fix triangulatePoint3 for calibrations with distortion

Prior implementation only used the K() portion of all Cal3 calibrations
for the linear triangulation of points with triangulatePoint3.
- Added tests for triangulation with non-Cal3_S2 calibrations.
- Added skew to the test Cal3_S2 calibration.
- Added an undistortMeasurements step to triangulatePoint3 so that
linear triangulation works for calibrations with distortion
coefficients.

gtsam/geometry/tests/testTriangulation.cpp

@@ -19,6 +19,7 @@
 
 #include <CppUnitLite/TestHarness.h>
 #include <gtsam/geometry/Cal3Bundler.h>
+#include <gtsam/geometry/Cal3DS2.h>
 #include <gtsam/geometry/CameraSet.h>
 #include <gtsam/geometry/PinholeCamera.h>
 #include <gtsam/geometry/SphericalCamera.h>
@@ -38,7 +39,7 @@ using namespace boost::assign;
 // Some common constants
 
 static const boost::shared_ptr<Cal3_S2> sharedCal =  //
-    boost::make_shared<Cal3_S2>(1500, 1200, 0, 640, 480);
+    boost::make_shared<Cal3_S2>(1500, 1200, 0.1, 640, 480);
 
 // Looking along X-axis, 1 meter above ground plane (x-y)
 static const Rot3 upright = Rot3::Ypr(-M_PI / 2, 0., -M_PI / 2);
@@ -95,11 +96,113 @@ TEST(triangulation, twoPoses) {
   EXPECT(assert_equal(Point3(4.995, 0.499167, 1.19814), *actual4, 1e-4));
 }
 
+//******************************************************************************
+// Simple test with a well-behaved two camera situation with Cal3S2 calibration.
+TEST(triangulation, twoPosesCal3S2) {
+    static const boost::shared_ptr<Cal3DS2> sharedDistortedCal =  //
+            boost::make_shared<Cal3DS2>(1500, 1200, 0, 640, 480, -.3, 0.1, 0.0001, -0.0003);
+
+    PinholeCamera<Cal3DS2> camera1Distorted(pose1, *sharedDistortedCal);
+
+    PinholeCamera<Cal3DS2> camera2Distorted(pose2, *sharedDistortedCal);
+
+// 1. Project two landmarks into two cameras and triangulate
+    Point2 z1Distorted = camera1Distorted.project(landmark);
+    Point2 z2Distorted = camera2Distorted.project(landmark);
+
+    vector<Pose3> poses;
+    Point2Vector measurements;
+
+    poses += pose1, pose2;
+    measurements += z1Distorted, z2Distorted;
+
+    double rank_tol = 1e-9;
+
+    // 1. Test simple DLT, perfect in no noise situation
+    bool optimize = false;
+    boost::optional<Point3> actual1 =  //
+            triangulatePoint3<Cal3DS2>(poses, sharedDistortedCal, measurements, rank_tol, optimize);
+    EXPECT(assert_equal(landmark, *actual1, 1e-7));
+
+    // 2. test with optimization on, same answer
+    optimize = true;
+    boost::optional<Point3> actual2 =  //
+            triangulatePoint3<Cal3DS2>(poses, sharedDistortedCal, measurements, rank_tol, optimize);
+    EXPECT(assert_equal(landmark, *actual2, 1e-7));
+
+    // 3. Add some noise and try again: result should be ~ (4.995,
+    // 0.499167, 1.19814)
+    measurements.at(0) += Point2(0.1, 0.5);
+    measurements.at(1) += Point2(-0.2, 0.3);
+    optimize = false;
+    boost::optional<Point3> actual3 =  //
+            triangulatePoint3<Cal3DS2>(poses, sharedDistortedCal, measurements, rank_tol, optimize);
+    EXPECT(assert_equal(Point3(4.995, 0.499167, 1.19814), *actual3, 1e-3));
+
+    // 4. Now with optimization on
+    optimize = true;
+    boost::optional<Point3> actual4 =  //
+            triangulatePoint3<Cal3DS2>(poses, sharedDistortedCal, measurements, rank_tol, optimize);
+    EXPECT(assert_equal(Point3(4.995, 0.499167, 1.19814), *actual4, 1e-3));
+}
+
+//******************************************************************************
+// Simple test with a well-behaved two camera situation with Fisheye calibration.
+TEST(triangulation, twoPosesFisheye) {
+    using Calibration = Cal3Fisheye;
+    static const boost::shared_ptr<Calibration> sharedDistortedCal =  //
+            boost::make_shared<Calibration>(1500, 1200, .1, 640, 480, -.3, 0.1, 0.0001, -0.0003);
+
+    PinholeCamera<Calibration> camera1Distorted(pose1, *sharedDistortedCal);
+
+    PinholeCamera<Calibration> camera2Distorted(pose2, *sharedDistortedCal);
+
+// 1. Project two landmarks into two cameras and triangulate
+    Point2 z1Distorted = camera1Distorted.project(landmark);
+    Point2 z2Distorted = camera2Distorted.project(landmark);
+
+    vector<Pose3> poses;
+    Point2Vector measurements;
+
+    poses += pose1, pose2;
+    measurements += z1Distorted, z2Distorted;
+
+    double rank_tol = 1e-9;
+
+    // 1. Test simple DLT, perfect in no noise situation
+    bool optimize = false;
+    boost::optional<Point3> actual1 =  //
+            triangulatePoint3<Calibration>(poses, sharedDistortedCal, measurements, rank_tol, optimize);
+    EXPECT(assert_equal(landmark, *actual1, 1e-7));
+
+    // 2. test with optimization on, same answer
+    optimize = true;
+    boost::optional<Point3> actual2 =  //
+            triangulatePoint3<Calibration>(poses, sharedDistortedCal, measurements, rank_tol, optimize);
+    EXPECT(assert_equal(landmark, *actual2, 1e-7));
+
+    // 3. Add some noise and try again: result should be ~ (4.995,
+    // 0.499167, 1.19814)
+    measurements.at(0) += Point2(0.1, 0.5);
+    measurements.at(1) += Point2(-0.2, 0.3);
+    optimize = false;
+    boost::optional<Point3> actual3 =  //
+            triangulatePoint3<Calibration>(poses, sharedDistortedCal, measurements, rank_tol, optimize);
+    EXPECT(assert_equal(Point3(4.995, 0.499167, 1.19814), *actual3, 1e-3));
+
+    // 4. Now with optimization on
+    optimize = true;
+    boost::optional<Point3> actual4 =  //
+            triangulatePoint3<Calibration>(poses, sharedDistortedCal, measurements, rank_tol, optimize);
+    EXPECT(assert_equal(Point3(4.995, 0.499167, 1.19814), *actual4, 1e-3));
+}
+
+
 //******************************************************************************
 // Similar, but now with Bundler calibration
 TEST(triangulation, twoPosesBundler) {
   boost::shared_ptr<Cal3Bundler> bundlerCal =  //
-      boost::make_shared<Cal3Bundler>(1500, 0, 0, 640, 480);
+      boost::make_shared<Cal3Bundler>(1500, 0.1, 0.2, 640, 480);
   PinholeCamera<Cal3Bundler> camera1(pose1, *bundlerCal);
   PinholeCamera<Cal3Bundler> camera2(pose2, *bundlerCal);
 
