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Hausdorff Distance

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Hausdorff Distance



19 Feb 2010 (Updated )

Calculates the Hausdorff Distance between two sets of points in a Euclidean metric space.

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The Hausdorff Distance is a mathematical construct to measure the "closeness" of two sets of points that are subsets of a metric space.

Such a measure may be used to assign a scalar score to the similarity between two trajectories, data clouds or any sets of points.

This function will return the Hausdorff Distance between two sets of points.

For more information on the Hausdorff Distance:


Hausdorff Distance inspired this file.

This file inspired Modified Hausdorff Distance and *Mex* Modified Hausdorff Distance For 2 D Point Sets.

MATLAB release MATLAB 7.8 (R2009a)
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Comments and Ratings (14)
29 Jan 2015 Zachary Danziger

@Yunus, Your question is a bit ambiguous. As written, the code will interpret your input sets as having one 2-dimensional point each, in which case we do expect a non-zero HD because the points are different, and in fact, are different precisely by their Euclidean distance. If you are interested in comparing sets with two 1-dimensional points each you need to transpose your inputs. Rows are treated as observations and columns as dimensions.

hd = HausdorffDist([1 2],[2 1]) -> 1.41
hd = HausdorffDist([1 2]',[2 1]') -> 0

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29 Jan 2015 Yunus Emre

Very useful code indeed. I have a question :

Assume that we have two sets, i.e {1,2} and {2,1}. The Hausdorff distance between these two sets are zero. However, in the code we got the value of Euclidean distance between points. Am I wrong?

06 Nov 2014 Zachary Danziger

@Shaan, One way would be to treat those images as vectors of pixels, and use the code on those vectors, however, many more nuanced implementations of HD for image comparison have been developed.

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06 Nov 2014 Shaan

Shaan (view profile)

How do you use this code to calculate Hausdorff distance between two binary images?

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16 May 2014 Amir Pasha Mahmoudzadeh

It is great code, but you need to fix your bugs: in order to achieve the same column for your both images, you can fix number of columns with the following codes:

nrows = max(size(I1,1), size(I2,1));
ncols = max(size(I1,2), size(I2,2));
nchannels = size(I1,3);

extendedI1 = [ I1, zeros(size(I1,1), ncols-size(I1,2), nchannels); ...
zeros(nrows-size(I1,1), ncols, nchannels)];

extendedI2 = [ I2, zeros(size(I2,1), ncols-size(I2,2), nchannels); ...
zeros(nrows-size(I2,1), ncols, nchannels)];


Also, Binary images don't give us the minimum numbers for Hausdorff Distance. I checked your codes with several binary images and all of the times the max Hausdorff Distance numbers were the correct answer, not the minimum number.

08 Feb 2014 Venkat R

Very fast and useful submission.
Works well for me. Thank you

09 Jan 2014 Pramit Mazumdar

I am having two vectors consisting of sequential locations visited by person-X and Y like:

X = [ (lat1,long1), (lat2,long2), (lat3,long3) ];

Y = [ (lat4,long4), (lat2,long2), (lat3,long3) ];

I need to find similarity between these two vectors. Can this Hausdorff distance help me in any way??

07 Aug 2013 Nejc Ilc  
03 Oct 2012 Zachary Danziger

Roel H,
Agreed on both counts. The code has been updated and re-posted. Doing some quick testing, the updates you recommended significantly improve speed for very large matrices, thank you.

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25 Sep 2012 Roel H

Roel H (view profile)

Nice code, thanks for writing this function!

Though I have a few remarks. For the largeMat case, it is better to use bsxfun instead of repmat, as it is more efficient(faster) for large matrices which obviously is the case. Also it may be an idea to postpone the "sqrt" call untill a maximum is found. This won't change the outcome, but should require less computations

%existing code:
minP = min(sqrt(sum((repmat(P(p,:),[sQ(1) 1]) - Q).^2,2)));
minP = min(sum((bsxfun(@minus,P(p,:),Q)).^2,2));

30 Apr 2012 Zachary Danziger

It was brought to my attention by Roey Baror of Tel-Aviv University that creating/outputting a matrix of distances between all points could quickly tax the system's memory for large matrices, such as high resolution images. The update provides a secondary algorithm to calculate the Hausdorff Distance without storing the large matrix in memory, and detects automatically when this secondary algorithm is necessary.

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24 Mar 2012 s_ppu

s_ppu (view profile)

12 Jul 2011 longan

longan (view profile)

07 Jan 2011 SasiKanth

SasiKanth (view profile)

Nice code and well commented to!

28 May 2010 1.1

Edits Added the matrix of distances as an output option. Fixed a bug that would cause an error if one of the sets was a single point. Removed excess calls to "size" and "length". - May 2010

15 Jun 2010 1.2

Generalizes the code to allow N-dimensional point sets. This update is inspired by file 27905, which has a good implementation of HD beyond 2-D sets of points.

30 Apr 2012 1.3

The code now automatically switches to a secondary algorithm when there is insufficient memory to compute and store a matrix containing distances between all constituent points. It also allows the user to manually choose the desired algorithm.

04 Oct 2012 1.4

Based on user comments, the algorithm for large data sets was updated for performance.

03 Apr 2013 1.6

An option for data visualization is now included.

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