Update with reviews

BGL/doc/BGL/BGL.txt

@@ -654,10 +654,10 @@ can be done directly using `Face_filtered_graph`.
 Using \ref BGLNamedParameters some of the many options of METIS can be customized,
 as shown in \ref BGL_polyhedron_3/polyhedron_partition.cpp "this example".
 
-\section BGLGraphcut Graphcut
+\section BGLGraphcut Graph Cut
 
-Optimal partition from a set of labels can be computed through a
+An optimal partition from a set of labels can be computed through a
-graphcut approach called Alpha Expansion
+graph cut approach called Alpha Expansion
 \cgalCite{boykov2001fastapproximate}. \cgal provides
 `CGAL::alpha_expansion_graphcut()` which, or a graph \f$(V,E)\f$, this
 function seeks for the partioning `f` that minimizes the following
@@ -695,6 +695,33 @@ Comparison of time and memory consumed by the different Alpha
 Expansion implementation.
 \cgalFigureEnd
 
+The following example shows how to apply the Alpha Expansion algorithm
+to a `boost::adjacency_list` describing a 2D array with 3 labels "X",
+" " and "O":
+
+\cgalExample{BGL_graphcut/alpha_expansion_example.cpp}
+
+The output of this program shows how the initial 2D array is
+regularized spatially:
+
+```
+Input:
+XOX   
+XX X O
+OX  OO
+X  OOX
+  OXOO
+
+Alpha expansion...
+
+Output:
+XXX   
+XX   O
+XX  OO
+X  OOO
+  OOOO
+```
+
 
 */
 } /* namespace CGAL */

BGL/examples/BGL_graphcut/CMakeLists.txt

@@ -0,0 +1,42 @@
+# Created by the script cgal_create_CMakeLists
+# This is the CMake script for compiling a set of CGAL applications.
+
+cmake_minimum_required(VERSION 3.1...3.15)
+
+project( BGL_graphcut )
+
+
+# CGAL and its components
+find_package( CGAL QUIET COMPONENTS  )
+
+if ( NOT CGAL_FOUND )
+
+  message(STATUS "This project requires the CGAL library, and will not be compiled.")
+  return()  
+
+endif()
+
+
+# Boost and its components
+find_package( Boost REQUIRED )
+
+if ( NOT Boost_FOUND )
+
+  message(STATUS "This project requires the Boost library, and will not be compiled.")
+
+  return()  
+
+endif()
+
+# include for local directory
+
+# include for local package
+
+
+# Creating entries for all C++ files with "main" routine
+# ##########################################################
+
+
+create_single_source_cgal_program( "alpha_expansion_example.cpp" )
+
+

BGL/examples/BGL_graphcut/alpha_expansion_example.cpp

@@ -0,0 +1,95 @@
+#include <CGAL/boost/graph/alpha_expansion_graphcut.h>
+#include <boost/graph/adjacency_list.hpp>
+
+struct Vertex_property
+{
+  int label;
+  std::vector<double> cost;
+};
+
+struct Edge_property
+{
+  double weight;
+};
+
+using Graph = boost::adjacency_list <boost::setS,
+                                     boost::vecS,
+                                     boost::undirectedS,
+                                     Vertex_property,
+                                     Edge_property>;
+using GT = boost::graph_traits<Graph>;
+using vertex_descriptor = GT::vertex_descriptor;
+using edge_descriptor = GT::edge_descriptor;
+
+int main()
+{
+  std::array<char, 3> labels = { 'X', ' ', 'O' };
+  
+  std::array<std::array<int, 6>, 5> input
+    = { { { 0, 2, 0, 1, 1, 1 },
+          { 0, 0, 1, 0, 1, 2 },
+          { 2, 0, 1, 1, 2, 2 },
+          { 0, 1, 1, 2, 2, 0 },
+          { 1, 1, 2, 0, 2, 2 } } };
+
+  std::array<std::array<vertex_descriptor, 6>, 5> vertices;
+
+  // Init vertices from values
+  Graph g;
+  for (std::size_t i = 0; i < input.size(); ++ i)
+    for (std::size_t j = 0; j < input[i].size(); ++ j)
+    {
+      vertices[i][j] = boost::add_vertex(g);
+      g[vertices[i][j]].label = input[i][j];
+
+      // Cost of assigning this vertex to any label is positive except
+      // for current label which is 0 (favor init solution)
+      g[vertices[i][j]].cost.resize(3, 1);
+      g[vertices[i][j]].cost[std::size_t(input[i][j])] = 0;
+    }
+
+  // Display input values
+  std::cerr << "Input:" << std::endl;
+  for (std::size_t i = 0; i < vertices.size(); ++ i)
+  {
+    for (std::size_t j = 0; j < vertices[i].size(); ++ j)
+      std::cerr << labels[std::size_t(g[vertices[i][j]].label)];
+    std::cerr << std::endl;
+  }
+
+  // Init adjacency
+  double weight = 0.5;
+  for (std::size_t i = 0; i < vertices.size(); ++ i)
+    for (std::size_t j = 0; j < vertices[i].size(); ++ j)
+    {
+      // Neighbor vertices are connected
+      if (i < vertices.size() - 1)
+      {
+        edge_descriptor ed = boost::add_edge (vertices[i][j], vertices[i+1][j], g).first;
+        g[ed].weight = weight;
+      }
+      if (j < vertices[i].size() - 1)
+      {
+        edge_descriptor ed = boost::add_edge (vertices[i][j], vertices[i][j+1], g).first;
+        g[ed].weight = weight;
+      }
+    }
+
+  std::cerr << std::endl << "Alpha expansion..." << std::endl << std::endl;
+  CGAL::alpha_expansion_graphcut (g,
+                                  get (&Edge_property::weight, g),
+                                  get (boost::vertex_index, g),
+                                  get (&Vertex_property::cost, g),
+                                  get (&Vertex_property::label, g));
+
+  // Display output graph
+  std::cerr << "Output:" << std::endl;
+  for (std::size_t i = 0; i < vertices.size(); ++ i)
+  {
+    for (std::size_t j = 0; j < vertices[i].size(); ++ j)
+      std::cerr << labels[std::size_t(g[vertices[i][j]].label)];
+    std::cerr << std::endl;
+  }
+      
+  return 0;
+}

