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/* This file is part of the Gudhi Library. The Gudhi library
* (Geometric Understanding in Higher Dimensions) is a generic C++
* library for computational topology.
*
* Author: François Godi
*
* Copyright (C) 2015 Inria
*
* Modification(s):
* - YYYY/MM Author: Description of the modification
*/
#ifndef DOC_BOTTLENECK_DISTANCE_INTRO_BOTTLENECK_DISTANCE_H_
#define DOC_BOTTLENECK_DISTANCE_INTRO_BOTTLENECK_DISTANCE_H_
// needs namespace for Doxygen to link on classes
namespace Gudhi {
// needs namespace for Doxygen to link on classes
namespace persistence_diagram {
/** \defgroup bottleneck_distance Bottleneck distance
*
* \author François Godi
* @{
*
* \section bottleneckdefinition Definition
*
* The bottleneck distance measures the similarity between two persistence diagrams. It is the shortest distance b for
* which there exists a perfect matching between the points of the two diagrams (completed with all the points on the
* diagonal in order to ignore cardinality mismatchs) such that any couple of matched points are at distance at most b.
*
* \image html perturb_pd.png On this picture, the red edges represent the matching. The bottleneck distance is the length of the longest edge.
*
* This implementation is based on ideas from "Geometry Helps in Bottleneck Matching and Related Problems"
* \cite DBLP:journals/algorithmica/EfratIK01. Another relevant publication, although it was not used is
* "Geometry Helps to Compare Persistence Diagrams" \cite Kerber:2017:GHC:3047249.3064175.
*/
/** @} */ // end defgroup bottleneck_distance
} // namespace persistence_diagram
} // namespace Gudhi
#endif // DOC_BOTTLENECK_DISTANCE_INTRO_BOTTLENECK_DISTANCE_H_
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