-///////////////////////////////////////////////////////////////////////////
-// This program is free software: you can redistribute it and/or modify //
-// it under the terms of the version 3 of the GNU General Public License //
-// as published by the Free Software Foundation. //
-// //
-// This program is distributed in the hope that it will be useful, but //
-// WITHOUT ANY WARRANTY; without even the implied warranty of //
-// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU //
-// General Public License for more details. //
-// //
-// You should have received a copy of the GNU General Public License //
-// along with this program. If not, see <http://www.gnu.org/licenses/>. //
-// //
-// Written by and Copyright (C) Francois Fleuret //
-// Contact <francois.fleuret@idiap.ch> for comments & bug reports //
-///////////////////////////////////////////////////////////////////////////
+/*
+ * mtp is the ``Multi Tracked Paths'', an implementation of the
+ * k-shortest paths algorithm for multi-target tracking.
+ *
+ * Copyright (c) 2012 Idiap Research Institute, http://www.idiap.ch/
+ * Written by Francois Fleuret <francois.fleuret@idiap.ch>
+ *
+ * This file is part of mtp.
+ *
+ * mtp is free software: you can redistribute it and/or modify it
+ * under the terms of the GNU General Public License version 3 as
+ * published by the Free Software Foundation.
+ *
+ * mtp is distributed in the hope that it will be useful, but WITHOUT
+ * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+ * or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+ * License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with selector. If not, see <http://www.gnu.org/licenses/>.
+ *
+ */
#include "mtp_graph.h"
-#include <iostream>
#include <float.h>
using namespace std;
class Edge {
public:
int id, occupied;
- scalar_t length, work_length;
+ scalar_t length, positivized_length;
Vertex *origin_vertex, *terminal_vertex;
// These are the links in the origin_vertex leaving edge list
- Edge *next, *pred;
+ Edge *next_leaving_edge, *pred_leaving_edge;
- inline void revert();
+ inline void invert();
};
class Vertex {
public:
- int id, iteration;
- Edge *root_edge;
+ int id;
+ Edge *leaving_edges;
scalar_t distance_from_source;
- Edge *best_pred_edge_to_source;
+ Edge *pred_edge_toward_source;
+
+ int last_change; // Used to mark which edges have already been
+ // processed in some methods
Vertex();
- inline void add_edge(Edge *e);
- inline void del_edge(Edge *e);
+
+ inline void add_leaving_edge(Edge *e);
+ inline void del_leaving_edge(Edge *e);
};
//////////////////////////////////////////////////////////////////////
-void Edge::revert() {
+void Edge::invert() {
length = - length;
- work_length = 0;
- origin_vertex->del_edge(this);
- terminal_vertex->add_edge(this);
+ positivized_length = - positivized_length;
+ origin_vertex->del_leaving_edge(this);
+ terminal_vertex->add_leaving_edge(this);
Vertex *t = terminal_vertex;
terminal_vertex = origin_vertex;
origin_vertex = t;
//////////////////////////////////////////////////////////////////////
Vertex::Vertex() {
- root_edge = 0;
-}
-
-void Vertex::add_edge(Edge *e) {
- e->next = root_edge;
- e->pred = 0;
- if(root_edge) { root_edge->pred = e; }
- root_edge = e;
+ leaving_edges = 0;
}
-void Vertex::del_edge(Edge *e) {
- if(e == root_edge) { root_edge = e->next; }
- if(e->pred) { e->pred->next = e->next; }
- if(e->next) { e->next->pred = e->pred; }
+void Vertex::add_leaving_edge(Edge *e) {
+ e->next_leaving_edge = leaving_edges;
+ e->pred_leaving_edge = 0;
+ if(leaving_edges) { leaving_edges->pred_leaving_edge = e; }
+ leaving_edges = e;
}
-//////////////////////////////////////////////////////////////////////
-
-void MTPGraph::print() {
- for(int k = 0; k < _nb_edges; k++) {
- Edge *e = _edges + k;
- cout << e->origin_vertex->id
- << " -> "
- << e->terminal_vertex->id
- << " "
- << e->length;
- if(e->occupied) {
- cout << " *";
- }
- cout << endl;
+void Vertex::del_leaving_edge(Edge *e) {
+ if(e == leaving_edges) {
+ leaving_edges = e->next_leaving_edge;
}
-}
-
-void MTPGraph::print_dot() {
- cout << "digraph {" << endl;
- cout << " node[shape=circle];" << endl;
- for(int k = 0; k < _nb_edges; k++) {
- Edge *e = _edges + k;
- if(e->occupied) {
- cout << " " << e->origin_vertex->id << " -> " << e->terminal_vertex->id
- << " [style=bold,color=black,label=\"" << -e->length << "\"];" << endl;
- } else {
