Hausdorff Distance

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

Description

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: http://en.wikipedia.org/wiki/Hausdorff_distance

Acknowledgements

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)

[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.

[Roel H]

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)));
%sugestion:
minP = min(sum((bsxfun(@minus,P(p,:),Q)).^2,2));

[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.

[s_ppu]

 

[longan]

 

[SasiKanth]

Nice code and well commented to!