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/* This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
* See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
* Author: François Godi
*
* Copyright (C) 2015 Inria
*
* Modification(s):
* - YYYY/MM Author: Description of the modification
* - 2019/06 Vincent Rouvreau : Fix #11 - Distance computation shall be better documented.
*/
#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,
* where the distance between points is the sup norm in \f$\mathbb{R}^2\f$ (not the Euclidean distance).
*
* \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.
*
* \section bottleneckdistanceprecision Distance computation
*
* The following example explains how the distance is computed:
*
* \code{.cpp}
#include <gudhi/Bottleneck.h>
#include <iostream>
#include <vector>
#include <utility> // for pair
int main() {
std::vector< std::pair<double, double> > diag1, diag2;
diag1.emplace_back(0., 0.);
diag2.emplace_back(0., 13.);
double b = Gudhi::persistence_diagram::bottleneck_distance(diag1, diag2);
std::clog << "Bottleneck distance = " << b << std::endl;
}
* \endcode
*
* \code Bottleneck distance = 6.5
* \endcode
*
* \image html bottleneck_distance_example.png The point (0, 13) is at distance 6.5 from the diagonal and more specifically from the point (6.5, 6.5)
*
* \section bottleneckbasicexample Basic example
*
* This other example computes the bottleneck distance from 2 persistence diagrams:
* \include Bottleneck_distance/bottleneck_basic_example.cpp
*
* \code
Bottleneck distance = 0.75
Approx bottleneck distance = 0.808176
* \endcode
*/
/** @} */ // end defgroup bottleneck_distance
} // namespace persistence_diagram
} // namespace Gudhi
#endif // DOC_BOTTLENECK_DISTANCE_INTRO_BOTTLENECK_DISTANCE_H_
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