- cout << " " << e->origin_vertex->id << " -> " << e->terminal_vertex->id
- << " [color=gray,label=\"" << e->length << "\"];" << endl;
- }
+ if(e->pred_leaving_edge) {
+ e->pred_leaving_edge->next_leaving_edge = e->next_leaving_edge;
+ }
+ if(e->next_leaving_edge) {
+ e->next_leaving_edge->pred_leaving_edge = e->pred_leaving_edge;
}
- cout << "}" << endl;
}
+//////////////////////////////////////////////////////////////////////
+
MTPGraph::MTPGraph(int nb_vertices, int nb_edges,
- int *from, int *to,
+ int *vertex_from, int *vertex_to,
int source, int sink) {
_nb_vertices = nb_vertices;
_nb_edges = nb_edges;
_source = &_vertices[source];
_sink = &_vertices[sink];
- for(int v = 0; v < _nb_vertices; v++) {
- _vertices[v].id = v;
+ for(int k = 0; k < _nb_vertices; k++) {
+ _vertices[k].id = k;
}
for(int e = 0; e < nb_edges; e++) {
- _vertices[from[e]].add_edge(_edges + e);
+ _vertices[vertex_from[e]].add_leaving_edge(_edges + e);
_edges[e].occupied = 0;
_edges[e].id = e;
- _edges[e].origin_vertex = _vertices + from[e];
- _edges[e].terminal_vertex = _vertices + to[e];
+ _edges[e].origin_vertex = _vertices + vertex_from[e];
+ _edges[e].terminal_vertex = _vertices + vertex_to[e];
}
+ paths = 0;
+ nb_paths = 0;
}
MTPGraph::~MTPGraph() {
delete[] _edges;
delete[] _front;
delete[] _new_front;
+ for(int p = 0; p < nb_paths; p++) delete paths[p];
+ delete[] paths;
}
-void MTPGraph::initialize_work_lengths_with_min() {
- scalar_t length_min = 0;
- for(int n = 0; n < _nb_vertices; n++) {
- for(Edge *e = _vertices[n].root_edge; e; e = e->next) {
- length_min = min(e->length, length_min);
+//////////////////////////////////////////////////////////////////////
+
+void MTPGraph::print(ostream *os) {
+ for(int k = 0; k < _nb_edges; k++) {
+ Edge *e = _edges + k;
+ (*os) << e->origin_vertex->id
+ << " -> "
+ << e->terminal_vertex->id
+ << " "
+ << e->length;
+ if(e->occupied) {
+ (*os) << " *";
}
+ (*os) << endl;
}
- for(int n = 0; n < _nb_vertices; n++) {
- for(Edge *e = _vertices[n].root_edge; e; e = e->next) {
- e->work_length = e->length - length_min;
+}
+
+void MTPGraph::print_dot(ostream *os) {
+ (*os) << "digraph {" << endl;
+ (*os) << " rankdir=\"LR\";" << endl;
+ (*os) << " node [shape=circle,width=0.75,fixedsize=true];" << endl;
+ (*os) << " edge [color=gray,arrowhead=open]" << endl;
+ (*os) << " " << _source->id << " [peripheries=2];" << endl;
+ (*os) << " " << _sink->id << " [peripheries=2];" << endl;
+ for(int k = 0; k < _nb_edges; k++) {
+ Edge *e = _edges + k;
+ (*os) << " " << e->origin_vertex->id << " -> " << e->terminal_vertex->id
+ << " [";
+ if(e->occupied) {
+ (*os) << "style=bold,color=black,";
}
+ (*os) << "label=\"" << e->length << "\"];" << endl;
}
+ (*os) << "}" << endl;
}
-void MTPGraph::update_work_lengths() {
+//////////////////////////////////////////////////////////////////////
+
+void MTPGraph::update_positivized_lengths() {
for(int k = 0; k < _nb_edges; k++) {
Edge *e = _edges + k;
- e->work_length += e->terminal_vertex->distance_from_source - e->terminal_vertex->distance_from_source;
+ e->positivized_length +=
+ e->origin_vertex->distance_from_source - e->terminal_vertex->distance_from_source;
}
}
-void MTPGraph::force_positive_work_lengths() {
+void MTPGraph::force_positivized_lengths() {
#ifdef VERBOSE
scalar_t residual_error = 0.0;
+ scalar_t max_error = 0.0;
#endif
- for(int n = 0; n < _nb_vertices; n++) {
- for(Edge *e = _vertices[n].root_edge; e; e = e->next) {
- if(e->work_length < 0) {
+ for(int k = 0; k < _nb_edges; k++) {
+ Edge *e = _edges + k;
+
+ if(e->positivized_length < 0) {
+
#ifdef VERBOSE
- residual_error -= e->work_length;
-#endif
- e->work_length = 0.0;
+ if((e->origin_vertex->last_change < 0 && e->terminal_vertex->last_change >= 0) ||
+ (e->origin_vertex->last_change >= 0 && e->terminal_vertex->last_change < 0)) {
+ cout << "Inconsistent non-connexity (this should never happen)." << endl;
+ abort();
+ }
+ if(e->origin_vertex->last_change >= 0 &&
+ e->terminal_vertex->last_change >= 0 &&
+ e->positivized_length < 0) {
+ residual_error -= e->positivized_length;
+ max_error = max(max_error, - e->positivized_length);
}
+#endif
+ e->positivized_length = 0.0;
}
}
#ifdef VERBOSE
- cerr << "residual_error " << residual_error << endl;
+ cerr << "residual_error " << residual_error << " max_error " << residual_error << endl;
#endif
}
-// This method does not change the edge occupation. It update
-// distance_from_source and best_pred_edge_to_source.
