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authorvrouvrea <vrouvrea@636b058d-ea47-450e-bf9e-a15bfbe3eedb>2016-04-14 07:17:44 +0000
committervrouvrea <vrouvrea@636b058d-ea47-450e-bf9e-a15bfbe3eedb>2016-04-14 07:17:44 +0000
commit4e784aca4df90d3fca9146bfd9e3feda98ce5f4c (patch)
tree89182d71a1cfe45b70410af70500e3e90f7aca52 /src/Witness_complex/doc/Witness_complex_doc.h
parentc829c36217c003b2068750aa8f23b6082636e6e1 (diff)
parentbaf1b5b39be90694b512fff9c79438bf362916f3 (diff)
Merge last trunk modifications (version 1.3.0)
git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/ST_cythonize@1113 636b058d-ea47-450e-bf9e-a15bfbe3eedb Former-commit-id: 608c3cb733a7723c865f82a4de9408c984227f1a
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+#ifndef WITNESS_COMPLEX_DOC_H_
+#define WITNESS_COMPLEX_DOC_H_
+
+/**
+ \defgroup witness_complex Witness complex
+
+ \author Siargey Kachanovich
+
+ \image html "Witness_complex_representation.png" "Witness complex representation"
+
+ \section Definitions
+
+ Witness complex \f$ Wit(W,L) \f$ is a simplicial complex defined on two sets of points in \f$\mathbb{R}^D\f$:
+
+ \li \f$W\f$ set of **witnesses** and
+ \li \f$L \subseteq W\f$ set of **landmarks**.
+
+ The simplices are based on landmarks
+ and a simplex belongs to the witness complex if and only if it is witnessed, that is:
+
+ \f$ \sigma \subset L \f$ is witnessed if there exists a point \f$w \in W\f$ such that
+ w is closer to the vertices of \f$ \sigma \f$ than other points in \f$ L \f$ and all of its faces are witnessed as well.
+
+ The data structure is described in \cite boissonnatmariasimplextreealgorithmica .
+
+ \section Implementation
+
+ The principal class of this module is Gudhi::Witness_complex.
+
+ In both cases, the constructor for this class takes a {witness}x{closest_landmarks} table, where each row represents a witness and consists of landmarks sorted by distance to this witness.
+ This table can be constructed by two additional classes Landmark_choice_by_furthest_point and Landmark_choice_by_random_point also included in the module.
+
+ *\image html "bench_Cy8.png" "Running time as function on number of landmarks" width=10cm
+ *\image html "bench_sphere.png" "Running time as function on number of witnesses for |L|=300" width=10cm
+
+
+ \copyright GNU General Public License v3.
+
+
+ */
+
+#endif // WITNESS_COMPLEX_DOC_H_