diff --git a/lib/matplotlib/image.py b/lib/matplotlib/image.py
index 81357ecb2cc4..b3813eac2b68 100644
--- a/lib/matplotlib/image.py
+++ b/lib/matplotlib/image.py
@@ -390,26 +390,27 @@ def _make_image(self, A, in_bbox, out_bbox, clip_bbox, magnification=1.0,
                 # float64's ability to represent changes.  Applying
                 # a norm first would be good, but ruins the interpolation
                 # of over numbers.
-                if self.norm.vmin is not None and self.norm.vmax is not None:
-                    dv = (np.float64(self.norm.vmax) -
-                          np.float64(self.norm.vmin))
-                    vmid = self.norm.vmin + dv / 2
-                    newmin = vmid - dv * 1.e7
-                    if newmin < a_min:
-                        newmin = None
-                    else:
-                        a_min = np.float64(newmin)
-                    newmax = vmid + dv * 1.e7
-                    if newmax > a_max:
-                        newmax = None
-                    else:
-                        a_max = np.float64(newmax)
-                    if newmax is not None or newmin is not None:
-                        A_scaled = np.clip(A_scaled, newmin, newmax)
+                self.norm.autoscale_None(A)
+                dv = (np.float64(self.norm.vmax) -
+                      np.float64(self.norm.vmin))
+                vmid = self.norm.vmin + dv / 2
+                fact = 1e7 if scaled_dtype == np.float64 else 1e4
+                newmin = vmid - dv * fact
+                if newmin < a_min:
+                    newmin = None
+                else:
+                    a_min = np.float64(newmin)
+                newmax = vmid + dv * fact
+                if newmax > a_max:
+                    newmax = None
+                else:
+                    a_max = np.float64(newmax)
+                if newmax is not None or newmin is not None:
+                    A_scaled = np.clip(A_scaled, newmin, newmax)
 
                 A_scaled -= a_min
                 # a_min and a_max might be ndarray subclasses so use
-                # asscalar to ensure they are scalars to avoid errors
+                # asscalar to avoid errors
                 a_min = np.asscalar(a_min.astype(scaled_dtype))
                 a_max = np.asscalar(a_max.astype(scaled_dtype))