Extend unit testing of omnidirectional projection

Test projection function and factors using a stereoscopic (xi=1) reference model, i.e the image height is given by y = 2 f tan(theta/2).

python/gtsam/tests/test_Cal3Unified.py

@@ -23,6 +23,89 @@ def test_Cal3Unified(self):
         self.assertEqual(K.fx(), 1.)
         self.assertEqual(K.fx(), 1.)
 
+    def test_distortion(self):
+        "Stereographic fisheye model of focal length f, defined as r/f = 2*tan(theta/2)"
+        fx, fy, s, u0, v0 = 2, 2, 0, 0, 0
+        k1, k2, p1, p2 = 0, 0, 0, 0
+        xi = 1
+        stereographic = gtsam.Cal3Unified(fx, fy, s, u0, v0, k1, k2, p1, p2, xi)
+        x, y, z = 1, 0, 1
+        u, v = stereographic.uncalibrate([x, y])
+        r = np.linalg.norm([x, y, z])
+        # Note: 2*tan(atan2(x, z)/2) = 2/(1+sqrt(x^2+z^2))
+        self.assertAlmostEqual(2*np.tan(np.arctan2(x, z)/2), 2/(1+r))
+        self.assertAlmostEqual(u, 2/(1+r))
+        x2, y2 = stereographic.calibrate([u, v])
+        self.assertAlmostEqual(x2, x)
+
+    def test_pinhole(self):
+        "Spatial stereographic camera projection"
+        x, y, z = 1.0, 0.0, 1.0
+        r = np.linalg.norm([x, y, z])
+        u, v = 2/(1+r), 0.0
+        objPoint = np.array([x, y, z])
+        imgPoint = np.array([u, v])
+        fx, fy, s, u0, v0 = 2, 2, 0, 0, 0
+        k1, k2, p1, p2 = 0, 0, 0, 0
+        xi = 1
+        stereographic = gtsam.Cal3Unified(fx, fy, s, u0, v0, k1, k2, p1, p2, xi)
+        pose = gtsam.Pose3()
+        camera = gtsam.PinholeCameraCal3Unified(pose, stereographic)
+        pt1 = camera.Project(objPoint)
+        self.gtsamAssertEquals(pt1, np.array([x/z, y/z]))
+        pt2 = camera.project(objPoint)
+        self.gtsamAssertEquals(pt2, np.array([u, v]))
+        obj1 = camera.backproject([u, v], z)
+        self.gtsamAssertEquals(obj1, np.array([x, y, z]))
+        r1 = camera.range(np.array([x, y, z]))
+        self.assertEqual(r1, r)
+
+    def test_generic_factor(self):
+        "Evaluate residual using pose and point as state variables"
+        fx, fy, s, u0, v0 = 2, 2, 0, 0, 0
+        k1, k2, p1, p2 = 0, 0, 0, 0
+        xi = 1
+        objPoint = np.array([1, 0, 1])
+        r = np.linalg.norm(objPoint)
+        imgPoint = np.array([2/(1+r), 0])
+        graph = gtsam.NonlinearFactorGraph()
+        state = gtsam.Values()
+        measured = imgPoint
+        noiseModel = gtsam.noiseModel.Isotropic.Sigma(2, 1)
+        poseKey = gtsam.symbol_shorthand.P(0)
+        pointKey = gtsam.symbol_shorthand.L(0)
+        k = gtsam.Cal3Unified(fx, fy, s, u0, v0, k1, k2, p1, p2, xi)
+        state.insert_pose3(poseKey, gtsam.Pose3())
+        state.insert_point3(pointKey, gtsam.Point3(objPoint))
+        factor = gtsam.GenericProjectionFactorCal3Unified(measured, noiseModel, poseKey, pointKey, k)
+        graph.add(factor)
+        score = graph.error(state)
+        self.assertAlmostEqual(score, 0)
+
+    def test_sfm_factor2(self):
+        "Evaluate residual with camera, pose and point as state variables"
+        fx, fy, s, u0, v0 = 2, 2, 0, 0, 0
+        k1, k2, p1, p2 = 0, 0, 0, 0
+        xi = 1
+        objPoint = np.array([1, 0, 1])
+        r = np.linalg.norm(objPoint)
+        imgPoint = np.array([2/(1+r), 0])
+        graph = gtsam.NonlinearFactorGraph()
+        state = gtsam.Values()
+        measured = imgPoint
+        noiseModel = gtsam.noiseModel.Isotropic.Sigma(2, 1)
+        cameraKey = gtsam.symbol_shorthand.K(0)
+        poseKey = gtsam.symbol_shorthand.P(0)
+        landmarkKey = gtsam.symbol_shorthand.L(0)
+        k = gtsam.Cal3Unified(fx, fy, s, u0, v0, k1, k2, p1, p2, xi)
+        state.insert_cal3unified(cameraKey, k)
+        state.insert_pose3(poseKey, gtsam.Pose3())
+        state.insert_point3(landmarkKey, gtsam.Point3(objPoint))
+        factor = gtsam.GeneralSFMFactor2Cal3Unified(measured, noiseModel, poseKey, landmarkKey, cameraKey)
+        graph.add(factor)
+        score = graph.error(state)
+        self.assertAlmostEqual(score, 0)
+
     def test_retract(self):
         expected = gtsam.Cal3Unified(100 + 2, 105 + 3, 0.0 + 4, 320 + 5, 240 + 6,
                                      1e-3 + 7, 2.0*1e-3 + 8, 3.0*1e-3 + 9, 4.0*1e-3 + 10, 0.1 + 1)