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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 curv = polygonCurvature(poly, M)
%POLYGONCURVATURE Estimate curvature on polygon vertices using polynomial fit.
%
% CURV = polygonCurvature(POLY, M)
% Estimate the curvature for each vertex of a polygon, using polynomial
% fit from the M vertices located around current vertex. M is usually an
% odd value, resulting in a symmetric neighborhood.
%
% Polynomial fitting is of degree 2.
%
%
% Example
% img = imread('circles.png');
% img = imfill(img, 'holes');
% imgf = imfilter(double(img), fspecial('gaussian', 7, 2));
% figure(1), imshow(imgf);
% contours = imContours(imgf, .5); poly = contours{1};
% poly2 = smoothPolygon(poly, 7);
% hold on; drawPolygon(poly2);
% curv = polygonCurvature(poly2, 11);
% figure; plot(curv);
% minima = bwlabel(imextendedmin(curv, .05));
% centroids = imCentroid(minima);
% inds = round(centroids(:,2));
% figure(1); hold on; drawPoint(poly2(inds, :), 'g*')
%
% See also
% polygons2d, polylineCurvature
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2018-03-02, using Matlab 9.3.0.713579 (R2017b)
% Copyright 2018-2023 INRA - Cepia Software Platform
% number of vertices of polygon
n = size(poly, 1);
% allocate memory for result
curv = zeros(n, 1);
% number of vertices before and after current vertex
s1 = floor((M - 1) / 2);
s2 = ceil((M - 1) / 2);
% parametrisation basis
% As we recenter the points, the constant factor is omitted
ti = (-s1:s2)';
X = [ti ti.^2];
% Iteration on vertex indices
for i = 1:n
% coordinate of current vertex, for recentring neighbor vertices
x0 = poly(i,1);
y0 = poly(i,2);
% indices of neighbors
inds = i-s1:i+s2;
inds = mod(inds-1, n) + 1;
% Least square estimation using mrdivide
xc = X \ (poly(inds,1) - x0);
yc = X \ (poly(inds,2) - y0);
% compute curvature
curv(i) = 2 * (xc(1)*yc(2) - xc(2)*yc(1) ) / power(xc(1)^2 + yc(1)^2, 3/2);
end
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