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<html><head><title>dlib C++ Library - min_cut_abstract.h</title></head><body bgcolor='white'><pre> |
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<font color='#009900'>// Copyright (C) 2012 Davis E. King ([email protected]) |
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</font><font color='#009900'>// License: Boost Software License See LICENSE.txt for the full license. |
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</font><font color='#0000FF'>#undef</font> DLIB_MIN_CuT_ABSTRACT_Hh_ |
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<font color='#0000FF'>#ifdef</font> DLIB_MIN_CuT_ABSTRACT_Hh_ |
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<font color='#0000FF'>#include</font> "<a style='text-decoration:none' href='../graph_utils.h.html'>../graph_utils.h</a>" |
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<font color='#009900'>// ---------------------------------------------------------------------------------------- |
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</font> |
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<font color='#0000FF'>namespace</font> dlib |
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<b>{</b> |
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<a name='node_label'/><font color='#009900'>/*!A node_label |
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The node_label type is the type used to label which part of a graph cut |
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a node is on. It is used by all the graph cut tools. The three possible |
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values of a node label are SOURCE_CUT, SINK_CUT, or FREE_NODE. |
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!*/</font> |
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<font color='#0000FF'>typedef</font> <font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>char</u></font> node_label; |
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<font color='#0000FF'>const</font> node_label SOURCE_CUT <font color='#5555FF'>=</font> <font color='#979000'>0</font>; |
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<font color='#0000FF'>const</font> node_label SINK_CUT <font color='#5555FF'>=</font> <font color='#979000'>254</font>; |
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<font color='#0000FF'>const</font> node_label FREE_NODE <font color='#5555FF'>=</font> <font color='#979000'>255</font>; |
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<font color='#009900'>// ---------------------------------------------------------------------------------------- |
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</font> |
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<font color='#0000FF'>class</font> <b><a name='flow_graph'></a>flow_graph</b> |
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<b>{</b> |
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<font color='#009900'>/*! |
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WHAT THIS OBJECT REPRESENTS |
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This object represents a flow capacity graph for use with the |
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min_cut algorithm defined below. In particular, this object |
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is a kind of directed graph where the edge weights specify the |
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flow capacities. |
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Note that there is no dlib::flow_graph object. What you are |
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looking at here is simply the interface definition for a graph |
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which can be used with the min_cut algorithm. You must implement |
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your own version of this object for the graph you wish to work with |
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and then pass it to the min_cut::operator() routine. |
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It's also worth pointing out that this graph has symmetric edge |
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connections. That is, if there is an edge from node A to node B |
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then there must also be an edge from node B to node A. |
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!*/</font> |
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<font color='#0000FF'>public</font>: |
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<font color='#0000FF'>class</font> <b><a name='out_edge_iterator'></a>out_edge_iterator</b> |
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<b>{</b> |
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<font color='#009900'>/*! |
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WHAT THIS OBJECT REPRESENTS |
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This is a simple forward iterator for iterating over the neighbors |
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of a node in the graph. It also represents the fact that the neighbors |
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are on the end of an outgoing edge. That is, the edge represents |
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the amount of flow which can flow towards the neighbor. |
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!*/</font> |
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<font color='#0000FF'>public</font>: |
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<b><a name='out_edge_iterator'></a>out_edge_iterator</b><font face='Lucida Console'>(</font> |
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<font face='Lucida Console'>)</font>; |
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<font color='#009900'>/*! |
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ensures |
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- constructs an iterator in an undefined state. It can't |
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be used until assigned with a valid iterator. |
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!*/</font> |
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<b><a name='out_edge_iterator'></a>out_edge_iterator</b><font face='Lucida Console'>(</font> |
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<font color='#0000FF'>const</font> out_edge_iterator<font color='#5555FF'>&</font> item |
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<font face='Lucida Console'>)</font>; |
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<font color='#009900'>/*! |
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ensures |
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- #*this is a copy of item |
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!*/</font> |
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out_edge_iterator<font color='#5555FF'>&</font> <b><a name='operator'></a>operator</b><font color='#5555FF'>=</font><font face='Lucida Console'>(</font> |
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<font color='#0000FF'>const</font> out_edge_iterator<font color='#5555FF'>&</font> item |
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<font face='Lucida Console'>)</font>; |
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<font color='#009900'>/*! |
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ensures |
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- #*this is a copy of item |
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- returns #*this |
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!*/</font> |
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<font color='#0000FF'><u>bool</u></font> <b><a name='operator'></a>operator</b><font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font> |
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<font color='#0000FF'>const</font> out_edge_iterator<font color='#5555FF'>&</font> item |
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<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>; |
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<font color='#009900'>/*! |
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requires |
