diff --git a/lib/matplotlib/artist.py b/lib/matplotlib/artist.py
index 981365d852be..24aaa349ee05 100644
--- a/lib/matplotlib/artist.py
+++ b/lib/matplotlib/artist.py
@@ -1365,7 +1365,9 @@ def format_cursor_data(self, data):
                     delta = np.diff(
                         self.norm.boundaries[neigh_idx:cur_idx + 2]
                     ).max()
-
+                elif self.norm.vmin == self.norm.vmax:
+                    # singular norms, use delta of 10% of only value
+                    delta = np.abs(self.norm.vmin * .1)
                 else:
                     # Midpoints of neighboring color intervals.
                     neighbors = self.norm.inverse(
diff --git a/lib/matplotlib/cbook.py b/lib/matplotlib/cbook.py
index e4f60aac37a8..2411784af3ec 100644
--- a/lib/matplotlib/cbook.py
+++ b/lib/matplotlib/cbook.py
@@ -2252,6 +2252,10 @@ def _g_sig_digits(value, delta):
     it is known with an error of *delta*.
     """
     if delta == 0:
+        if value == 0:
+            # if both value and delta are 0, np.spacing below returns 5e-324
+            # which results in rather silly results
+            return 3
         # delta = 0 may occur when trying to format values over a tiny range;
         # in that case, replace it by the distance to the closest float.
         delta = abs(np.spacing(value))
diff --git a/lib/matplotlib/tests/test_image.py b/lib/matplotlib/tests/test_image.py
index dfacfccb3e0e..6de1754f9ed7 100644
--- a/lib/matplotlib/tests/test_image.py
+++ b/lib/matplotlib/tests/test_image.py
@@ -390,7 +390,8 @@ def test_cursor_data_nonuniform(xy, data):
         ([[.123, .987]], "[0.123]"),
         ([[np.nan, 1, 2]], "[]"),
         ([[1, 1+1e-15]], "[1.0000000000000000]"),
-        ([[-1, -1]], "[-1.0000000000000000]"),
+        ([[-1, -1]], "[-1.0]"),
+        ([[0, 0]], "[0.00]"),
     ])
 def test_format_cursor_data(data, text):
     from matplotlib.backend_bases import MouseEvent