BGL/include/CGAL/boost/graph/alpha_expansion_graphcut.h

@@ -473,7 +473,7 @@ double alpha_expansion_graphcut (const InputGraph& input_graph,
 /**
    \ingroup PkgBGLPartition
 
-   Regularizes a partition of a graph into `n` labels using the Alpha
+   regularizes a partition of a graph into `n` labels using the Alpha
    Expansion algorithm \cgalCite{Boykov2001FastApproximate}.
 
    For a graph \f$(V,E)\f$, this function seeks for the partioning `f`
@@ -487,7 +487,7 @@ double alpha_expansion_graphcut (const InputGraph& input_graph,
    \f$\{v0,v1\}\f$ and \f$C(f_v)\f$ is the cost of assigning the
    vertex \f$v\f$ to the labeling \f$f\f$.
 
-   \tparam InputGraph a model of `Graph`
+   \tparam InputGraph a model of `VertexAndEdgeListGraph`
 
    \tparam EdgeWeightMap a model of `ReadablePropertyMap` with
    `boost::graph_traits<InputGraph>::%edge_descriptor` as key and `double`
@@ -532,9 +532,11 @@ double alpha_expansion_graphcut (const InputGraph& input_graph,
 
    \param vertex_label_cost_map a property map providing, for each
    vertex, an `std::vector` containing the cost of this vertex to
-   belong to each label. For example,
+   belong to each label. Each `std::vector` should have the same size
-   `get(vertex_label_cost_map, vd)[label_idx]` returns the cost
+   `n` (which is the number of labels), each label being indexed from
-   of vertex `vd` to belong to the label `label_idx`.
+   `0` to `n-1`. For example, `get(vertex_label_cost_map,
+   vd)[label_idx]` returns the cost of vertex `vd` to belong to the
+   label `label_idx`.
 */
 template <typename InputGraph,
           typename EdgeWeightMap,
@@ -571,7 +573,7 @@ double alpha_expansion_graphcut (const InputGraph& input_graph,
   std::vector<Vertex_descriptor> inserted_vertices;
   inserted_vertices.resize(num_vertices (input_graph));
 
-  std::size_t number_of_labels = get(vertex_label_cost_map, *std::begin(vertices(input_graph))).size();
+  std::size_t number_of_labels = get(vertex_label_cost_map, *(vertices(input_graph).first)).size();
 
   bool success;
   do {
@@ -588,7 +590,7 @@ double alpha_expansion_graphcut (const InputGraph& input_graph,
 
       // For E-Data
       // add every input vertex as a vertex to the graph, put edges to source & sink vertices
-      for (input_vertex_descriptor vd : vertices(input_graph))
+      for (input_vertex_descriptor vd : CGAL::make_range(vertices(input_graph)))
       {
         std::size_t vertex_i = get(vertex_index_map, vd);
         Vertex_descriptor new_vertex = alpha_expansion.add_vertex();
@@ -609,7 +611,7 @@ double alpha_expansion_graphcut (const InputGraph& input_graph,
 
       // For E-Smooth
       // add edge between every vertex,
-      for (input_edge_descriptor ed : edges(input_graph))
+      for (input_edge_descriptor ed : CGAL::make_range(edges(input_graph)))
       {
         input_vertex_descriptor vd1 = source(ed, input_graph);
         input_vertex_descriptor vd2 = target(ed, input_graph);
@@ -659,7 +661,7 @@ double alpha_expansion_graphcut (const InputGraph& input_graph,
       min_cut = flow;
       success = true;
       //update labeling
-      for (input_vertex_descriptor vd : vertices (input_graph))
+      for (input_vertex_descriptor vd : CGAL::make_range(vertices (input_graph)))
       {
         std::size_t vertex_i = get (vertex_index_map, vd);
         alpha_expansion.update(vertex_label_map, inserted_vertices, vd, vertex_i, alpha);