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## Copyright (C) 2004-2011 David Legland <david.legland@grignon.inra.fr>
## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
## 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.
## -*- texinfo -*-
## @deftypefn {Function File} {[@var{coefs} @var{bnds}]=} polynomialCurveSetFit (@var{img})
## @deftypefnx {Function File} {@dots{} =} polynomalCurveSetFit (@var{img}, @var{deg})
## @deftypefnx {Function File} {[@dots{} @var{lbl}] =} polynomalCurveSetFit (@dots{})
## Fit a set of polynomial curves to a segmented image
##
## Result is a cell array of matrices. Each matrix is @var{deg}+1-by-2, and
## contains coefficients of polynomial curve for each coordinate.
## @var{bnds} contains the boundary of the parametrizations.
## @var{img} is first binarised, then skeletonized.
##
## Also returns an image of labels @var{lbl} for the segmented curves. The max label
## is the number of curves, and the length of @var{coefs}.
##
## Requires the toolboxes:
## - Optimization
## - Image Processing
##
## @seealso{polynomialCurves2d, polynomialCurveFit}
## @end deftypefn
function [coefs bnds lblBranches] = polynomialCurveSetFit(seg, varargin)
# default degree for curves
deg = 2;
if ~isempty(varargin)
deg = varargin{1};
end
# ajoute un contour
seg([1 end], :) = 1;
seg(:, [1 end]) = 1;
# skeletise le segmentat
seg = bwmorph(seg, 'shrink', Inf);
# compute image of multiple points (intersections between curves)
imgNodes = imfilter(double(seg), ones([3 3])) .* seg > 3;
# compute coordinate of nodes, as c entroids of the multiple points
lblNodes = bwlabel(imgNodes, 4);
struct = regionprops(lblNodes, 'Centroid');
nodes = zeros(length(struct), 2);
for i=1:length(struct)
nodes(i, 1:2) = struct(i).Centroid;
end
# enleve les bords de l'image
seg([1 end], :) = 0;
seg(:, [1 end]) = 0;
# Isoles les branches
imgBranches = seg & ~imgNodes;
lblBranches = bwlabel(imgBranches, 8);
# # donne une couleur a chaque branche, et affiche
# map = colorcube(max(lblBranches(:))+1);
# rgbBranches = label2rgb(lblBranches, map, 'w', 'shuffle');
# imshow(rgbBranches);
# number of curves
nBranches = max(lblBranches(:));
# allocate memory
coefs = cell(nBranches, 1);
bnds = cell(nBranches, 1);
# For each curve, find interpolated polynomial curve
for i = 1:nBranches
# extract points corresponding to current curve
imgBranch = lblBranches == i;
points = chainPixels (imgBranch);
# check number of points is sufficient
if size(points, 1) < max(deg+1-2, 2)
# find labels of nodes
inds = unique(lblNodes(imdilate(imgBranch, true (3,3))));
inds = inds(inds ~= 0);
if length(inds) < 2
warning ("geometry:poylnomialCurveSetFit", ...
['Could not find extremities of branch number ' num2str(i)]);
continue;
end
# consider extremity nodes
node0 = nodes(inds(1), :);
node1 = nodes(inds(2), :);
# use only a linear approximation
xc = zeros(1, deg+1);
yc = zeros(1, deg+1);
xc(1) = node0(1);
yc(1) = node0(2);
xc(2) = node1(1)-node0(1);
yc(2) = node1(2)-node0(2);
# assigne au tableau de courbes
coefs{i} = [xc;yc];
bnds{i} = [0 1];
# next branch
continue;
end
# find nodes closest to first and last points of the current curve
[dist, ind0] = minDistancePoints(points(1, :), nodes); ##ok<*ASGLU>
[dist, ind1] = minDistancePoints(points(end, :), nodes);
# add nodes to the curve.
points = [nodes(ind0,:); points; nodes(ind1,:)]; ##ok<AGROW>
# parametrization of the polyline
t = parametrize(points);
t = t / max(t);
# fit a polynomial curve to the set of points
[xc yc] = polynomialCurveFit(...
t, points, deg, ...
0, {points(1,1), points(1,2)},...
1, {points(end,1), points(end,2)});
# stores result
coefs{i} = [xc;yc];
bnds{i} = t([1 end]);
end
endfunction
function points = chainPixels(img, varargin)
#CHAINPIXELS return the list of points which constitute a curve on image
# output = chainPixels(input)
conn = 8;
if ~isempty(varargin)
conn = varargin{1};
end
# matrice de voisinage
if conn == 4
f = [0 1 0;1 1 1;0 1 0];
elseif conn == 8
f = ones([3 3]);
end
# find extremity points
nb = imfilter(double(img), f) .* img;
imgEnding = nb == 2 | nb == 1;
[yi xi] = find(imgEnding);
# extract coordinates of points
[y x] = find(img);
# index of first point
if isempty(xi)
# take arbitrary point
ind = 1;
else
ind = find(x==xi(1) & y==yi(1));
end
# allocate memory
points = zeros(length(x), 2);
if conn == 8
for i = 1:size(points, 1)
# avoid multiple neighbors (can happen in loops)
ind = ind(1);
# add current point to chained curve
points(i,:) = [x(ind) y(ind)];
# remove processed coordinate
x(ind) = [];
y(ind) = [];
# find next candidate
ind = find(abs(x-points(i,1))<=1 & abs(y-points(i,2))<=1);
end
else
for i = 1:size(points, 1)
# avoid multiple neighbors (can happen in loops)
ind = ind(1);
# add current point to chained curve
points(i,:) = [x(ind) y(ind)];
# remove processed coordinate
x(ind) = [];
y(ind) = [];
# find next candidate
ind = find(abs(x-points(i,1)) + abs(y-points(i,2)) <=1 );
end
end
endfunction
%!demo
%! [m, cmap] = imread ("default.img");
%! m = ind2gray (m, cmap);
%! mbw = im2bw(m, graythresh(m)*1.3);
%!
%! [c t] = polynomialCurveSetFit (mbw);
%!
%! figure(1)
%! clf;
%! imshow (m)
%! hold on
%! for i=1:numel(c)
%! if !isempty (c{i})
%! drawPolynomialCurve (t{i}, c{i}(1,:),c{i}(2,:));
%! endif
%! endfor
%!
%! hold off