diff --git a/gtsam/geometry/PinholeCamera.h b/gtsam/geometry/PinholeCamera.h
index 632f6de86..e900d5a85 100644
--- a/gtsam/geometry/PinholeCamera.h
+++ b/gtsam/geometry/PinholeCamera.h
@@ -200,57 +200,33 @@ public:
 
   typedef Eigen::Matrix<double, 2, DimK> Matrix2K;
 
-  /** project a point from world coordinate to the image
-   *  @param pw is a point in world coordinates
-   *  @param Dpose is the Jacobian w.r.t. pose3
-   *  @param Dpoint is the Jacobian w.r.t. point3
-   *  @param Dcal is the Jacobian w.r.t. calibration
+  /** project a point from world coordinate to the image, fixed Jacobians
+   *  @param pw is a point in the world coordinate
    */
-  Point2 project(const Point3& pw, OptionalJacobian<2, 6> Dpose = boost::none,
-      OptionalJacobian<2, 3> Dpoint = boost::none,
-      OptionalJacobian<2, DimK> Dcal = boost::none) const {
-
-    // project to normalized coordinates
-    const Point2 pn = PinholeBase::project2(pw, Dpose, Dpoint);
-
-    // uncalibrate to pixel coordinates
-    Matrix2 Dpi_pn;
-    const Point2 pi = calibration().uncalibrate(pn, Dcal,
-        Dpose || Dpoint ? &Dpi_pn : 0);
-
-    // If needed, apply chain rule
-    if (Dpose)
-      *Dpose = Dpi_pn * *Dpose;
-    if (Dpoint)
-      *Dpoint = Dpi_pn * *Dpoint;
-
+  Point2 project2(const Point3& pw, OptionalJacobian<2, dimension> Dcamera =
+      boost::none, OptionalJacobian<2, 3> Dpoint = boost::none) const {
+    // We just call 3-derivative version in Base
+    Matrix26 Dpose;
+    Eigen::Matrix<double, 2, DimK> Dcal;
+    Point2 pi = Base::project(pw, Dcamera ? &Dpose : 0, Dpoint,
+        Dcamera ? &Dcal : 0);
+    if (Dcamera)
+      *Dcamera << Dpose, Dcal;
     return pi;
   }
 
   /** project a point from world coordinate to the image, fixed Jacobians
    *  @param pw is a point in the world coordinate
    */
-  Point2 project2(
-      const Point3& pw, //
-      OptionalJacobian<2, dimension> Dcamera = boost::none,
-      OptionalJacobian<2, 3> Dpoint = boost::none) const {
-
-    // project to normalized coordinates
+  Point2 project2(const Unit3& pw, OptionalJacobian<2, dimension> Dcamera =
+      boost::none, OptionalJacobian<2, 3> Dpoint = boost::none) const {
+    // We just call 3-derivative version in Base
     Matrix26 Dpose;
-    const Point2 pn = PinholeBase::project2(pw, Dpose, Dpoint);
-
-    // uncalibrate to pixel coordinates
-    Matrix2K Dcal;
-    Matrix2 Dpi_pn;
-    const Point2 pi = calibration().uncalibrate(pn, Dcamera ? &Dcal : 0,
-        Dcamera || Dpoint ? &Dpi_pn : 0);
-
-    // If needed, calculate derivatives
+    Eigen::Matrix<double, 2, DimK> Dcal;
+    Point2 pi = Base::project(pw, Dcamera ? &Dpose : 0, Dpoint,
+        Dcamera ? &Dcal : 0);
     if (Dcamera)
-      *Dcamera << Dpi_pn * Dpose, Dcal;
-    if (Dpoint)
-      *Dpoint = Dpi_pn * (*Dpoint);
-
+      *Dcamera << Dpose, Dcal;
     return pi;
   }
 
diff --git a/gtsam/geometry/tests/testPinholeCamera.cpp b/gtsam/geometry/tests/testPinholeCamera.cpp
index 0e610d8d6..74bc4ca2a 100644
--- a/gtsam/geometry/tests/testPinholeCamera.cpp
+++ b/gtsam/geometry/tests/testPinholeCamera.cpp
@@ -45,10 +45,10 @@ static const Point3 point2(-0.08, 0.08, 0.0);
 static const Point3 point3( 0.08, 0.08, 0.0);
 static const Point3 point4( 0.08,-0.08, 0.0);
 
-static const Point3 point1_inf(-0.16,-0.16, -1.0);
-static const Point3 point2_inf(-0.16, 0.16, -1.0);
-static const Point3 point3_inf( 0.16, 0.16, -1.0);
-static const Point3 point4_inf( 0.16,-0.16, -1.0);
+static const Unit3 point1_inf(-0.16,-0.16, -1.0);
+static const Unit3 point2_inf(-0.16, 0.16, -1.0);
+static const Unit3 point3_inf( 0.16, 0.16, -1.0);
+static const Unit3 point4_inf( 0.16,-0.16, -1.0);
 
 /* ************************************************************************* */
 TEST( PinholeCamera, constructor)
@@ -154,9 +154,9 @@ TEST( PinholeCamera, backprojectInfinity2)
   Rot3 rot(1., 0., 0., 0., 0., 1., 0., -1., 0.); // a camera1 looking down
   Camera camera(Pose3(rot, origin), K);
 
-  Point3 actual = camera.backprojectPointAtInfinity(Point2());
-  Point3 expected(0., 1., 0.);
-  Point2 x = camera.projectPointAtInfinity(expected);
+  Unit3 actual = camera.backprojectPointAtInfinity(Point2());
+  Unit3 expected(0., 1., 0.);
+  Point2 x = camera.project(expected);
 
   EXPECT(assert_equal(expected, actual));
   EXPECT(assert_equal(Point2(), x));
@@ -169,9 +169,9 @@ TEST( PinholeCamera, backprojectInfinity3)
   Rot3 rot(1., 0., 0., 0., 1., 0., 0., 0., 1.); // identity
   Camera camera(Pose3(rot, origin), K);
 
-  Point3 actual = camera.backprojectPointAtInfinity(Point2());
-  Point3 expected(0., 0., 1.);
-  Point2 x = camera.projectPointAtInfinity(expected);
+  Unit3 actual = camera.backprojectPointAtInfinity(Point2());
+  Unit3 expected(0., 0., 1.);
+  Point2 x = camera.project(expected);
 
   EXPECT(assert_equal(expected, actual));
   EXPECT(assert_equal(Point2(), x));
@@ -197,17 +197,17 @@ TEST( PinholeCamera, Dproject)
 }
 
 /* ************************************************************************* */
-static Point2 projectInfinity3(const Pose3& pose, const Point3& point3D, const Cal3_S2& cal) {
-  return Camera(pose,cal).projectPointAtInfinity(point3D);
+static Point2 projectInfinity3(const Pose3& pose, const Unit3& point3D, const Cal3_S2& cal) {
+  return Camera(pose,cal).project(point3D);
 }
 
 TEST( PinholeCamera, Dproject_Infinity)
 {
   Matrix Dpose, Dpoint, Dcal;
-  Point3 point3D(point1.x(), point1.y(), -10.0); // a point in front of the camera1
+  Unit3 point3D(point1.x(), point1.y(), -10.0); // a point in front of the camera1
 
   // test Projection
-  Point2 actual = camera.projectPointAtInfinity(point3D, Dpose, Dpoint, Dcal);
+  Point2 actual = camera.project(point3D, Dpose, Dpoint, Dcal);
   Point2 expected(-5.0, 5.0);
   EXPECT(assert_equal(actual, expected,  1e-7));