testPinholeCamera.cpp
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1 /* ----------------------------------------------------------------------------
2 
3  * GTSAM Copyright 2010, Georgia Tech Research Corporation,
4  * Atlanta, Georgia 30332-0415
5  * All Rights Reserved
6  * Authors: Frank Dellaert, et al. (see THANKS for the full author list)
7 
8  * See LICENSE for the license information
9 
10  * -------------------------------------------------------------------------- */
11 
18 #include <gtsam/geometry/PinholeCamera.h>
19 #include <gtsam/geometry/Cal3_S2.h>
20 #include <gtsam/geometry/Cal3Bundler.h>
21 #include <gtsam/geometry/Pose2.h>
22 #include <gtsam/base/Testable.h>
23 #include <gtsam/base/numericalDerivative.h>
24 
25 #include <CppUnitLite/TestHarness.h>
26 
27 #include <cmath>
28 #include <iostream>
29 
30 using namespace std::placeholders;
31 using namespace std;
32 using namespace gtsam;
33 
34 typedef PinholeCamera<Cal3_S2> Camera;
35 
36 static const Cal3_S2 K(625, 625, 0, 0, 0);
37 
38 static const Pose3 pose(Rot3(Vector3(1, -1, -1).asDiagonal()), Point3(0, 0, 0.5));
39 static const Camera camera(pose, K);
40 
41 static const Pose3 pose1(Rot3(), Point3(0, 1, 0.5));
42 static const Camera camera1(pose1, K);
43 
44 static const Point3 point1(-0.08,-0.08, 0.0);
45 static const Point3 point2(-0.08, 0.08, 0.0);
46 static const Point3 point3( 0.08, 0.08, 0.0);
47 static const Point3 point4( 0.08,-0.08, 0.0);
48 
49 static const Unit3 point1_inf(-0.16,-0.16, -1.0);
50 static const Unit3 point2_inf(-0.16, 0.16, -1.0);
51 static const Unit3 point3_inf( 0.16, 0.16, -1.0);
52 static const Unit3 point4_inf( 0.16,-0.16, -1.0);
53 
54 /* ************************************************************************* */
55 TEST( PinholeCamera, constructor)
56 {
57  EXPECT(assert_equal( K, camera.calibration()));
58  EXPECT(assert_equal( pose, camera.pose()));
59 }
60 
61 //******************************************************************************
62 TEST(PinholeCamera, Create) {
63 
64  Matrix actualH1, actualH2;
65  EXPECT(assert_equal(camera, Camera::Create(pose,K, actualH1, actualH2)));
66 
67  // Check derivative
68  std::function<Camera(Pose3, Cal3_S2)> f = //
69  std::bind(Camera::Create, std::placeholders::_1, std::placeholders::_2,
70  nullptr, nullptr);
71  Matrix numericalH1 = numericalDerivative21<Camera,Pose3,Cal3_S2>(f,pose,K);
72  EXPECT(assert_equal(numericalH1, actualH1, 1e-9));
73  Matrix numericalH2 = numericalDerivative22<Camera,Pose3,Cal3_S2>(f,pose,K);
74  EXPECT(assert_equal(numericalH2, actualH2, 1e-8));
75 }
76 
77 //******************************************************************************
78 TEST(PinholeCamera, Pose) {
79 
80  Matrix actualH;
81  EXPECT(assert_equal(pose, camera.getPose(actualH)));
82 
83  // Check derivative
84  std::function<Pose3(Camera)> f = //
85  std::bind(&Camera::getPose, std::placeholders::_1, nullptr);
86  Matrix numericalH = numericalDerivative11<Pose3,Camera>(f,camera);
87  EXPECT(assert_equal(numericalH, actualH, 1e-9));
88 }
89 
90 /* ************************************************************************* */
91 TEST( PinholeCamera, level2)
92 {
93  // Create a level camera, looking in Y-direction
94  Pose2 pose2(0.4,0.3,M_PI/2.0);
95  Camera camera = Camera::Level(K, pose2, 0.1);
96 
97  // expected
98  Point3 x(1,0,0),y(0,0,-1),z(0,1,0);
99  Rot3 wRc(x,y,z);
100  Pose3 expected(wRc,Point3(0.4,0.3,0.1));
101  EXPECT(assert_equal( camera.pose(), expected));
102 }
103 
104 /* ************************************************************************* */