-void MTPGraph::find_shortest_path(Vertex **_front, Vertex **_new_front) {
+int MTPGraph::is_dag() {
+ Vertex *v;
+ Edge *e;
+
+ // We put everybody in the front
+ for(int k = 0; k < _nb_vertices; k++) {
+ _vertices[k].last_change = -1;
+ _front[k] = &_vertices[k];
+ }
+
+ int iteration = 0;
+ int front_size = _nb_vertices, pred_front_size;
+
+ do {
+ // We set the last_change field of all the vertices with incoming
+ // edges to the current iteration value
+ for(int f = 0; f < front_size; f++) {
+ v = _front[f];
+ for(e = v->leaving_edges; e; e = e->next_leaving_edge) {
+ e->terminal_vertex->last_change = iteration;
+ }
+ }
+
+ pred_front_size = front_size;
+ front_size = 0;
+
+ // We keep all the vertices with incoming nodes
+ for(int f = 0; f < pred_front_size; f++) {
+ v = _front[f];
+ if(v->last_change == iteration) {
+ _front[front_size++] = v;
+ }
+ }
+
+ iteration++;
+ } while(front_size < pred_front_size);
+
+ return front_size == 0;
+}
+
+// This method does not change the edge occupation. It only set
+// properly, for every vertex, the fields distance_from_source and
+// pred_edge_toward_source.
+
+void MTPGraph::find_shortest_path() {
Vertex **tmp_front;
- int tmp_front_size;
Vertex *v, *tv;
+ Edge *e;
scalar_t d;
- for(int v = 0; v < _nb_vertices; v++) {
- _vertices[v].distance_from_source = FLT_MAX;
- _vertices[v].best_pred_edge_to_source = 0;
- _vertices[v].iteration = 0;
+#ifdef DEBUG
+ if(is_dag()) {
+ cout << "find_shortest_path: DAG -> ok" << endl;
+ } else {
+ for(int e = 0; e < _nb_edges; e++) {
+ if(_edges[e].positivized_length < 0) abort();
+ }
+ cout << "find_shortest_path: All positivized_length are positive -> ok" << endl;
+ }
+#endif
+
+ for(int k = 0; k < _nb_vertices; k++) {
+ _vertices[k].distance_from_source = FLT_MAX;
+ _vertices[k].pred_edge_toward_source = 0;
+ _vertices[k].last_change = -1;
}
int iteration = 0;
- int _front_size = 0, _new_front_size;
- _front[_front_size++] = _source;
+ int front_size = 0, new_front_size;
+ _front[front_size++] = _source;
_source->distance_from_source = 0;
do {
- _new_front_size = 0;
- iteration++;
- for(int f = 0; f < _front_size; f++) {
+ new_front_size = 0;
+
+ for(int f = 0; f < front_size; f++) {
v = _front[f];
- for(Edge *e = v->root_edge; e; e = e->next) {
- d = v->distance_from_source + e->work_length;
+ for(e = v->leaving_edges; e; e = e->next_leaving_edge) {
+ d = v->distance_from_source + e->positivized_length;
tv = e->terminal_vertex;
if(d < tv->distance_from_source) {
tv->distance_from_source = d;
- tv->best_pred_edge_to_source = e;
- if(tv->iteration < iteration) {
- _new_front[_new_front_size++] = tv;
- tv->iteration = iteration;
+ tv->pred_edge_toward_source = e;
+ if(tv->last_change < iteration) {
+ _new_front[new_front_size++] = tv;
+ tv->last_change = iteration;
}
}
}
}
- tmp_front = _new_front;
- _new_front = _front;
- _front = tmp_front;
+ tmp_front = _new_front; _new_front = _front; _front = tmp_front;
+
+ front_size = new_front_size;
- tmp_front_size = _new_front_size;
- _new_front_size = _front_size;
- _front_size = tmp_front_size;
- } while(_front_size > 0);
+ iteration++;
+ } while(front_size > 0);
}
-void MTPGraph::find_best_paths(scalar_t *lengths, int *result_edge_occupation) {
+void MTPGraph::find_best_paths(scalar_t *lengths) {
scalar_t total_length;
Vertex *v;
Edge *e;
for(int e = 0; e < _nb_edges; e++) {
_edges[e].length = lengths[e];
- _edges[e].work_length = _edges[e].length;
+ _edges[e].occupied = 0;
+ _edges[e].positivized_length = _edges[e].length;
}
- // We use one iteration of find_shortest_path simply to propagate
- // the distance to make all the edge lengths positive.
