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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,
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## 2 Redistributions in binary form must reproduce the above copyright
## notice, this list of conditions and the following disclaimer in the
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##
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## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
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function [hd, ind1, ind2] = hausdorffDistance(pts1, pts2)
%HAUSDORFFDISTANCE Hausdorff distance between two point sets.
%
% HD = hausdorffDistance(PTS1, PTS2)
% Computes the Hausdorff distance between the two point sets PTS1 and
% PTS2. The Hausdorf distance can be used to compare two shapes.
%
% The distance between a point x and a set Y is given by:
% d(x, Y) = inf { d(x,y) | y in Y }
% The distance between two non empty sets X and Y is given by:
% d(X, Y) = sup { d(x,Y) | x in X }
% The Hausdorff distance between sets X and Y distance is defined as the
% maximum of d(X,Y) and d(Y,X):
% HD(X,Y) = max { d(X,Y), d(Y,X) }
%
%
% Example
% % Compute Hausdorff distance between an ellipse and a rectangle
% % first define two shapes
% rect = resamplePolygon(orientedBoxToPolygon([20 30 80 40 30]), 60);
% poly = ellipseToPolygon([20 30 40 20 30], 500);
% % display the shapes
% figure; hold on
% drawPolygon(poly, 'b');
% drawPolygon(rect, 'g');
% axis equal;
% % compute hausdorff distance
% [hd ind1 ind2] = hausdorffDistance(poly, rect);
% p1h = poly(ind1, :);
% p2h = rect(ind2, :);
% drawPoint([p1h;p2h], 'mo');
% drawEdge([p1h p2h], 'm')
%
% See also
% points2d, minDistancePoints
%
% References
% http://en.wikipedia.org/wiki/Hausdorff_distance
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2012-05-04, using Matlab 7.9.0.529 (R2009b)
% Copyright 2012-2023 INRAE - Cepia Software Platform
% distance from pts1 to pts2
[dists1, ind12] = minDistancePoints(pts1, pts2);
[max1, ind11] = max(dists1);
% distance from pts2 to pts1
[dists2, ind22] = minDistancePoints(pts2, pts1);
[max2, ind21] = max(dists2);
% keep the max of the two distances
hd = max(max1, max2);
% keep the rigt indices
if max1 > max2
ind1 = ind11;
ind2 = ind12(ind11);
else
ind1 = ind22(ind21);
ind2 = ind21;
end
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