Add some better examples.

README.md

@@ -104,55 +104,142 @@ print(ssim_score_0.shape, ssim_score_1.shape)
 
 ## As A Loss
 
-![prediction](https://user-images.githubusercontent.com/26847524/174814849-f80ec67c-5397-4ce6-bf4e-8b0aa568ed6f.png)
+As you can see from the respective thresholds of the two cases below, it is easier to optimize towards MSSIM=1 than MSSIM=-1.
+
+### Optimize towards MSSIM=1
+
+![prediction](https://user-images.githubusercontent.com/26847524/174930091-9d7f7505-1752-423a-b7c3-d4dbfeb8d336.png)
 
 ```python
 import matplotlib.pyplot as plt
 import torch
 from pytorch_ssim import SSIM
 from skimage import data
-from torch.optim import Adam
+from torch import optim
 
-
-original_image = data.camera() / 255
+original_image = data.moon() / 255
 target_image = torch.from_numpy(original_image).unsqueeze(0).unsqueeze(0).float().cuda()
-predicted_image = torch.rand_like(
+predicted_image = torch.zeros_like(
     target_image, device=target_image.device, dtype=target_image.dtype, requires_grad=True
 )
 initial_image = predicted_image.clone()
 
 ssim = SSIM().cuda()
 initial_ssim_value = ssim(predicted_image, target_image)
-print(f"Initial ssim: {initial_ssim_value.item():.4f}")
-ssim_value = initial_ssim_value
 
-optimizer = Adam([predicted_image], lr=0.01)
+ssim_value = initial_ssim_value
+optimizer = optim.Adam([predicted_image], lr=0.01)
 loss_curves = []
-while ssim_value < 0.95:
+while ssim_value < 0.999:
     ssim_out = 1 - ssim(predicted_image, target_image)
     loss_curves.append(ssim_out.item())
     ssim_value = 1 - ssim_out.item()
+    print(ssim_value)
     ssim_out.backward()
     optimizer.step()
     optimizer.zero_grad()
 
-fig, axes = plt.subplots(nrows=1, ncols=4, figsize=(8, 2))
+fig, axes = plt.subplots(nrows=2, ncols=4, figsize=(8, 4))
 ax = axes.ravel()
 
 ax[0].imshow(original_image, cmap=plt.cm.gray, vmin=0, vmax=1)
 ax[0].set_title("Original Image")
 
 ax[1].imshow(initial_image.squeeze().detach().cpu().numpy(), cmap=plt.cm.gray, vmin=0, vmax=1)
-ax[1].set_xlabel(f"SSIM: {initial_ssim_value:.4f}")
+ax[1].set_xlabel(f"SSIM: {initial_ssim_value:.5f}")
 ax[1].set_title("Initial Image")
 
 ax[2].imshow(predicted_image.squeeze().detach().cpu().numpy(), cmap=plt.cm.gray, vmin=0, vmax=1)
-ax[2].set_xlabel(f"SSIM: {ssim_value:.4f}")
+ax[2].set_xlabel(f"SSIM: {ssim_value:.5f}")
 ax[2].set_title("Predicted Image")
 
 ax[3].plot(loss_curves)
 ax[3].set_title("SSIM Loss Curve")
 
+ax[4].set_title("Original Image")
+ax[4].hist(original_image.ravel(), bins=256)
+ax[4].ticklabel_format(axis="y", style="scientific", scilimits=(0, 0))
+ax[4].set_xlabel("Pixel Intensity")
+
+ax[5].set_title("Initial Image")
+ax[5].hist(initial_image.squeeze().detach().cpu().numpy().ravel(), bins=256)
+ax[5].ticklabel_format(axis="y", style="scientific", scilimits=(0, 0))
+ax[5].set_xlabel("Pixel Intensity")
+
+ax[6].set_title("Predicted Image")
+ax[6].hist(predicted_image.squeeze().detach().cpu().numpy().ravel(), bins=256)
+ax[6].ticklabel_format(axis="y", style="scientific", scilimits=(0, 0))
+ax[6].set_xlabel("Pixel Intensity")
+
+plt.tight_layout()
+plt.savefig("prediction.png")
+```
+
+### Optimize towards MSSIM=-1
+
+![prediction](https://user-images.githubusercontent.com/26847524/174929574-5332cab2-104f-4aab-a4e5-35e7635a793f.png)
+
+```python
+import matplotlib.pyplot as plt
+import torch
+from pytorch_ssim import SSIM
+from skimage import data
+from torch import optim
+
+original_image = data.moon() / 255
+target_image = torch.from_numpy(original_image).unsqueeze(0).unsqueeze(0).float().cuda()
+predicted_image = torch.zeros_like(
+    target_image, device=target_image.device, dtype=target_image.dtype, requires_grad=True
+)
+initial_image = predicted_image.clone()
+
+ssim = SSIM(L=original_image.max() - original_image.min()).cuda()
+initial_ssim_value = ssim(predicted_image, target_image)
+
+ssim_value = initial_ssim_value
+optimizer = optim.Adam([predicted_image], lr=0.01)
+loss_curves = []
+while ssim_value > -0.94:
+    ssim_out = ssim(predicted_image, target_image)
+    loss_curves.append(ssim_out.item())
+    ssim_value = ssim_out.item()
+    print(ssim_value)
+    ssim_out.backward()
+    optimizer.step()
+    optimizer.zero_grad()
+
+fig, axes = plt.subplots(nrows=2, ncols=4, figsize=(8, 4))
+ax = axes.ravel()
+
+ax[0].imshow(original_image, cmap=plt.cm.gray, vmin=0, vmax=1)
+ax[0].set_title("Original Image")
+
+ax[1].imshow(initial_image.squeeze().detach().cpu().numpy(), cmap=plt.cm.gray, vmin=0, vmax=1)
+ax[1].set_xlabel(f"SSIM: {initial_ssim_value:.5f}")
+ax[1].set_title("Initial Image")
+
+ax[2].imshow(predicted_image.squeeze().detach().cpu().numpy(), cmap=plt.cm.gray, vmin=0, vmax=1)
+ax[2].set_xlabel(f"SSIM: {ssim_value:.5f}")
+ax[2].set_title("Predicted Image")
+
+ax[3].plot(loss_curves)
+ax[3].set_title("SSIM Loss Curve")
+
+ax[4].set_title("Original Image")
+ax[4].hist(original_image.ravel(), bins=256)
+ax[4].ticklabel_format(axis="y", style="scientific", scilimits=(0, 0))
+ax[4].set_xlabel("Pixel Intensity")
+
+ax[5].set_title("Initial Image")
+ax[5].hist(initial_image.squeeze().detach().cpu().numpy().ravel(), bins=256)
+ax[5].ticklabel_format(axis="y", style="scientific", scilimits=(0, 0))
+ax[5].set_xlabel("Pixel Intensity")
+
+ax[6].set_title("Predicted Image")
+ax[6].hist(predicted_image.squeeze().detach().cpu().numpy().ravel(), bins=256)
+ax[6].ticklabel_format(axis="y", style="scientific", scilimits=(0, 0))
+ax[6].set_xlabel("Pixel Intensity")
+
 plt.tight_layout()
 plt.savefig("prediction.png")
 ```