diff options
author | skachano <skachano@636b058d-ea47-450e-bf9e-a15bfbe3eedb> | 2016-09-28 12:33:22 +0000 |
---|---|---|
committer | skachano <skachano@636b058d-ea47-450e-bf9e-a15bfbe3eedb> | 2016-09-28 12:33:22 +0000 |
commit | d16822ea1d3cedea66dcddd390becdd4cbb557bb (patch) | |
tree | b1c592e415f43c1be425608db861e5348e61dcf3 /src/Witness_complex/doc/Witness_complex_doc.h | |
parent | 1c09c91ddf4d38196a91bbff5ae432fb13be6762 (diff) | |
parent | a138c9ed4fb9770a3612ff4ee0f914942bbe9724 (diff) |
Merged trunk into relaxed witness branch
git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/relaxed-witness@1579 636b058d-ea47-450e-bf9e-a15bfbe3eedb
Former-commit-id: a9ca2e7a968ebf4bb80cfa795965ae78511e8dd4
Diffstat (limited to 'src/Witness_complex/doc/Witness_complex_doc.h')
-rw-r--r-- | src/Witness_complex/doc/Witness_complex_doc.h | 42 |
1 files changed, 42 insertions, 0 deletions
diff --git a/src/Witness_complex/doc/Witness_complex_doc.h b/src/Witness_complex/doc/Witness_complex_doc.h new file mode 100644 index 00000000..60dfd27b --- /dev/null +++ b/src/Witness_complex/doc/Witness_complex_doc.h @@ -0,0 +1,42 @@ +#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_ |