diff --git a/piqa/__init__.py b/piqa/__init__.py
index 6bba34a..75114ad 100644
--- a/piqa/__init__.py
+++ b/piqa/__init__.py
@@ -5,4 +5,4 @@
 specific image quality assessement metric.
 """
 
-__version__ = '1.0.8'
+__version__ = '1.0.9'
diff --git a/piqa/gmsd.py b/piqa/gmsd.py
index 0a0c7c1..dc0d86b 100644
--- a/piqa/gmsd.py
+++ b/piqa/gmsd.py
@@ -69,12 +69,15 @@ def _gmsd(
 
     # Gradient magnitude similarity
     gms_num = (2. - alpha) * gm_xy + c
-    gms_den = gm_x ** 2 + gm_y ** 2 - alpha * gm_xy + c
+    gms_den = gm_x ** 2 + gm_y ** 2 + c
+
+    if alpha > 0.:
+        gms_den = gms_den - alpha * gm_xy
+
     gms = gms_num / gms_den
 
     # Gradient magnitude similarity deviation
-    gmsd = (gms - gms.mean((-1, -2), keepdim=True)) ** 2
-    gmsd = torch.sqrt(gmsd.mean((-1, -2)))
+    gmsd = torch.std(gms, dim=(-1, -2))
 
     return gmsd
 
diff --git a/piqa/ssim.py b/piqa/ssim.py
index 7a3467a..c2e3c7e 100644
--- a/piqa/ssim.py
+++ b/piqa/ssim.py
@@ -89,20 +89,20 @@ def ssim_per_channel(
     mu_x = filter2d(x, window)
     mu_y = filter2d(y, window)
 
-    mu_x_sq = mu_x ** 2
-    mu_y_sq = mu_y ** 2
+    mu_xx = mu_x ** 2
+    mu_yy = mu_y ** 2
     mu_xy = mu_x * mu_y
 
     # Variance (sigma)
-    sigma_x_sq = filter2d(x ** 2, window) - mu_x_sq
-    sigma_y_sq = filter2d(y ** 2, window) - mu_y_sq
+    sigma_xx = filter2d(x ** 2, window) - mu_xx
+    sigma_yy = filter2d(y ** 2, window) - mu_yy
     sigma_xy = filter2d(x * y, window) - mu_xy
 
     # Contrast sensitivity
-    cs = (2. * sigma_xy + c2) / (sigma_x_sq + sigma_y_sq + c2)
+    cs = (2. * sigma_xy + c2) / (sigma_xx + sigma_yy + c2)
 
     # Structural similarity
-    ss = (2. * mu_x * mu_y + c1) / (mu_x_sq + mu_y_sq + c1) * cs
+    ss = (2. * mu_xy + c1) / (mu_xx + mu_yy + c1) * cs
 
     return ss.mean((-1, -2)), cs.mean((-1, -2))