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@ -657,7 +657,7 @@ as shown in \ref BGL_polyhedron_3/polyhedron_partition.cpp "this example".
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\section BGLGraphcut Graph Cut
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An optimal partition from a set of labels can be computed through a
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graph cut approach called Alpha Expansion
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graph cut approach called alpha expansion
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\cgalCite{Boykov2001FastApproximate}. \cgal provides
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`CGAL::alpha_expansion_graphcut()` which, for a graph \f$(V,E)\f$,
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computes the partition `f` that minimizes the following cost function:
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@ -690,11 +690,11 @@ list_ version provides a good compromise and is therefore the default
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implementation.
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\cgalFigureBegin{alpha_exp, alpha_expansion.png}
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Comparison of time and memory consumed by the different Alpha
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Expansion implementation.
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Comparison of time and memory consumed by the different alpha
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expansion implementation.
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\cgalFigureEnd
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The following example shows how to apply the Alpha Expansion algorithm
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The following example shows how to apply the alpha expansion algorithm
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to a `boost::adjacency_list` describing a 2D array with 3 labels "X",
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" " and "O":
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@ -449,8 +449,8 @@ public:
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/**
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\ingroup PkgBGLPartition
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regularizes a partition of a graph into `n` labels using the Alpha
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Expansion algorithm \cgalCite{Boykov2001FastApproximate}.
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regularizes a partition of a graph into `n` labels using the alpha
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expansion algorithm \cgalCite{Boykov2001FastApproximate}.
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For a graph \f$(V,E)\f$, this function computes a partition `f`
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that minimizes the following cost function:
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@ -504,7 +504,7 @@ public:
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\cgalParamEnd
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\cgalParamBegin{implementation_tag}
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tag used to select
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which implementation of the Alpha Expansion should be
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which implementation of the alpha expansion should be
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used. Available implementation tags are:
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- `CGAL::Alpha_expansion_boost_adjacency_list` (default)
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- `CGAL::Alpha_expansion_boost_compressed_sparse_row_tag`
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@ -21,7 +21,7 @@ This component implements the algorithm described in \cgalCite{cgal:lm-clscm-12}
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- a set of labels (for example: _ground_, _building_, _vegetation_) is defined by the user;
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- a classifier is defined and trained: from the set of values taken by the features at an input item, it measures the likelihood of this item to belong to one label or another;
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- classification is computed itemwise using the classifier;
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- additional regularization can be used by smoothing either locally or globally through a _Graph Cut_ \cgalCite{Boykov2001FastApproximate} approach.
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- additional regularization can be used by smoothing either locally or globally through a _graph cut_ \cgalCite{Boykov2001FastApproximate} approach.
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\cgalFigureBegin{Classification_organization_fig,organization.svg}
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Organization of the package.
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@ -431,7 +431,7 @@ quantifies the strengh of the regularization, \f$i \sim j\f$
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represents the pairs of neighboring items and
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\f$\mathbf{1}_{\{.\}}\f$ the characteristic function.
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A _Graph Cut_ based algorithm (Alpha Expansion) is used to quickly reach
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A _graph cut_ based algorithm (alpha expansion) is used to quickly reach
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an approximate solution close to the global optimum of this energy.
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This method allows to consistently segment the input data set in
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