1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
|
/* ----------------------------------------------------------------------------
* GTSAM Copyright 2010, Georgia Tech Research Corporation,
* Atlanta, Georgia 30332-0415
* All Rights Reserved
* Authors: Frank Dellaert, et al. (see THANKS for the full author list)
* See LICENSE for the license information
* -------------------------------------------------------------------------- */
/**
* @file TriangulationLOSTExample.cpp
* @author Akshay Krishnan
* @brief This example runs triangulation several times using 3 different
* approaches: LOST, DLT, and DLT with optimization. It reports the covariance
* and the runtime for each approach.
*
* @date 2022-07-10
*/
#include <gtsam/geometry/Cal3_S2.h>
#include <gtsam/geometry/PinholeCamera.h>
#include <gtsam/geometry/Point2.h>
#include <gtsam/geometry/Point3.h>
#include <gtsam/geometry/Pose3.h>
#include <gtsam/geometry/Rot3.h>
#include <gtsam/geometry/triangulation.h>
#include <chrono>
#include <iostream>
#include <random>
using namespace std;
using namespace gtsam;
static std::mt19937 rng(42);
void PrintCovarianceStats(const Matrix& mat, const std::string& method) {
Matrix centered = mat.rowwise() - mat.colwise().mean();
Matrix cov = (centered.adjoint() * centered) / double(mat.rows() - 1);
std::cout << method << " covariance: " << std::endl;
std::cout << cov << std::endl;
std::cout << "Trace sqrt: " << sqrt(cov.trace()) << std::endl << std::endl;
}
void PrintDuration(const std::chrono::nanoseconds dur, double num_samples,
const std::string& method) {
double nanoseconds = dur.count() / num_samples;
std::cout << "Time taken by " << method << ": " << nanoseconds * 1e-3
<< std::endl;
}
void GetLargeCamerasDataset(CameraSet<PinholeCamera<Cal3_S2>>* cameras,
std::vector<Pose3>* poses, Point3* point,
Point2Vector* measurements) {
const double minXY = -10, maxXY = 10;
const double minZ = -20, maxZ = 0;
const int nrCameras = 500;
cameras->reserve(nrCameras);
poses->reserve(nrCameras);
measurements->reserve(nrCameras);
*point = Point3(0.0, 0.0, 10.0);
std::uniform_real_distribution<double> rand_xy(minXY, maxXY);
std::uniform_real_distribution<double> rand_z(minZ, maxZ);
Cal3_S2 identityK;
for (int i = 0; i < nrCameras; ++i) {
Point3 wti(rand_xy(rng), rand_xy(rng), rand_z(rng));
Pose3 wTi(Rot3(), wti);
poses->push_back(wTi);
cameras->emplace_back(wTi, identityK);
measurements->push_back(cameras->back().project(*point));
}
}
void GetSmallCamerasDataset(CameraSet<PinholeCamera<Cal3_S2>>* cameras,
std::vector<Pose3>* poses, Point3* point,
Point2Vector* measurements) {
Pose3 pose1;
Pose3 pose2(Rot3(), Point3(5., 0., -5.));
Cal3_S2 identityK;
PinholeCamera<Cal3_S2> camera1(pose1, identityK);
PinholeCamera<Cal3_S2> camera2(pose2, identityK);
*point = Point3(0, 0, 1);
cameras->push_back(camera1);
cameras->push_back(camera2);
*poses = {pose1, pose2};
*measurements = {camera1.project(*point), camera2.project(*point)};
}
Point2Vector AddNoiseToMeasurements(const Point2Vector& measurements,
const double measurementSigma) {
std::normal_distribution<double> normal(0.0, measurementSigma);
Point2Vector noisyMeasurements;
noisyMeasurements.reserve(measurements.size());
for (const auto& p : measurements) {
noisyMeasurements.emplace_back(p.x() + normal(rng), p.y() + normal(rng));
}
return noisyMeasurements;
}
/* ************************************************************************* */
int main(int argc, char* argv[]) {
CameraSet<PinholeCamera<Cal3_S2>> cameras;
std::vector<Pose3> poses;
Point3 landmark;
Point2Vector measurements;
GetLargeCamerasDataset(&cameras, &poses, &landmark, &measurements);
// GetSmallCamerasDataset(&cameras, &poses, &landmark, &measurements);
const double measurementSigma = 1e-2;
SharedNoiseModel measurementNoise =
noiseModel::Isotropic::Sigma(2, measurementSigma);
const long int nrTrials = 1000;
Matrix errorsDLT = Matrix::Zero(nrTrials, 3);
Matrix errorsLOST = Matrix::Zero(nrTrials, 3);
Matrix errorsDLTOpt = Matrix::Zero(nrTrials, 3);
double rank_tol = 1e-9;
boost::shared_ptr<Cal3_S2> calib = boost::make_shared<Cal3_S2>();
std::chrono::nanoseconds durationDLT;
std::chrono::nanoseconds durationDLTOpt;
std::chrono::nanoseconds durationLOST;
for (int i = 0; i < nrTrials; i++) {
Point2Vector noisyMeasurements =
AddNoiseToMeasurements(measurements, measurementSigma);
auto lostStart = std::chrono::high_resolution_clock::now();
boost::optional<Point3> estimateLOST = triangulatePoint3<Cal3_S2>(
cameras, noisyMeasurements, rank_tol, false, measurementNoise, true);
durationLOST += std::chrono::high_resolution_clock::now() - lostStart;
auto dltStart = std::chrono::high_resolution_clock::now();
boost::optional<Point3> estimateDLT = triangulatePoint3<Cal3_S2>(
cameras, noisyMeasurements, rank_tol, false, measurementNoise, false);
durationDLT += std::chrono::high_resolution_clock::now() - dltStart;
auto dltOptStart = std::chrono::high_resolution_clock::now();
boost::optional<Point3> estimateDLTOpt = triangulatePoint3<Cal3_S2>(
cameras, noisyMeasurements, rank_tol, true, measurementNoise, false);
durationDLTOpt += std::chrono::high_resolution_clock::now() - dltOptStart;
errorsLOST.row(i) = *estimateLOST - landmark;
errorsDLT.row(i) = *estimateDLT - landmark;
errorsDLTOpt.row(i) = *estimateDLTOpt - landmark;
}
PrintCovarianceStats(errorsLOST, "LOST");
PrintCovarianceStats(errorsDLT, "DLT");
PrintCovarianceStats(errorsDLTOpt, "DLT_OPT");
PrintDuration(durationLOST, nrTrials, "LOST");
PrintDuration(durationDLT, nrTrials, "DLT");
PrintDuration(durationDLTOpt, nrTrials, "DLT_OPT");
}
|