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- *this and item are iterators over the neighbors for the |
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same node. |
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ensures |
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- returns false if *this and item both reference the same |
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node in the graph and true otherwise. |
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!*/</font> |
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out_edge_iterator<font color='#5555FF'>&</font> <b><a name='operator'></a>operator</b><font color='#5555FF'>+</font><font color='#5555FF'>+</font><font face='Lucida Console'>(</font> |
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<font face='Lucida Console'>)</font>; |
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<font color='#009900'>/*! |
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ensures |
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- advances *this to the next neighbor node. |
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- returns a reference to the updated *this |
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(i.e. this is the ++object form of the increment operator) |
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!*/</font> |
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<b>}</b>; |
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<font color='#0000FF'>class</font> <b><a name='in_edge_iterator'></a>in_edge_iterator</b> |
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<b>{</b> |
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<font color='#009900'>/*! |
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WHAT THIS OBJECT REPRESENTS |
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This is a simple forward iterator for iterating over the neighbors |
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of a node in the graph. It also represents the fact that the neighbors |
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are on the end of an incoming edge. That is, the edge represents |
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the amount of flow which can flow out of the neighbor node. |
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!*/</font> |
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<font color='#0000FF'>public</font>: |
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<b><a name='in_edge_iterator'></a>in_edge_iterator</b><font face='Lucida Console'>(</font> |
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<font face='Lucida Console'>)</font>; |
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<font color='#009900'>/*! |
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ensures |
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- constructs an iterator in an undefined state. It can't |
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be used until assigned with a valid iterator. |
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!*/</font> |
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<b><a name='in_edge_iterator'></a>in_edge_iterator</b><font face='Lucida Console'>(</font> |
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<font color='#0000FF'>const</font> in_edge_iterator<font color='#5555FF'>&</font> item |
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<font face='Lucida Console'>)</font>; |
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<font color='#009900'>/*! |
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ensures |
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- #*this is a copy of item |
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!*/</font> |
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in_edge_iterator<font color='#5555FF'>&</font> <b><a name='operator'></a>operator</b><font color='#5555FF'>=</font><font face='Lucida Console'>(</font> |
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<font color='#0000FF'>const</font> in_edge_iterator<font color='#5555FF'>&</font> item |
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<font face='Lucida Console'>)</font>; |
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<font color='#009900'>/*! |
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ensures |
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- #*this is a copy of item |
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- returns #*this |
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!*/</font> |
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<font color='#0000FF'><u>bool</u></font> <b><a name='operator'></a>operator</b><font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font> |
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<font color='#0000FF'>const</font> in_edge_iterator<font color='#5555FF'>&</font> item |
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<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>; |
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<font color='#009900'>/*! |
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requires |
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- *this and item are iterators over the neighbors for the |
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same node. |
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ensures |
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- returns false if *this and item both reference the same |
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node in the graph and true otherwise. |
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!*/</font> |
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in_edge_iterator<font color='#5555FF'>&</font> <b><a name='operator'></a>operator</b><font color='#5555FF'>+</font><font color='#5555FF'>+</font><font face='Lucida Console'>(</font> |
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<font face='Lucida Console'>)</font>; |
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<font color='#009900'>/*! |
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ensures |
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- advances *this to the next neighbor node. |
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- returns a reference to the updated *this |
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(i.e. this is the ++object form of the increment operator) |
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!*/</font> |
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<b>}</b>; |
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<font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> <b><a name='number_of_nodes'></a>number_of_nodes</b> <font face='Lucida Console'>(</font> |
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<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>; |
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<font color='#009900'>/*! |
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ensures |
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- returns the number of nodes in the graph. |
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!*/</font> |
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out_edge_iterator <b><a name='out_begin'></a>out_begin</b><font face='Lucida Console'>(</font> |
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<font color='#0000FF'>const</font> <font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font><font color='#5555FF'>&</font> idx |
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<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>; |
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<font color='#009900'>/*! |
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requires |
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- idx < number_of_nodes() |
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ensures |
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- returns an iterator pointing to the first neighboring node of |
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the idx-th node. If no such node exists then returns out_end(idx). |
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- The returned iterator also represents the directed edge going from |
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node idx to the neighbor. |
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!*/</font> |