- find_shortest_path(_front, _new_front);
- update_work_lengths();
-
- // #warning
- // initialize_work_lengths_with_min();
+ // We call find_shortest_path here to set properly the distances to
+ // the source, so that we can make all the edge lengths positive at
+ // the first iteration.
+ find_shortest_path();
do {
- force_positive_work_lengths();
- find_shortest_path(_front, _new_front);
- update_work_lengths();
+ update_positivized_lengths();
+ force_positivized_lengths();
+ find_shortest_path();
total_length = 0.0;
- // Do we reach the _sink?
- if(_sink->best_pred_edge_to_source) {
- // If yes, compute the length of the best path
+ // Do we reach the sink?
+ if(_sink->pred_edge_toward_source) {
+ // If yes, compute the length of the best path according to the
+ // original edge lengths
v = _sink;
- while(v->best_pred_edge_to_source) {
- total_length += v->best_pred_edge_to_source->length;
- v = v->best_pred_edge_to_source->origin_vertex;
+ while(v->pred_edge_toward_source) {
+ total_length += v->pred_edge_toward_source->length;
+ v = v->pred_edge_toward_source->origin_vertex;
}
// If that length is negative
if(total_length < 0.0) {
#ifdef VERBOSE
- cout << "Found a path of length " << total_length << endl;
+ cerr << "Found a path of length " << total_length << endl;
#endif
// Invert all the edges along the best path
v = _sink;
- while(v->best_pred_edge_to_source) {
- e = v->best_pred_edge_to_source;
+ while(v->pred_edge_toward_source) {
+ e = v->pred_edge_toward_source;
v = e->origin_vertex;
- e->revert();
+ e->invert();
+ // This is the only place where we change the occupations of
+ // edges
e->occupied = 1 - e->occupied;
}
}
} while(total_length < 0.0);
+ // Put back the graph in its original state (i.e. invert edges which
+ // have been inverted in the process)
for(int k = 0; k < _nb_edges; k++) {
- Edge *e = _edges + k;
- if(e->occupied) { e->revert(); }
- result_edge_occupation[k] = e->occupied;
+ e = _edges + k;
+ if(e->occupied) { e->invert(); }
+ }
+}
+
+int MTPGraph::retrieve_one_path(Edge *e, Path *path) {
+ Edge *f, *next = 0;
+ int l = 0;
+
+ if(path) {
+ path->nodes[l++] = e->origin_vertex->id;
+ path->length = e->length;
+ } else l++;
+
+ while(e->terminal_vertex != _sink) {
+ if(path) {
+ path->nodes[l++] = e->terminal_vertex->id;
+ path->length += e->length;
+ } else l++;
+ int nb_choices = 0;
+ for(f = e->terminal_vertex->leaving_edges; f; f = f->next_leaving_edge) {
+ if(f->occupied) { nb_choices++; next = f; }
+ }
+
+#ifdef DEBUG
+ if(nb_choices == 0) {
+ cerr << "retrieve_one_path: Non-sink end point." << endl;
+ abort();
+ }
+ if(nb_choices > 1) {
+ cerr << "retrieve_one_path: Non node-disjoint paths." << endl;
+ abort();
+ }
+#endif
+
+ e = next;
+ }
+
+ if(path) {
+ path->nodes[l++] = e->terminal_vertex->id;
+ path->length += e->length;
+ } else l++;
+
+ return l;
+}
+
+void MTPGraph::retrieve_disjoint_paths() {
+ Edge *e;
+
+ for(int p = 0; p < nb_paths; p++) delete paths[p];
+ delete[] paths;
+
+ nb_paths = 0;
+ for(e = _source->leaving_edges; e; e = e->next_leaving_edge) {
+ if(e->occupied) { nb_paths++; }
+ }
+
+ paths = new Path *[nb_paths];
+
+ int p = 0;
+ for(e = _source->leaving_edges; e; e = e->next_leaving_edge) {
+ if(e->occupied) {
+ int l = retrieve_one_path(e, 0);
+ paths[p] = new Path(l);
+ retrieve_one_path(e, paths[p]);
+ p++;
+ }
}
}
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