105 TEST( PinholeCamera, lookat)
106 {
107  // Create a level camera, looking in Y-direction
108  Point3 C(10,0,0);
109  Camera camera = Camera::Lookat(C, Point3(0,0,0), Point3(0,0,1));
110 
111  // expected
112  Point3 xc(0,1,0),yc(0,0,-1),zc(-1,0,0);
113  Pose3 expected(Rot3(xc,yc,zc),C);
114  EXPECT(assert_equal(camera.pose(), expected));
115 
116  Point3 C2(30,0,10);
117  Camera camera2 = Camera::Lookat(C2, Point3(0,0,0), Point3(0,0,1));
118 
119  Matrix R = camera2.pose().rotation().matrix();
120  Matrix I = trans(R)*R;
121  EXPECT(assert_equal(I, I_3x3));
122 }
123 
124 /* ************************************************************************* */
125 TEST( PinholeCamera, project)
126 {
127  EXPECT(assert_equal( camera.project(point1), Point2(-100, 100) ));
128  EXPECT(assert_equal( camera.project(point2), Point2(-100, -100) ));
129  EXPECT(assert_equal( camera.project(point3), Point2( 100, -100) ));
130  EXPECT(assert_equal( camera.project(point4), Point2( 100, 100) ));
131 }
132 
133 /* ************************************************************************* */
134 TEST( PinholeCamera, backproject)
135 {
136  EXPECT(assert_equal( camera.backproject(Point2(-100, 100), 0.5), point1));
137  EXPECT(assert_equal( camera.backproject(Point2(-100, -100), 0.5), point2));
138  EXPECT(assert_equal( camera.backproject(Point2( 100, -100), 0.5), point3));
139  EXPECT(assert_equal( camera.backproject(Point2( 100, 100), 0.5), point4));
140 }
141 
142 /* ************************************************************************* */
143 TEST( PinholeCamera, backprojectInfinity)
144 {
145  EXPECT(assert_equal( camera.backprojectPointAtInfinity(Point2(-100, 100)), point1_inf));
146  EXPECT(assert_equal( camera.backprojectPointAtInfinity(Point2(-100, -100)), point2_inf));
147  EXPECT(assert_equal( camera.backprojectPointAtInfinity(Point2( 100, -100)), point3_inf));
148  EXPECT(assert_equal( camera.backprojectPointAtInfinity(Point2( 100, 100)), point4_inf));
149 }
150 
151 /* ************************************************************************* */
152 TEST( PinholeCamera, backproject2)
153 {
154  Point3 origin(0,0,0);
155  Rot3 rot(1., 0., 0., 0., 0., 1., 0., -1., 0.); // a camera1 looking down
156  Camera camera(Pose3(rot, origin), K);
157 
158  Point3 actual = camera.backproject(Point2(0,0), 1.);
159  Point3 expected(0., 1., 0.);
160  pair<Point2, bool> x = camera.projectSafe(expected);
161 
162  EXPECT(assert_equal(expected, actual));
163  EXPECT(assert_equal(Point2(0,0), x.first));
164  EXPECT(x.second);
165 }
166 
167 /* ************************************************************************* */
168 TEST( PinholeCamera, backprojectInfinity2)
169 {
170  Point3 origin(0,0,0);
171  Rot3 rot(1., 0., 0., 0., 0., 1., 0., -1., 0.); // a camera1 looking down
172  Camera camera(Pose3(rot, origin), K);
173 
174  Unit3 actual = camera.backprojectPointAtInfinity(Point2(0,0));
175  Unit3 expected(0., 1., 0.);
176  Point2 x = camera.project(expected);
177 
178  EXPECT(assert_equal(expected, actual));
179  EXPECT(assert_equal(Point2(0,0), x));
180 }
181 
182 /* ************************************************************************* */
183 TEST( PinholeCamera, backprojectInfinity3)
184 {
185  Point3 origin(0,0,0);
186  Rot3 rot(1., 0., 0., 0., 1., 0., 0., 0., 1.); // identity
187  Camera camera(Pose3(rot, origin), K);
188 
189  Unit3 actual = camera.backprojectPointAtInfinity(Point2(0,0));
190  Unit3 expected(0., 0., 1.);
191  Point2 x = camera.project(expected);
192 
193  EXPECT(assert_equal(expected, actual));