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in_edge_iterator <b><a name='in_begin'></a>in_begin</b><font face='Lucida Console'>(</font> |
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<font color='#0000FF'>const</font> <font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font><font color='#5555FF'>&</font> idx |
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<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>; |
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<font color='#009900'>/*! |
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requires |
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- idx < number_of_nodes() |
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ensures |
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- returns an iterator pointing to the first neighboring node of |
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the idx-th node. If no such node exists then returns in_end(idx). |
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- The returned iterator also represents the directed edge going from |
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the neighbor to node idx. |
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!*/</font> |
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out_edge_iterator <b><a name='out_end'></a>out_end</b><font face='Lucida Console'>(</font> |
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<font color='#0000FF'>const</font> <font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font><font color='#5555FF'>&</font> idx |
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<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>; |
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<font color='#009900'>/*! |
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requires |
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- idx < number_of_nodes() |
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ensures |
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- returns an iterator to one past the last neighboring node of |
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the idx-th node. |
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!*/</font> |
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in_edge_iterator <b><a name='in_end'></a>in_end</b><font face='Lucida Console'>(</font> |
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<font color='#0000FF'>const</font> <font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font><font color='#5555FF'>&</font> idx |
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<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>; |
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<font color='#009900'>/*! |
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requires |
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- idx < number_of_nodes() |
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ensures |
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- returns an iterator to one past the last neighboring node of |
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the idx-th node. |
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!*/</font> |
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<font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> <b><a name='node_id'></a>node_id</b> <font face='Lucida Console'>(</font> |
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<font color='#0000FF'>const</font> out_edge_iterator<font color='#5555FF'>&</font> it |
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<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>; |
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<font color='#009900'>/*! |
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requires |
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- it == a valid iterator (i.e. it must be in the range [out_begin(idx), out_end(idx)) |
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for some valid idx) |
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ensures |
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- returns a number IDX such that: |
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- 0 <= IDX < number_of_nodes() |
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- IDX == The index which uniquely identifies the node pointed to by the |
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iterator it. This number can be used with any member function in this |
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object which expect a node index. (e.g. get_label(IDX) == the label for the |
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node pointed to by it) |
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!*/</font> |
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<font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> <b><a name='node_id'></a>node_id</b> <font face='Lucida Console'>(</font> |
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<font color='#0000FF'>const</font> in_edge_iterator<font color='#5555FF'>&</font> it |
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<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>; |
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<font color='#009900'>/*! |
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requires |
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- it == a valid iterator (i.e. it must be in the range [in_begin(idx), in_end(idx)) |
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for some valid idx) |
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ensures |
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- returns a number IDX such that: |
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- 0 <= IDX < number_of_nodes() |
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- IDX == The index which uniquely identifies the node pointed to by the |
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iterator it. This number can be used with any member function in this |
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object which expect a node index. (e.g. get_label(IDX) == the label for the |
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node pointed to by it) |
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!*/</font> |
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<font color='#009900'>// This typedef should be for a type like int or double. It |
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</font> <font color='#009900'>// must also be capable of representing signed values. |
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</font> <font color='#0000FF'>typedef</font> an_integer_or_real_type edge_type; |
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edge_type <b><a name='get_flow'></a>get_flow</b> <font face='Lucida Console'>(</font> |
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<font color='#0000FF'>const</font> <font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font><font color='#5555FF'>&</font> idx1, |
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<font color='#0000FF'>const</font> <font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font><font color='#5555FF'>&</font> idx2 |
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<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>; |
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<font color='#009900'>/*! |
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requires |
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- idx1 < number_of_nodes() |
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- idx2 < number_of_nodes() |
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- idx1 and idx2 are neighbors in the graph |
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ensures |
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- returns the residual flow capacity from the idx1-th node to the idx2-th node. |
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- It is valid for this function to return a floating point value of infinity. |
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This value means this edge has an unlimited capacity. |
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!*/</font> |
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edge_type <b><a name='get_flow'></a>get_flow</b> <font face='Lucida Console'>(</font> |
