hausdorffDistance

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

0001 function [hd, ind1, ind2] = hausdorffDistance(pts1, pts2)
0002 %HAUSDORFFDISTANCE  Hausdorff distance between two point sets.
0003 %
0004 %   HD = hausdorffDistance(PTS1, PTS2)
0005 %   Computes the Hausdorff distance between the two point sets PTS1 and
0006 %   PTS2. The Hausdorf distance can be used to compare two shapes.
0007 %
0008 %   The distance between a point x and a set Y is given by:
0009 %     d(x, Y) = inf { d(x,y) | y in Y }
0010 %   The distance between two non empty sets X and Y is given by:
0011 %     d(X, Y) = sup { d(x,Y) | x in X }
0012 %   The Hausdorff distance between sets X and Y distance is defined as the
0013 %   maximum of d(X,Y) and d(Y,X):
0014 %     HD(X,Y) = max { d(X,Y), d(Y,X) }
0015 %
0016 %
0017 %   Example
0018 %   % Compute Hausdorff distance between an ellipse and a rectangle
0019 %     % first define two shapes
0020 %     rect = resamplePolygon(orientedBoxToPolygon([20 30 80 40 30]), 60);
0021 %     poly = ellipseToPolygon([20 30 40 20 30], 500);
0022 %     % display the shapes
0023 %     figure; hold on
0024 %     drawPolygon(poly, 'b');
0025 %     drawPolygon(rect, 'g');
0026 %     axis equal;
0027 %     % compute hausdorff distance
0028 %     [hd ind1 ind2] = hausdorffDistance(poly, rect);
0029 %     p1h = poly(ind1, :);
0030 %     p2h = rect(ind2, :);
0031 %     drawPoint([p1h;p2h], 'mo');
0032 %     drawEdge([p1h p2h], 'm')
0033 %
0034 %   See also
0035 %     points2d, minDistancePoints
0036 %
0037 %   References
0038 %   http://en.wikipedia.org/wiki/Hausdorff_distance
0039 %
0040 
0041 % ------
0042 % Author: David Legland
0043 % e-mail: david.legland@inrae.fr
0044 % Created: 2012-05-04,    using Matlab 7.9.0.529 (R2009b)
0045 % Copyright 2012 INRAE - Cepia Software Platform.
0046 
0047 % distance from pts1 to pts2
0048 [dists1, ind12] = minDistancePoints(pts1, pts2);
0049 [max1, ind11] = max(dists1);
0050 
0051 % distance from pts2 to pts1
0052 [dists2, ind22] = minDistancePoints(pts2, pts1);
0053 [max2, ind21] = max(dists2);
0054 
0055 % keep the max of the two distances
0056 hd = max(max1, max2);
0057 
0058 % keep the rigt indices
0059 if max1 > max2
0060     ind1 = ind11;
0061     ind2 = ind12(ind11);
0062 else
0063     ind1 = ind22(ind21);
0064     ind2 = ind21;
0065 end