194  EXPECT(assert_equal(Point2(0,0), x));
195 }
196 
197 /* ************************************************************************* */
198 static Point2 project3(const Pose3& pose, const Point3& point, const Cal3_S2& cal) {
199  return Camera(pose,cal).project(point);
200 }
201 
202 /* ************************************************************************* */
203 TEST( PinholeCamera, Dproject)
204 {
205  Matrix Dpose, Dpoint, Dcal;
206  Point2 result = camera.project(point1, Dpose, Dpoint, Dcal);
207  Matrix numerical_pose = numericalDerivative31(project3, pose, point1, K);
208  Matrix Hexpected2 = numericalDerivative32(project3, pose, point1, K);
209  Matrix numerical_cal = numericalDerivative33(project3, pose, point1, K);
210  EXPECT(assert_equal(Point2(-100, 100), result));
211  EXPECT(assert_equal(numerical_pose, Dpose, 1e-7));
212  EXPECT(assert_equal(Hexpected2, Dpoint, 1e-7));
213  EXPECT(assert_equal(numerical_cal, Dcal, 1e-7));
214 }
215 
216 /* ************************************************************************* */
217 static Point2 projectInfinity3(const Pose3& pose, const Unit3& point3D, const Cal3_S2& cal) {
218  return Camera(pose,cal).project(point3D);
219 }
220 
221 TEST( PinholeCamera, Dproject_Infinity)
222 {
223  Matrix Dpose, Dpoint, Dcal;
224  Unit3 point3D(point1.x(), point1.y(), -10.0); // a point in front of the camera1
225 
226  // test Projection
227  Point2 actual = camera.project(point3D, Dpose, Dpoint, Dcal);
228  Point2 expected(-5.0, 5.0);
229  EXPECT(assert_equal(actual, expected, 1e-7));
230 
231  // test Jacobians
232  Matrix numerical_pose = numericalDerivative31(projectInfinity3, pose, point3D, K);
233  Matrix Hexpected2 = numericalDerivative32(projectInfinity3, pose, point3D, K);
234  Matrix numerical_point2x2 = Hexpected2.block(0,0,2,2); // only the direction to the point matters
235  Matrix numerical_cal = numericalDerivative33(projectInfinity3, pose, point3D, K);
236  EXPECT(assert_equal(numerical_pose, Dpose, 1e-7));
237  EXPECT(assert_equal(numerical_point2x2, Dpoint, 1e-7));
238  EXPECT(assert_equal(numerical_cal, Dcal, 1e-7));
239 }
240 
241 /* ************************************************************************* */
242 static Point2 project4(const Camera& camera, const Point3& point) {
243  return camera.project2(point);
244 }
245 
246 /* ************************************************************************* */
247 TEST( PinholeCamera, Dproject2)
248 {
249  Matrix Dcamera, Dpoint;
250  Point2 result = camera.project2(point1, Dcamera, Dpoint);
251  Matrix Hexpected1 = numericalDerivative21(project4, camera, point1);
252  Matrix Hexpected2 = numericalDerivative22(project4, camera, point1);
253  EXPECT(assert_equal(result, Point2(-100, 100) ));
254  EXPECT(assert_equal(Hexpected1, Dcamera, 1e-7));
255  EXPECT(assert_equal(Hexpected2, Dpoint, 1e-7));
256 }
257 
258 /* ************************************************************************* */
259 // Add a test with more arbitrary rotation
260 TEST( PinholeCamera, Dproject3)
261 {
262  static const Pose3 pose1(Rot3::Ypr(0.1, -0.1, 0.4), Point3(0, 0, -10));
263  static const Camera camera(pose1);
264  Matrix Dpose, Dpoint;
265  camera.project2(point1, Dpose, Dpoint);
266  Matrix numerical_pose = numericalDerivative21(project4, camera, point1);
267  Matrix numerical_point = numericalDerivative22(project4, camera, point1);
268  CHECK(assert_equal(numerical_pose, Dpose, 1e-7));
269  CHECK(assert_equal(numerical_point, Dpoint, 1e-7));
270 }
271 
272 /* ************************************************************************* */
