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

Package: matgeom