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<font color='#0000FF'>const</font> out_edge_iterator<font color='#5555FF'>&</font> it |
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<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>; |
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<font color='#009900'>/*! |
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requires |
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- it == a valid iterator (i.e. it must be in the range [out_begin(idx), out_end(idx)) |
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for some valid idx) |
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ensures |
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- let IDX = node_id(it) |
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- it represents the directed edge from a node, call it H, to the node IDX. Therefore, |
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this function returns get_flow(H,IDX) |
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- It is valid for this function to return a floating point value of infinity. |
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This value means this edge has an unlimited capacity. |
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!*/</font> |
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edge_type <b><a name='get_flow'></a>get_flow</b> <font face='Lucida Console'>(</font> |
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<font color='#0000FF'>const</font> in_edge_iterator<font color='#5555FF'>&</font> it |
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<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>; |
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<font color='#009900'>/*! |
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requires |
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- it == a valid iterator (i.e. it must be in the range [in_begin(idx), in_end(idx)) |
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for some valid idx) |
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ensures |
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- let IDX = node_id(it) |
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- it represents the directed edge from node IDX to another node, call it H. Therefore, |
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this function returns get_flow(IDX,H) |
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- It is valid for this function to return a floating point value of infinity. |
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This value means this edge has an unlimited capacity. |
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!*/</font> |
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<font color='#0000FF'><u>void</u></font> <b><a name='adjust_flow'></a>adjust_flow</b> <font face='Lucida Console'>(</font> |
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<font color='#0000FF'>const</font> <font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font><font color='#5555FF'>&</font> idx1, |
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<font color='#0000FF'>const</font> <font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font><font color='#5555FF'>&</font> idx2, |
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<font color='#0000FF'>const</font> edge_type<font color='#5555FF'>&</font> value |
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<font face='Lucida Console'>)</font>; |
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<font color='#009900'>/*! |
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requires |
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- idx1 < number_of_nodes() |
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- idx2 < number_of_nodes() |
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- idx1 and idx2 are neighbors in the graph |
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ensures |
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- #get_flow(idx1,idx2) == get_flow(idx1,idx2) + value |
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- #get_flow(idx2,idx1) == get_flow(idx2,idx1) - value |
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!*/</font> |
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<font color='#0000FF'><u>void</u></font> <b><a name='set_label'></a>set_label</b> <font face='Lucida Console'>(</font> |
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<font color='#0000FF'>const</font> <font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font><font color='#5555FF'>&</font> idx, |
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node_label value |
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<font face='Lucida Console'>)</font>; |
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<font color='#009900'>/*! |
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requires |
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- idx < number_of_nodes() |
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ensures |
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- #get_label(idx) == value |
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!*/</font> |
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node_label <b><a name='get_label'></a>get_label</b> <font face='Lucida Console'>(</font> |
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<font color='#0000FF'>const</font> <font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font><font color='#5555FF'>&</font> idx |
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<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>; |
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<font color='#009900'>/*! |
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requires |
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- idx < number_of_nodes() |
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ensures |
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- returns the label for the idx-th node in the graph. |
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!*/</font> |
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<b>}</b>; |
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<font color='#009900'>// ---------------------------------------------------------------------------------------- |
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</font> |
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<font color='#0000FF'>template</font> <font color='#5555FF'><</font> |
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<font color='#0000FF'>typename</font> flow_graph |
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<font color='#5555FF'>></font> |
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<font color='#0000FF'>typename</font> flow_graph::edge_type <b><a name='graph_cut_score'></a>graph_cut_score</b> <font face='Lucida Console'>(</font> |
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<font color='#0000FF'>const</font> flow_graph<font color='#5555FF'>&</font> g |
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<font face='Lucida Console'>)</font>; |
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<font color='#009900'>/*! |
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requires |
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- flow_graph == an object with an interface compatible with the flow_graph |
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object defined at the top of this file, or, an implementation of |
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dlib/directed_graph/directed_graph_kernel_abstract.h. |
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ensures |
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- returns the sum of the outgoing flows from nodes with a label of SOURCE_CUT |
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to nodes with a label != SOURCE_CUT. Note that for a directed_graph object, |
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the labels are stored in the node's data field. |
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!*/</font> |
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<font color='#009900'>// ---------------------------------------------------------------------------------------- |
