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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 = imageBoundaryGraph(img)
%IMAGEBOUNDARYGRAPH Convert boundary of a 2D/3D binary image into a graph or mesh.
%
% [NODES, EDGES] = imageBoundaryGraph(IMG) (2D)
% [NODES, EDGES, FACES] = imageBoundaryGraph(IMG) (3D)
% Creates a graph on the boundary of binary image IMG. Each pixel is
% considered as a unit square (or cube), centered on integer coordinates.
% Boundary of the shape is selected as a graph.
%
% Result is a set of nodes with (x,y) or (x,y,z) coordinates, a set of
% edges linking two neighbour nodes, and in 3D also a set of square
% faces, containing reference to each 4-tuple of nodes.
%
% The resulting shell is open if the binary structure touches edges of
% image.
%
% See also
% patch, drawMesh
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2004-06-28
% Copyright 2004-2023 INRA - TPV URPOI - BIA IMASTE
%% Initialisations
% retrieve image size
dim = size(img);
nd = length(dim);
if nd==2 && (dim(1)==1 || dim(2)==1)
nd=1;
end
% initialize result arrays
nodes = zeros([0 nd]); % coordinates of vertices
edges = zeros([0 2]); % first node and second nodes
faces = zeros([0 4]); % indices of 4 corners of each square face
%% Main processing
% switch processing depending on dimension
if nd == 1
img = img(:)>0;
D1 = size(img,1);
nodes = find(img(1:D1-1) ~= img(2:D1))+.5;
if nargout == 1
varargout{1} = nodes;
end
return
elseif nd == 2
D1 = size(img, 1);
D2 = size(img, 2);
px = [];
py = [];
ind = find(img(1:D1-1, :) ~= img(2:D1, :));
[x, y] = ind2sub([D1-1 D2], ind);
px = [px; reshape([x+.5 x+.5]', length(x)*2,1)];
py = [py; reshape([y-.5 y+.5]', length(x)*2,1)];
ind = find(img(:, 1:D2-1) ~= img(:, 2:D2));
[x, y] = ind2sub([D1 D2-1], ind);
px = [px; reshape([x-.5 x+.5]', length(x)*2,1)];
py = [py; reshape([y+.5 y+.5]', length(x)*2,1)];
[nodes, i, j] = unique([py px], 'rows'); %#ok<ASGLU>
ne = floor(size(px, 1)/2);
edges = repmat(1:2, [ne 1]) + repmat((0:2:2*ne-1)', [1 2]);
for i=1:length(edges(:))
edges(i) = j(edges(i));
end
edges = unique(sort(edges, 2), 'rows');
elseif nd == 3
D1 = size(img, 1);
D2 = size(img, 2);
D3 = size(img, 3);
px = [];
py = [];
pz = [];
ind = find(img(1:D1-1, :, :) ~= img(2:D1, :, :));
[x, y, z] = ind2sub([D1-1 D2 D3], ind);
px = [px; reshape([x+.5 x+.5 x+.5 x+.5]', length(x)*4,1)];
py = [py; reshape([y-.5 y+.5 y+.5 y-.5]', length(x)*4,1)];
pz = [pz; reshape([z-.5 z-.5 z+.5 z+.5]', length(x)*4,1)];
ind = find(img(:, 1:D2-1, :) ~= img(:, 2:D2, :));
[x, y, z] = ind2sub([D1 D2-1 D3], ind);
px = [px; reshape([x-.5 x-.5 x+.5 x+.5]', length(x)*4,1)];
py = [py; reshape([y+.5 y+.5 y+.5 y+.5]', length(x)*4,1)];
pz = [pz; reshape([z-.5 z+.5 z+.5 z-.5]', length(x)*4,1)];
ind = find(img(:, :, 1:D3-1) ~= img(:, :, 2:D3));
[x, y, z] = ind2sub([D1 D2 D3-1], ind);
px = [px; reshape([x-.5 x+.5 x+.5 x-.5]', length(x)*4,1)];
py = [py; reshape([y-.5 y-.5 y+.5 y+.5]', length(x)*4,1)];
pz = [pz; reshape([z+.5 z+.5 z+.5 z+.5]', length(x)*4,1)];
[nodes, i, j] = unique([py px pz], 'rows'); %#ok<ASGLU>
nf = floor(size(px, 1)/4);
faces = repmat(1:4, [nf 1]) + repmat((0:4:4*nf-1)', [1 4]);
for i=1:length(faces(:))
faces(i) = j(faces(i));
end
edges = [edges ; [faces(:,1) faces(:,2)]];
edges = [edges ; [faces(:,2) faces(:,3)]];
edges = [edges ; [faces(:,3) faces(:,4)]];
edges = [edges ; [faces(:,4) faces(:,1)]];
edges = unique(sort(edges, 2), 'rows');
end
%% format output arguments
if nargout == 3
varargout{1} = nodes;
varargout{2} = edges;
varargout{3} = faces;
elseif nargout == 2
varargout{1} = nodes;
varargout{2} = edges;
elseif nargout == 1
graph.nodes = nodes;
graph.edges = edges;
graph.faces = faces;
varargout{1} = graph;
end
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