Talk:Hausdorff distance

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[edit] Is the figure wrong?

The figure doesn't seem to fit the definition of Hausdorff distance.

To get sup_x inf_y d(x,y), you want to choose an x in X that is maximally distant from Y. That would not be a point right on the near boundary of X, but on the opposite side (which is not pictured in the figure.)

For example, take the left line segment in the figure, the one supposedly exhibiting sup_x inf_y d(x,y). Take the point in X at the end of it. Now move that point a ways up into the interior of X. Now you have an x in X with a larger value of inf_y d(x,y). —Preceding unsigned comment added by 128.226.120.167 (talk) 16:17, 30 October 2007 (UTC)

If we suppose that X should be the complement of the green part (instead of X=the green part, as indicated in the picture), then perhaps this figure will work. --Kompik 19:28, 3 December 2007 (UTC)

The figure is indeed entirely wrong and needs to be replaced as soon as possible as it is no doubt causing a lot of confusion.

Kompik suggests that assigning X as the complement of the green part would make it work, and this is true for X. However, this would only solve the problem for the directed Hausdorff distance from X to Y (in essence, we should demonstrate that the Hausdorff distance is in fact the maximum of both directed distances). Also, the local maximum to the right remains confusing and as would be that the figures would be touching. Instead, I suggest an illustration with points instead of blobs: illustrate that the maximum distance of all paths between each point in X to a nearest point in Y is the Hausdorff distance. In other words: each point in X is at most d_H(X,Y) from Y.

This page has an excellent demonstration that could perhaps be animated in a GIF file. — Stimpy _talk 09:48, 3 January 2008 (UTC)

That link seems to have stopped working (404 Not Found).  --Lambiam 19:51, 11 April 2008 (UTC)

The answer is yes. I try a new version of this figure. Rocchini (talk) 12:53, 6 May 2008 (UTC)

I think the figure is correct as long as we take X and Y as being the green and blue lines respectively. The confusion arises if we try to interpret X and Y as being the regions enclosed by these lines, in which case the Hausdorff distnace from each point of X to the set Y is 0, as X is contained in Y. And if we assume that Y is the region outside of the blue line then we don't even have a Hausdorff distance between X and Y because Y is no longer a compact set. I have added a caption to the image to try to clarify the correct interpretation. Gandalf61 (talk) 11:22, 19 May 2008 (UTC)