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</font> |
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<font color='#0000FF'>class</font> <b><a name='min_cut'></a>min_cut</b> |
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<b>{</b> |
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<font color='#009900'>/*! |
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WHAT THIS OBJECT REPRESENTS |
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This is a function object which can be used to find the min cut |
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on a graph. |
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The implementation is based on the method described in the following |
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paper: |
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An Experimental Comparison of Min-Cut/Max-Flow Algorithms for |
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Energy Minimization in Vision, by Yuri Boykov and Vladimir Kolmogorov, |
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in PAMI 2004. |
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!*/</font> |
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<font color='#0000FF'>public</font>: |
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<b><a name='min_cut'></a>min_cut</b><font face='Lucida Console'>(</font> |
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<font face='Lucida Console'>)</font>; |
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<font color='#009900'>/*! |
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ensures |
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- this object is properly initialized |
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!*/</font> |
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<font color='#0000FF'>template</font> <font color='#5555FF'><</font> |
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<font color='#0000FF'>typename</font> flow_graph |
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<font color='#5555FF'>></font> |
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<font color='#0000FF'><u>void</u></font> <b><a name='operator'></a>operator</b><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font face='Lucida Console'>(</font> |
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flow_graph<font color='#5555FF'>&</font> g, |
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<font color='#0000FF'>const</font> <font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> source_node, |
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<font color='#0000FF'>const</font> <font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> sink_node |
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<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>; |
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<font color='#009900'>/*! |
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requires |
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- flow_graph == an object with an interface compatible with the flow_graph |
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object defined at the top of this file. |
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- source_node != sink_node |
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- source_node < g.number_of_nodes() |
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- sink_node < g.number_of_nodes() |
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- for all valid i and j: |
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- g.get_flow(i,j) >= 0 |
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(i.e. all the flow capacities/edge weights are non-negative) |
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- g does not contain any self loops. That is, no nodes are neighbors with |
|
themselves. |
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ensures |
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- Finds the minimum cut on the given graph. That is, this function finds |
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a labeling of nodes in g such that graph_cut_score(g) would be minimized. Note |
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that the flow values in #g are modified by this algorithm so if you want |
|
to obtain the min cut score you must call min_cut::operator(), then copy |
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the flow values back into #g, and then call graph_cut_score(#g). But in most |
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cases you don't care about the value of the min cut score, rather, you |
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just want the labels in #g. |
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- #g.get_label(source_node) == SOURCE_CUT |
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- #g.get_label(sink_node) == SINK_CUT |
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- for all valid i: |
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- #g.get_label(i) == SOURCE_CUT, SINK_CUT, or FREE_NODE |
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- if (#g.get_label(i) == SOURCE_CUT) then |
|
- The minimum cut of g places node i into the source side of the cut. |
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- if (#g.get_label(i) == SINK_CUT) then |
|
- The minimum cut of g places node i into the sink side of the cut. |
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- if (#g.get_label(i) == FREE_NODE) then |
|
- Node i can be labeled SOURCE_CUT or SINK_CUT. Both labelings |
|
result in the same cut score. |
|
- When interpreting g as a graph of flow capacities from the source_node |
|
to the sink_node we can say that the min cut problem is equivalent to |
|
the max flow problem. This equivalent problem is to find out how to push |
|
as much "flow" from the source node to the sink node as possible. |
|
Upon termination, #g will contain the final flow residuals in addition to |
|
the graph cut labels. That is, for all valid i and j: |
|
- #g.get_flow(i,j) == the residual flow capacity left after the max |
|
possible amount of flow is passing from the source node to the sink |
|
node. For example, this means that #g.get_flow(i,j) == 0 whenever |
|
node i is in the SOURCE_CUT and j is in the SINK_CUT. |
|
- #g.get_flow(i,j) >= 0 |
|
!*/</font> |
|
|
|
<font color='#0000FF'>template</font> <font color='#5555FF'><</font> |
|
<font color='#0000FF'>typename</font> directed_graph |
|
<font color='#5555FF'>></font> |
|
<font color='#0000FF'><u>void</u></font> <b><a name='operator'></a>operator</b><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font face='Lucida Console'>(</font> |
|
directed_graph<font color='#5555FF'>&</font> g, |
|
<font color='#0000FF'>const</font> <font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> source_node, |
|
<font color='#0000FF'>const</font> <font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> sink_node |
|
<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>; |
|
<font color='#009900'>/*! |
|
requires |
|
- directed_graph == an implementation of dlib/directed_graph/directed_graph_kernel_abstract.h |
|
- directed_graph::type == node_label |
|
- directed_graph::edge_type == and integer or double type |
|
- source_node != sink_node |
|
- source_node < g.number_of_nodes() |
|
- sink_node < g.number_of_nodes() |
|
- for all valid i and j: |
|
- edge(g,i,j) >= 0 |
|
(i.e. all the flow capacities/edge weights are positive) |
|
- graph_contains_length_one_cycle(g) == false |
|
- graph_has_symmetric_edges(g) == true |
|
ensures |
|
- This routine simply converts g into a flow graph and calls the version |
|
of operator() defined above. Note that the conversion is done in O(1) |
|
time, it's just an interface adaptor. |
|
- edge weights in g correspond to network flows while the .data field of |
|
each node in g corresponds to the graph node labels. |
|
- upon termination, the flows and labels in g will have been modified |
|
as described in the above operator() routine. |
|
!*/</font> |
|
<b>}</b>; |
|
|
|
<font color='#009900'>// ---------------------------------------------------------------------------------------- |
|
</font> |
|
<b>}</b> |
|
|
|
<font color='#0000FF'>#endif</font> <font color='#009900'>// DLIB_MIN_CuT_ABSTRACT_Hh_ |
|
</font> |
|
|
|
|
|
</pre></body></html> |
