diff --git a/lib/matplotlib/cbook.py b/lib/matplotlib/cbook.py
index bc7e4df568b4..6451a908baa6 100644
--- a/lib/matplotlib/cbook.py
+++ b/lib/matplotlib/cbook.py
@@ -2244,6 +2244,21 @@ def _reshape_2D(X):
     return X
 
 
+def ensure_3d(arr):
+    """
+    Return a version of arr with ndim==3, with extra dimensions added
+    at the end of arr.shape as needed.
+    """
+    arr = np.asanyarray(arr)
+    if arr.ndim == 1:
+        arr = arr[:, None, None]
+    elif arr.ndim == 2:
+        arr = arr[:, :, None]
+    elif arr.ndim > 3 or arr.ndim < 1:
+        raise ValueError("cannot convert arr to 3-dimensional")
+    return arr
+
+
 def violin_stats(X, method, points=100):
     '''
     Returns a list of dictionaries of data which can be used to draw a series
diff --git a/lib/matplotlib/path.py b/lib/matplotlib/path.py
index 2e0d86456167..ca80f4cbb6b7 100644
--- a/lib/matplotlib/path.py
+++ b/lib/matplotlib/path.py
@@ -24,7 +24,7 @@
 from numpy import ma
 
 from matplotlib import _path
-from matplotlib.cbook import simple_linear_interpolation, maxdict
+from matplotlib.cbook import simple_linear_interpolation, maxdict, ensure_3d
 from matplotlib import rcParams
 
 
@@ -988,7 +988,7 @@ def get_path_collection_extents(
     if len(paths) == 0:
         raise ValueError("No paths provided")
     return Bbox.from_extents(*_path.get_path_collection_extents(
-        master_transform, paths, np.atleast_3d(transforms),
+        master_transform, paths, ensure_3d(transforms),
         offsets, offset_transform))
 
 
diff --git a/lib/matplotlib/tests/test_cbook.py b/lib/matplotlib/tests/test_cbook.py
index 2b916b08566f..b244e761cf8f 100644
--- a/lib/matplotlib/tests/test_cbook.py
+++ b/lib/matplotlib/tests/test_cbook.py
@@ -376,3 +376,11 @@ def test_step_fails():
                   np.arange(12))
     assert_raises(ValueError, cbook._step_validation,
                   np.arange(12), np.arange(3))
+
+
+def test_ensure_3d():
+    assert_array_equal([[[1]], [[2]], [[3]]],
+                       cbook.ensure_3d([1, 2, 3]))
+    assert_array_equal([[[1], [2]], [[3], [4]]],
+                       cbook.ensure_3d([[1, 2], [3, 4]]))
+    assert_raises(ValueError, cbook.ensure_3d, [[[[1]]]])
diff --git a/lib/matplotlib/transforms.py b/lib/matplotlib/transforms.py
index 812047910e11..1eac27fc52ee 100644
--- a/lib/matplotlib/transforms.py
+++ b/lib/matplotlib/transforms.py
@@ -48,6 +48,7 @@
     from sets import Set as set
 
 from .path import Path
+from .cbook import ensure_3d
 
 DEBUG = False
 # we need this later, but this is very expensive to set up
@@ -667,7 +668,7 @@ def count_overlaps(self, bboxes):
         bboxes is a sequence of :class:`BboxBase` objects
         """
         return count_bboxes_overlapping_bbox(
-            self, np.atleast_3d([np.array(x) for x in bboxes]))
+            self, ensure_3d([np.array(x) for x in bboxes]))
 
     def expanded(self, sw, sh):
         """