diff --git a/skimage/transform/_geometric.py b/skimage/transform/_geometric.py
index 5fe2cbf0..3437945d 100644
--- a/skimage/transform/_geometric.py
+++ b/skimage/transform/_geometric.py
@@ -261,6 +261,10 @@ class ProjectiveTransform(GeometricTransform):
             else:
                 tform = ProjectiveTransform
             return tform(other.params.dot(self.params))
+        elif (hasattr(other, '__name__')
+                and other.__name__ == 'inverse'
+                and hasattr(get_bound_method_class(other), '_inv_matrix')):
+            return ProjectiveTransform(self._inv_matrix.dot(self.params))
         else:
             raise TypeError("Cannot combine transformations of differing "
                             "types.")
@@ -789,6 +793,7 @@ TRANSFORMS = {
     'projective': ProjectiveTransform,
     'polynomial': PolynomialTransform,
 }
+
 HOMOGRAPHY_TRANSFORMS = (
     SimilarityTransform,
     AffineTransform,
diff --git a/skimage/transform/tests/test_geometric.py b/skimage/transform/tests/test_geometric.py
index 14a9305c..2d81a23d 100644
--- a/skimage/transform/tests/test_geometric.py
+++ b/skimage/transform/tests/test_geometric.py
@@ -218,6 +218,9 @@ def test_union():
     assert_array_almost_equal(tform._matrix, tform3._matrix)
     assert tform.__class__ == ProjectiveTransform
 
+    tform = AffineTransform(scale=(0.1, 0.1), rotation=0.3)
+    assert_array_almost_equal((tform + tform.inverse).params, np.eye(3))
+
 
 def test_union_differing_types():
     tform1 = SimilarityTransform()