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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 m = curveMoment(curve, p, q)
%CURVEMOMENT Compute inertia moment of a 2D curve.
% M = curveMoment(CURVE, P, Q)
%
% Example
% curveMoment
%
% See also
% polygons2d, curveCMoment, curveCSMoment
%
% Reference
% Based on ideas and references in:
% "Affine curve moment invariants for shape recognition"
% Dongmin Zhao and Jie Chen
% Pattern Recognition, 1997, vol. 30, pp. 865-901
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2009-03-25, using Matlab 7.7.0.471 (R2008b)
% Copyright 2009-2023 INRA - Cepia Software Platform
% coordinate of vertices
px = curve(:,1);
py = curve(:,2);
% compute centroids of line segments
cx = (px(1:end-1)+px(2:end))/2;
cy = (py(1:end-1)+py(2:end))/2;
% compute length of each line segment
dl = hypot(px(2:end)-px(1:end-1), py(2:end)-py(1:end-1));
% compute moment
m = zeros(size(p));
for i=1:length(p(:))
m(i) = sum(cx(:).^p(i) .* cy(:).^q(i) .* dl(:));
end
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