N is the array of
% nodes, E is the array of edges, and F is a 4-columns array containing
% indices of vertices of each face.
% IMG can be either 2D or 3D image.
% This functions uses only 4 neighbors in 2D, and 6 neighbors in 3D.
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2004-06-28
% Copyright 2004-2023 INRA - TPV URPOI - BIA IMASTE
%% Initialisations
nodes = [];
edges = zeros(0, 2);
faces = zeros(0, 4);
cells = [];
dim = size(img);
nd = ndims(img);
%% Main processing
if nd == 2
% Process planar image
N1 = dim(1);
N2 = dim(2);
% first find nodes, equivalent to pixels
ind = find(img);
[x, y] = ind2sub([N1 N2], ind);
nodes = [x y];
% find vertical edges
ind = find(img(1:N1, 1:N2-1) & img(1:N1, 2:N2));
for i=1:length(ind)
[x, y] = ind2sub([N1 N2-1], ind(i));
i1 = find(ismember(nodes, [x y], 'rows'));
i2 = find(ismember(nodes, [x y+1], 'rows'));
edges(size(edges, 1)+1, 1:2) = [i1 i2];
end
% find horizontal edges
ind = find(img(1:N1-1, 1:N2) & img(2:N1, 1:N2));
for i=1:length(ind)
[x, y] = ind2sub([N1-1 N2], ind(i));
i1 = find(ismember(nodes, [x y], 'rows'));
i2 = find(ismember(nodes, [x+1 y], 'rows'));
edges(size(edges, 1)+1, 1:2) = [i1 i2];
end
% find faces
ind = find(img(1:N1-1, 1:N2-1) & img(2:N1, 1:N2-1) & ...
img(1:N1-1, 2:N2) & img(2:N1, 2:N2) );
for i=1:length(ind)
[x, y] = ind2sub([N1-1 N2-1], ind(i));
i1 = find(ismember(nodes, [x y], 'rows'));
i2 = find(ismember(nodes, [x+1 y], 'rows'));
i3 = find(ismember(nodes, [x+1 y+1], 'rows'));
i4 = find(ismember(nodes, [x y+1], 'rows'));
faces(size(faces, 1)+1, 1:4) = [i1 i2 i3 i4];
end
elseif nd == 3
% Process 3D image
N1 = dim(1);
N2 = dim(2);
N3 = dim(3);
% first find nodes, equivalent to pixels
ind = find(img);
[x, y, z] = ind2sub([N1 N2 N3], ind);
nodes = [x y z];
% find edges in direction 1
ind = find(img(1:N1-1, 1:N2, 1:N3) & img(2:N1, 1:N2, 1:N3));
[x, y, z] = ind2sub([N1-1 N2 N3], ind);
i1 = find(ismember(nodes, [x y z], 'rows'));
i2 = find(ismember(nodes, [x+1 y z], 'rows'));
edges = [edges ; [i1 i2]];
% find edges in direction 2
ind = find(img(1:N1, 1:N2-1, 1:N3) & img(1:N1, 2:N2, 1:N3));
[x, y, z] = ind2sub([N1 N2-1 N3], ind);
i1 = find(ismember(nodes, [x y z], 'rows'));
i2 = find(ismember(nodes, [x y+1 z], 'rows'));
edges = [edges ; [i1 i2]];
% find edges in direction 3
ind = find(img(1:N1, 1:N2, 1:N3-1) & img(1:N1, 1:N2, 2:N3));
[x, y, z] = ind2sub([N1 N2 N3-1], ind);
i1 = find(ismember(nodes, [x y z], 'rows'));
i2 = find(ismember(nodes, [x y z+1], 'rows'));
edges = [edges ; [i1 i2]];
% find faces in direction 1
ind = find(img(1:N1, 1:N2-1, 1:N3-1) & img(1:N1, 1:N2-1, 2:N3) & ...
img(1:N1, 2:N2, 1:N3-1) & img(1:N1, 2:N2, 2:N3) );
[x, y, z] = ind2sub([N1 N2-1 N3-1], ind);
i1 = find(ismember(nodes, [x y z], 'rows'));
i2 = find(ismember(nodes, [x y+1 z], 'rows'));
i3 = find(ismember(nodes, [x y+1 z+1], 'rows'));
i4 = find(ismember(nodes, [x y z+1], 'rows'));
faces = [faces; [i1 i2 i3 i4]];
% find faces in direction 2
ind = find(img(1:N1-1, 1:N2, 1:N3-1) & img(1:N1-1, 1:N2, 2:N3) & ...
img(2:N1, 1:N2, 1:N3-1) & img(2:N1, 1:N2, 2:N3) );
[x, y, z] = ind2sub([N1-1 N2 N3-1], ind);
i1 = find(ismember(nodes, [x y z], 'rows'));
i2 = find(ismember(nodes, [x+1 y z], 'rows'));
i3 = find(ismember(nodes, [x+1 y z+1], 'rows'));
i4 = find(ismember(nodes, [x y z+1], 'rows'));
faces = [faces; [i1 i2 i3 i4]];
% find faces in direction 3
ind = find(img(1:N1-1, 1:N2-1, 1:N3) & img(1:N1-1, 2:N2, 1:N3) & ...
img(2:N1, 1:N2-1, 1:N3) & img(2:N1, 2:N2, 1:N3) );
[x, y, z] = ind2sub([N1-1 N2-1 N3], ind);
i1 = find(ismember(nodes, [x y z], 'rows'));
i2 = find(ismember(nodes, [x+1 y z], 'rows'));
i3 = find(ismember(nodes, [x+1 y+1 z], 'rows'));
i4 = find(ismember(nodes, [x y+1 z], 'rows'));
faces = [faces; [i1 i2 i3 i4]];
end
%% Format output
if nargout == 1
graph.nodes = nodes;
graph.edges = edges;
graph.faces = faces;
if nd > 2
graph.cells = cells;
end
varargout{1} = graph;
elseif nargout == 2
varargout{1} = nodes;
varargout{2} = edges;
elseif nargout == 3
varargout{1} = nodes;
varargout{2} = edges;
varargout{3} = faces;
end
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