@@ -126,7 +229,7 @@ TEST(triangulation, twoPosesBundler) {
 
   boost::optional<Point3> actual2 =  //
       triangulatePoint3<Cal3Bundler>(poses, bundlerCal, measurements, rank_tol, optimize);
-  EXPECT(assert_equal(Point3(4.995, 0.499167, 1.19847), *actual2, 1e-4));
+  EXPECT(assert_equal(Point3(4.995, 0.499167, 1.19847), *actual2, 1e-3));
 }
 
 //******************************************************************************

gtsam/geometry/triangulation.h

@@ -227,6 +227,35 @@ std::vector<Matrix34, Eigen::aligned_allocator<Matrix34>> projectionMatricesFrom
   return projection_matrices;
 }
 
+/** Remove distortion for measurements so as if the measurements came from a pinhole camera.
+ *
+ * Removes distortion but maintains the K matrix of the initial sharedCal. Operates by calibrating using
+ * full calibration and uncalibrating with only the pinhole component of the calibration.
+ * @tparam CALIBRATION Calibration type to use.
+ * @param sharedCal Calibration with which measurements were taken.
+ * @param measurements Vector of measurements to undistort.
+ * @return measurements with the effect of the distortion of sharedCal removed.
+ */
+template <class CALIBRATION>
+Point2Vector undistortMeasurements(boost::shared_ptr<CALIBRATION> sharedCal, const Point2Vector& measurements) {
+    const auto& K = sharedCal->K();
+    Cal3_S2 pinholeCalibration(K(0,0), K(1,1), K(0,1), K(0,2), K(1,2));
+    Point2Vector undistortedMeasurements;
+    // Calibrate with sharedCal and uncalibrate with pinhole version of sharedCal so that measurements are undistorted.
+    std::transform(measurements.begin(), measurements.end(), std::back_inserter(undistortedMeasurements), [&sharedCal, &pinholeCalibration](auto& measurement) {
+        return pinholeCalibration.uncalibrate(sharedCal->calibrate(measurement));
+    });
+
+    return undistortedMeasurements;
+}
+
+/** Specialization for Cal3_S2 as it doesn't need to be undistorted. */
+template <>
+Point2Vector undistortMeasurements(boost::shared_ptr<Cal3_S2> sharedCal, const Point2Vector& measurements) {
+    return measurements;
+}
+
+
 /**
  * Function to triangulate 3D landmark point from an arbitrary number
  * of poses (at least 2) using the DLT. The function checks that the
@@ -253,8 +282,11 @@ Point3 triangulatePoint3(const std::vector<Pose3>& poses,
   // construct projection matrices from poses & calibration
   auto projection_matrices = projectionMatricesFromPoses(poses, sharedCal);
 
+  // Undistort the measurements, leaving only the pinhole elements in effect.
+  auto undistortedMeasurements = undistortMeasurements<CALIBRATION>(sharedCal, measurements);
+
   // Triangulate linearly
-  Point3 point = triangulateDLT(projection_matrices, measurements, rank_tol);
+  Point3 point = triangulateDLT(projection_matrices, undistortedMeasurements, rank_tol);
 
   // Then refine using non-linear optimization
   if (optimize)