From 01b7bec722e18851acfc826ca572d01a127339c1 Mon Sep 17 00:00:00 2001 From: mcarrier Date: Tue, 9 May 2017 14:04:29 +0000 Subject: git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/Nerve_GIC@2408 636b058d-ea47-450e-bf9e-a15bfbe3eedb Former-commit-id: 324d557360a52e7181d9cf3c7d77c8445a367808 --- src/Nerve_GIC/doc/Intro_graph_induced_complex.h | 72 +++++++++++++++++-------- 1 file changed, 49 insertions(+), 23 deletions(-) (limited to 'src/Nerve_GIC/doc/Intro_graph_induced_complex.h') diff --git a/src/Nerve_GIC/doc/Intro_graph_induced_complex.h b/src/Nerve_GIC/doc/Intro_graph_induced_complex.h index 0b51e345..44e23983 100644 --- a/src/Nerve_GIC/doc/Intro_graph_induced_complex.h +++ b/src/Nerve_GIC/doc/Intro_graph_induced_complex.h @@ -33,9 +33,7 @@ namespace graph_induced_complex { * * @{ * - * \section complexes Graph induced complexes (GIC) and Nerves - * - * GIC and Nerves are simplicial complexes built on top of a point cloud P. + * \section nerves Nerves * * \subsection nervedefinition Nerve definition * @@ -46,78 +44,106 @@ namespace graph_induced_complex { * * \subsection nerveexample Example * - * This example builds the Nerve of a point cloud sampled on a 3D human shape. - * The cover C comes from the preimages of intervals covering the height function. + * This example builds the Nerve of a point cloud sampled on a 3D human shape (human.off). + * The cover C comes from the preimages of intervals (10 intervals with gain 0.3) + * covering the height function (coordinate 2), + * which are then refined into their connected components using the triangulation of the .OFF file. * All intervals have the resolution (either the length or the number of the intervals) * and gain (overlap percentage). * - * \include + * \include Nerve_GIC/Nerve.cpp * * When launching: * - * \code $> + * \code $> ./Nerve ../../../data/points/human.off 2 10 0.3 * \endcode * * the program output is: * - * \include + * \include Nerve_GIC/Nerve.txt + * + * \section gic Graph Induced Complexes (GIC) * - * \section gicdefinition GIC definition + * \subsection gicdefinition GIC definition * * Again, assume you are given a cover C of your point cloud P. Moreover, assume * you are also given a graph G built on top of P. Then, for any clique in G * whose nodes all belong to different elements of C, the GIC includes a corresponding * simplex, whose dimension is the number of nodes in the clique minus one. + * See this article + * for more details. * * \subsection gicexample Example * - * This example builds the GIC of a point cloud sampled on a 3D human shape. - * The cover C comes from the preimages of intervals covering the height function, - * and the graph G comes from a Rips complex built with a threshold parameter. + * This example builds the GIC of a point cloud sampled on a 3D human shape (human.off). + * The cover C comes from the preimages of intervals (with length 0.1 and gain 0) + * covering the height function (coordinate 2), + * and the graph G comes from a Rips complex built with threshold 0.1. * Note that if the gain is too big, the number of cliques increases a lot, * which make the computation time much larger. * - * \include + * \include Nerve_GIC/GIC.cpp * * When launching: * - * \code $> + * \code $> ./GIC ../../../data/points/human.off 0.1 2 0.1 0 * \endcode * * the program output is: * - * \include + * \include Nerve_GIC/GIC.txt * * \subsection mapperdeltadefinition Mapper Delta * * If one restricts to the cliques in G whose nodes all belong to preimages of consecutive * intervals (assuming the cover of the height function is minimal, i.e. no more than * two intervals can intersect at a time), the GIC is of dimension one, i.e. a graph. - * We call this graph the Mapper Delta, since it is related to the usual Mapper (see - * this article ). + * We call this graph the Mapper Delta, since it is related to the usual Mapper. See + * this article for more details. * * \subsection mapperdeltaexample Example * * Mapper Delta comes with optimal selection for the Rips threshold, * the resolution and the gain of the function cover. In this example, - * we compute the Mapper Delta of a point cloud sampled on a 3D human shape, + * we compute the Mapper Delta of a point cloud sampled on a 3D human shape (human.off), * where the graph G comes from a Rips complex with optimal threshold, - * and the cover C comes from the preimages of intervals covering the height function, + * and the cover C comes from the preimages of intervals covering the height function (coordinate 2), * with optimal resolution and gain. Note that optimal threshold, resolution and gain * also exist for the Nerve of this cover. * - * \include + * \include Nerve_GIC/MapperDeltaCoord.cpp * * When launching: * - * \code $> + * \code $> ./MapperDeltaCoord ../../../data/points/human.off 2 * \endcode * * the program output is: * - * \include + * \include MapperDeltaCoord.txt + * + * We also provide an example on a set of 72 pictures taken around the same object (lucky_cat.off). + * The function is now the first eigenfunction given by PCA, whose values + * are written in a file (lucky_cat_PCA1). Threshold, resolution and gain are automatically selected as before. + * + * \include Nerve_GIC/MapperDeltaFunc.cpp + * + * When launching: + * + * \code $> ./MapperDeltaFunc ../../../data/points/COIL_database/lucky_cat.off ../../../data/points/COIL_database/lucky_cat_PCA1 + * \endcode + * + * the program output is: + * + * \include MapperDeltaFunc.txt + * + * If you have python and firefox, all the previous .txt files can then be plotted using + * Kepler-Mapper + * with the following: + * + * \code python visu.py && firefox SC_visu.html + * \endcode * - * * \copyright GNU General Public License v3. * \verbatim Contact: gudhi-users@lists.gforge.inria.fr \endverbatim */ -- cgit v1.2.3