1// Ceres Solver - A fast non-linear least squares minimizer
2// Copyright 2010, 2011, 2012 Google Inc. All rights reserved.
3// http://code.google.com/p/ceres-solver/
4//
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6// modification, are permitted provided that the following conditions are met:
7//
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9//   this list of conditions and the following disclaimer.
10// * Redistributions in binary form must reproduce the above copyright notice,
11//   this list of conditions and the following disclaimer in the documentation
12//   and/or other materials provided with the distribution.
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14//   used to endorse or promote products derived from this software without
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16//
17// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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28//
29// Author: kushalav@google.com (Avanish Kushal)
30
31// This include must come before any #ifndef check on Ceres compile options.
32#include "ceres/internal/port.h"
33
34#ifndef CERES_NO_SUITESPARSE
35
36#include "ceres/visibility.h"
37
38#include <cmath>
39#include <ctime>
40#include <algorithm>
41#include <set>
42#include <vector>
43#include <utility>
44#include "ceres/block_structure.h"
45#include "ceres/collections_port.h"
46#include "ceres/graph.h"
47#include "glog/logging.h"
48
49namespace ceres {
50namespace internal {
51
52void ComputeVisibility(const CompressedRowBlockStructure& block_structure,
53                       const int num_eliminate_blocks,
54                       vector< set<int> >* visibility) {
55  CHECK_NOTNULL(visibility);
56
57  // Clear the visibility vector and resize it to hold a
58  // vector for each camera.
59  visibility->resize(0);
60  visibility->resize(block_structure.cols.size() - num_eliminate_blocks);
61
62  for (int i = 0; i < block_structure.rows.size(); ++i) {
63    const vector<Cell>& cells = block_structure.rows[i].cells;
64    int block_id = cells[0].block_id;
65    // If the first block is not an e_block, then skip this row block.
66    if (block_id >= num_eliminate_blocks) {
67      continue;
68    }
69
70    for (int j = 1; j < cells.size(); ++j) {
71      int camera_block_id = cells[j].block_id - num_eliminate_blocks;
72      DCHECK_GE(camera_block_id, 0);
73      DCHECK_LT(camera_block_id, visibility->size());
74      (*visibility)[camera_block_id].insert(block_id);
75    }
76  }
77}
78
79Graph<int>* CreateSchurComplementGraph(const vector<set<int> >& visibility) {
80  const time_t start_time = time(NULL);
81  // Compute the number of e_blocks/point blocks. Since the visibility
82  // set for each e_block/camera contains the set of e_blocks/points
83  // visible to it, we find the maximum across all visibility sets.
84  int num_points = 0;
85  for (int i = 0; i < visibility.size(); i++) {
86    if (visibility[i].size() > 0) {
87      num_points = max(num_points, (*visibility[i].rbegin()) + 1);
88    }
89  }
90
91  // Invert the visibility. The input is a camera->point mapping,
92  // which tells us which points are visible in which
93  // cameras. However, to compute the sparsity structure of the Schur
94  // Complement efficiently, its better to have the point->camera
95  // mapping.
96  vector<set<int> > inverse_visibility(num_points);
97  for (int i = 0; i < visibility.size(); i++) {
98    const set<int>& visibility_set = visibility[i];
99    for (set<int>::const_iterator it = visibility_set.begin();
100         it != visibility_set.end();
101         ++it) {
102      inverse_visibility[*it].insert(i);
103    }
104  }
105
106  // Map from camera pairs to number of points visible to both cameras
107  // in the pair.
108  HashMap<pair<int, int>, int > camera_pairs;
109
110  // Count the number of points visible to each camera/f_block pair.
111  for (vector<set<int> >::const_iterator it = inverse_visibility.begin();
112       it != inverse_visibility.end();
113       ++it) {
114    const set<int>& inverse_visibility_set = *it;
115    for (set<int>::const_iterator camera1 = inverse_visibility_set.begin();
116         camera1 != inverse_visibility_set.end();
117         ++camera1) {
118      set<int>::const_iterator camera2 = camera1;
119      for (++camera2; camera2 != inverse_visibility_set.end(); ++camera2) {
120        ++(camera_pairs[make_pair(*camera1, *camera2)]);
121      }
122    }
123  }
124
125  Graph<int>* graph = new Graph<int>();
126
127  // Add vertices and initialize the pairs for self edges so that self
128  // edges are guaranteed. This is needed for the Canonical views
129  // algorithm to work correctly.
130  static const double kSelfEdgeWeight = 1.0;
131  for (int i = 0; i < visibility.size(); ++i) {
132    graph->AddVertex(i);
133    graph->AddEdge(i, i, kSelfEdgeWeight);
134  }
135
136  // Add an edge for each camera pair.
137  for (HashMap<pair<int, int>, int>::const_iterator it = camera_pairs.begin();
138       it != camera_pairs.end();
139       ++it) {
140    const int camera1 = it->first.first;
141    const int camera2 = it->first.second;
142    CHECK_NE(camera1, camera2);
143
144    const int count = it->second;
145    // Static cast necessary for Windows.
146    const double weight = static_cast<double>(count) /
147        (sqrt(static_cast<double>(
148                  visibility[camera1].size() * visibility[camera2].size())));
149    graph->AddEdge(camera1, camera2, weight);
150  }
151
152  VLOG(2) << "Schur complement graph time: " << (time(NULL) - start_time);
153  return graph;
154}
155
156}  // namespace internal
157}  // namespace ceres
158
159#endif  // CERES_NO_SUITESPARSE
160