Computing the minimum Hausdorff distance for point sets under translation

1990 ◽  
Author(s):  
Daniel P. Huttenlocher ◽  
Klara Kedem
Keyword(s):  
Hausdorff Distance ◽  
Point Sets

scholarly journals The directed Hausdorff distance between imprecise point sets

2011 ◽  
Vol 412 (32) ◽  
pp. 4173-4186 ◽  
Author(s):  
Christian Knauer ◽  
Maarten Löffler ◽  
Marc Scherfenberg ◽  
Thomas Wolle
Keyword(s):  
Hausdorff Distance ◽  
Point Sets

APPROXIMATE NEAREST NEIGHBOR SEARCH UNDER TRANSLATION INVARIANT HAUSDORFF DISTANCE

2011 ◽  
Vol 21 (03) ◽  
pp. 369-381
Author(s):  
CHRISTIAN KNAUER ◽  
MARC SCHERFENBERG
Keyword(s):  
Hausdorff Distance ◽  
Nearest Neighbor ◽  
Nearest Neighbor Search ◽  
Query Point ◽  
Point Sets ◽  
Translation Invariant ◽  
Approximation Factor ◽  
Neighbor Search ◽  
Point Set ◽  
Search Reduction

We present an embedding and search reduction which allow us to build the first data structure for the nearest neighbor search among small point sets with respect to the directed Hausdorff distance under translation. The search structure is non-heuristic in the sense that the quality of the results, the performance, and the space bound are guaranteed. Let n denote the number of point sets in the data base, s the maximal size of a point set, and d the dimension of the points. The nearest neighbor of a query point set under the translation invariant directed Hausdorff distance can be approximated by one or several nearest neighbor searches for single points in the Euclidean embedding space ℝd(s-1). The approximation factor is [Formula: see text] in case of even s and [Formula: see text] when s is odd. Depending on the direction of the Hausdorff distance either the number of queries or the space requirements are exponential in s. Furthermore it is shown how to find the exact nearest neighbor under the directed Hausdorff distance without transformation of the point sets within some weaker time and space bounds.

scholarly journals An efficient approach to directly compute the exact Hausdorff distance for 3D point sets

2017 ◽  
Vol 24 (3) ◽  
pp. 261-277 ◽  
Author(s):  
Dejun Zhang ◽  
Fazhi He ◽  
Soonhung Han ◽  
Lu Zou ◽  
Yiqi Wu ◽  
...  
Keyword(s):  
Hausdorff Distance ◽  
Point Sets ◽  
Efficient Approach

A local start search algorithm to compute exact Hausdorff Distance for arbitrary point sets

2017 ◽  
Vol 67 ◽  
pp. 139-148 ◽  
Author(s):  
Yilin Chen ◽  
Fazhi He ◽  
Yiqi Wu ◽  
Neng Hou
Keyword(s):  
Hausdorff Distance ◽  
Search Algorithm ◽  
Arbitrary Point ◽  
Point Sets

scholarly journals The Directed Hausdorff Distance between Imprecise Point Sets

2009 ◽  
pp. 720-729 ◽  
Author(s):  
Christian Knauer ◽  
Maarten Löffler ◽  
Marc Scherfenberg ◽  
Thomas Wolle
Keyword(s):  
Hausdorff Distance ◽  
Point Sets
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