# Hausdorff Distance

**URL:** <https://discourse.slicer.org/t/hausdorff-distance/8443>\
**Category:** Support\
**Tags:** slicerrt\
**Created:** [September 16, 2019, 10:05am UTC](https://discourse.slicer.org/t/hausdorff-distance/8443 "2019-09-16T10:05:21Z")\
**Posts on this page:** 8\
**Page:** 1

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**Author:** ![MFS-YES](https://avatars.discourse-cdn.com/v4/letter/m/bbe5ce/32.png) [@MFS-YES](https://discourse.slicer.org/u/MFS-YES)\
**Post date:** [September 16, 2019, 10:05am UTC](https://discourse.slicer.org/t/hausdorff-distance/8443/1 "2019-09-16T10:05:21Z")

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Hello!  
I compute Dice and Hausdorff Distance, you can see the result. So, I know that Dice similarity ranged from 0 to 1. How Hausdorff distance was ranged? Consequently, how to interpret this result. Any explanation will be helpful. Thanks! ![mmexport1568627962647](https://us1.discourse-cdn.com/flex002/uploads/slicer/original/3X/7/a/7a11f564140c946ade8775e5feeaa801b780f82d.png)

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**Author:** ![cpinter](https://sea2.discourse-cdn.com/flex002/user_avatar/discourse.slicer.org/cpinter/32/7995_2.png) [@cpinter](https://discourse.slicer.org/u/cpinter)\
**Post date:** [September 16, 2019, 1:43pm UTC](https://discourse.slicer.org/t/hausdorff-distance/8443/2 "2019-09-16T13:43:44Z")

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Hausdorff distance is millimeters.

Here’s the wikipedia page for the Hausdorff distance that explains the concept with a helpful figure

> **[Hausdorff distance](https://en.wikipedia.org/wiki/Hausdorff_distance)**
>
> In mathematics, the Hausdorff distance, or Hausdorff metric, also called Pompeiu–Hausdorff distance, measures how far two subsets of a metric space are from each other. It turns the set of non-empty compact subsets of a metric space into a metric space in its own right. It is named after Felix Hausdorff.
> Informally, two sets are close in the Hausdorff distance if every point of either set is close to some point of the other set. The Hausdorff distance is the longest distance you can be forced to...

Here is the doxygen page from the Plastimatch Hausdorff algorithm with equations (this is what the module uses, need to scroll down a bit)  
[http://plastimatch.org/doxygen/classHausdorff\_\_distance.html](http://plastimatch.org/doxygen/classHausdorff__distance.html)

By the way this last link is referenced from the module documentation  
[https://www.slicer.org/wiki/Documentation/Nightly/Modules/SegmentComparison](https://www.slicer.org/wiki/Documentation/Nightly/Modules/SegmentComparison)

It is generally a good idea to look at the documentation, as many times you will find useful information there.

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<div class="post-metadata">

**Author:** ![MFS-YES](https://avatars.discourse-cdn.com/v4/letter/m/bbe5ce/32.png) [@MFS-YES](https://discourse.slicer.org/u/MFS-YES)\
**Post date:** [September 17, 2019, 4:02am UTC](https://discourse.slicer.org/t/hausdorff-distance/8443/3 "2019-09-17T04:02:52Z")

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Thank! ![Emoji](https://s.yimg.com/nq/yemoji_assets/latest/yemoji_assets/1f44d.png "Emoji")

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**Author:** ![John\_Agapito](https://sea2.discourse-cdn.com/flex002/user_avatar/discourse.slicer.org/john_agapito/32/12206_2.png) [@John\_Agapito](https://discourse.slicer.org/u/John_Agapito)\
**Post date:** [September 14, 2021, 8:00pm UTC](https://discourse.slicer.org/t/hausdorff-distance/8443/4 "2021-09-14T20:00:22Z")

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on a related note…does anyone have any information on whether the plastimatch Hausdorff or DICE calculations have been validated against any other viable option?

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**Author:** ![gcsharp](https://sea2.discourse-cdn.com/flex002/user_avatar/discourse.slicer.org/gcsharp/32/863_2.png) [@gcsharp](https://discourse.slicer.org/u/gcsharp)\
**Post date:** [September 14, 2021, 8:05pm UTC](https://discourse.slicer.org/t/hausdorff-distance/8443/5 "2021-09-14T20:05:50Z")

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Yes, we validated it against analytic solids prior to using it to score the MICCAI 2015 H&N Grand Challenge. That means comparing translated and resized cubes, spheres, and cylinders, and comparing against the analytic solution.

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**Author:** ![John\_Agapito](https://sea2.discourse-cdn.com/flex002/user_avatar/discourse.slicer.org/john_agapito/32/12206_2.png) [@John\_Agapito](https://discourse.slicer.org/u/John_Agapito)\
**Post date:** [September 15, 2021, 12:29pm UTC](https://discourse.slicer.org/t/hausdorff-distance/8443/6 "2021-09-15T12:29:01Z")

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Thanks Greg - are there any publications or links to details available anywhere?  
We’d like to use slicerRT to assess AI contouring quality in a research project.

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**Author:** ![gcsharp](https://sea2.discourse-cdn.com/flex002/user_avatar/discourse.slicer.org/gcsharp/32/863_2.png) [@gcsharp](https://discourse.slicer.org/u/gcsharp)\
**Post date:** [September 17, 2021, 7:34pm UTC](https://discourse.slicer.org/t/hausdorff-distance/8443/7 "2021-09-17T19:34:51Z")

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Hi John. I checked, but that information was not included in the paper. I guess you could cite as “Personal communication”. Sorry.

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**Author:** ![John\_Agapito](https://sea2.discourse-cdn.com/flex002/user_avatar/discourse.slicer.org/john_agapito/32/12206_2.png) [@John\_Agapito](https://discourse.slicer.org/u/John_Agapito)\
**Post date:** [September 18, 2021, 11:25am UTC](https://discourse.slicer.org/t/hausdorff-distance/8443/8 "2021-09-18T11:25:33Z")

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Thanks for checking Greg. Much obliged.