273 static double range0(const Camera& camera, const Point3& point) {
274  return camera.range(point);
275 }
276 
277 /* ************************************************************************* */
278 TEST( PinholeCamera, range0) {
279  Matrix D1; Matrix D2;
280  double result = camera.range(point1, D1, D2);
281  Matrix Hexpected1 = numericalDerivative21(range0, camera, point1);
282  Matrix Hexpected2 = numericalDerivative22(range0, camera, point1);
283  EXPECT_DOUBLES_EQUAL(distance3(point1, camera.pose().translation()), result,
284  1e-9);
285  EXPECT(assert_equal(Hexpected1, D1, 1e-7));
286  EXPECT(assert_equal(Hexpected2, D2, 1e-7));
287 }
288 
289 /* ************************************************************************* */
290 static double range1(const Camera& camera, const Pose3& pose) {
291  return camera.range(pose);
292 }
293 
294 /* ************************************************************************* */
295 TEST( PinholeCamera, range1) {
296  Matrix D1; Matrix D2;
297  double result = camera.range(pose1, D1, D2);
298  Matrix Hexpected1 = numericalDerivative21(range1, camera, pose1);
299  Matrix Hexpected2 = numericalDerivative22(range1, camera, pose1);
300  EXPECT_DOUBLES_EQUAL(1, result, 1e-9);
301  EXPECT(assert_equal(Hexpected1, D1, 1e-7));
302  EXPECT(assert_equal(Hexpected2, D2, 1e-7));
303 }
304 
305 /* ************************************************************************* */
306 typedef PinholeCamera<Cal3Bundler> Camera2;
307 static const Cal3Bundler K2(625, 1e-3, 1e-3);
308 static const Camera2 camera2(pose1, K2);
309 static double range2(const Camera& camera, const Camera2& camera2) {
310  return camera.range<Cal3Bundler>(camera2);
311 }
312 
313 /* ************************************************************************* */
314 TEST( PinholeCamera, range2) {
315  Matrix D1; Matrix D2;
316  double result = camera.range<Cal3Bundler>(camera2, D1, D2);
317  Matrix Hexpected1 = numericalDerivative21(range2, camera, camera2);
318  Matrix Hexpected2 = numericalDerivative22(range2, camera, camera2);
319  EXPECT_DOUBLES_EQUAL(1, result, 1e-9);
320  EXPECT(assert_equal(Hexpected1, D1, 1e-7));
321  EXPECT(assert_equal(Hexpected2, D2, 1e-7));
322 }
323 
324 /* ************************************************************************* */
325 static const CalibratedCamera camera3(pose1);
326 static double range3(const Camera& camera, const CalibratedCamera& camera3) {
327  return camera.range(camera3);
328 }
329 
330 /* ************************************************************************* */
331 TEST( PinholeCamera, range3) {
332  Matrix D1; Matrix D2;
333  double result = camera.range(camera3, D1, D2);
334  Matrix Hexpected1 = numericalDerivative21(range3, camera, camera3);
335  Matrix Hexpected2 = numericalDerivative22(range3, camera, camera3);
336  EXPECT_DOUBLES_EQUAL(1, result, 1e-9);
337  EXPECT(assert_equal(Hexpected1, D1, 1e-7));
338  EXPECT(assert_equal(Hexpected2, D2, 1e-7));
339 }
340 
341 /* ************************************************************************* */
342 TEST( PinholeCamera, Cal3Bundler) {
343  Cal3Bundler calibration;
344  Pose3 wTc;
345  PinholeCamera<Cal3Bundler> camera(wTc, calibration);
346  Point2 p(50, 100);
347  camera.backproject(p, 10);
348 }
349 
350 /* ************************************************************************* */
351 int main() { TestResult tr; return TestRegistry::runAllTests(tr); }
352 /* ************************************************************************* */
353 
354 
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