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Spatial Transformer Networks Tutorial

Author: Ghassen HAMROUNI

../_images/FSeq.png

In this tutorial, you will learn how to augment your network using a visual attention mechanism called spatial transformer networks. You can read more about the spatial transformer networks in the DeepMind paper

Spatial transformer networks are a generalization of differentiable attention to any spatial transformation. Spatial transformer networks (STN for short) allow a neural network to learn how to perform spatial transformations on the input image in order to enhance the geometric invariance of the model. For example, it can crop a region of interest, scale and correct the orientation of an image. It can be a useful mechanism because CNNs are not invariant to rotation and scale and more general affine transformations.

One of the best things about STN is the ability to simply plug it into any existing CNN with very little modification.

# License: BSD
# Author: Ghassen Hamrouni

from __future__ import print_function
import torch
import torch.nn as nn
import torch.nn.functional as F
import torch.optim as optim
import torchvision
from torchvision import datasets, transforms
import matplotlib.pyplot as plt
import numpy as np

plt.ion()   # interactive mode
<contextlib.ExitStack object at 0x7f3547afd690>

Loading the data

In this post we experiment with the classic MNIST dataset. Using a standard convolutional network augmented with a spatial transformer network.

from six.moves import urllib
opener = urllib.request.build_opener()
opener.addheaders = [('User-agent', 'Mozilla/5.0')]
urllib.request.install_opener(opener)

device = torch.device("cuda" if torch.cuda.is_available() else "cpu")

# Training dataset
train_loader = torch.utils.data.DataLoader(
    datasets.MNIST(root='.', train=True, download=True,
                   transform=transforms.Compose([
                       transforms.ToTensor(),
                       transforms.Normalize((0.1307,), (0.3081,))
                   ])), batch_size=64, shuffle=True, num_workers=4)
# Test dataset
test_loader = torch.utils.data.DataLoader(
    datasets.MNIST(root='.', train=False, transform=transforms.Compose([
        transforms.ToTensor(),
        transforms.Normalize((0.1307,), (0.3081,))
    ])), batch_size=64, shuffle=True, num_workers=4)
Downloading http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz
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Downloading http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz
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Downloading http://yann.lecun.com/exdb/mnist/t10k-images-idx3-ubyte.gz
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Downloading http://yann.lecun.com/exdb/mnist/t10k-labels-idx1-ubyte.gz
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Depicting spatial transformer networks

Spatial transformer networks boils down to three main components :

  • The localization network is a regular CNN which regresses the transformation parameters. The transformation is never learned explicitly from this dataset, instead the network learns automatically the spatial transformations that enhances the global accuracy.

  • The grid generator generates a grid of coordinates in the input image corresponding to each pixel from the output image.

  • The sampler uses the parameters of the transformation and applies it to the input image.

../_images/stn-arch.png

Note

We need the latest version of PyTorch that contains affine_grid and grid_sample modules.

class Net(nn.Module):
    def __init__(self):
        super(Net, self).__init__()
        self.conv1 = nn.Conv2d(1, 10, kernel_size=5)
        self.conv2 = nn.Conv2d(10, 20, kernel_size=5)
        self.conv2_drop = nn.Dropout2d()
        self.fc1 = nn.Linear(320, 50)
        self.fc2 = nn.Linear(50, 10)

        # Spatial transformer localization-network
        self.localization = nn.Sequential(
            nn.Conv2d(1, 8, kernel_size=7),
            nn.MaxPool2d(2, stride=2),
            nn.ReLU(True),
            nn.Conv2d(8, 10, kernel_size=5),
            nn.MaxPool2d(2, stride=2),
            nn.ReLU(True)
        )

        # Regressor for the 3 * 2 affine matrix
        self.fc_loc = nn.Sequential(
            nn.Linear(10 * 3 * 3, 32),
            nn.ReLU(True),
            nn.Linear(32, 3 * 2)
        )

        # Initialize the weights/bias with identity transformation
        self.fc_loc[2].weight.data.zero_()
        self.fc_loc[2].bias.data.copy_(torch.tensor([1, 0, 0, 0, 1, 0], dtype=torch.float))

    # Spatial transformer network forward function
    def stn(self, x):
        xs = self.localization(x)
        xs = xs.view(-1, 10 * 3 * 3)
        theta = self.fc_loc(xs)
        theta = theta.view(-1, 2, 3)

        grid = F.affine_grid(theta, x.size())
        x = F.grid_sample(x, grid)

        return x

    def forward(self, x):
        # transform the input
        x = self.stn(x)

        # Perform the usual forward pass
        x = F.relu(F.max_pool2d(self.conv1(x), 2))
        x = F.relu(F.max_pool2d(self.conv2_drop(self.conv2(x)), 2))
        x = x.view(-1, 320)
        x = F.relu(self.fc1(x))
        x = F.dropout(x, training=self.training)
        x = self.fc2(x)
        return F.log_softmax(x, dim=1)


model = Net().to(device)

Training the model

Now, let’s use the SGD algorithm to train the model. The network is learning the classification task in a supervised way. In the same time the model is learning STN automatically in an end-to-end fashion.

optimizer = optim.SGD(model.parameters(), lr=0.01)


def train(epoch):
    model.train()
    for batch_idx, (data, target) in enumerate(train_loader):
        data, target = data.to(device), target.to(device)

        optimizer.zero_grad()
        output = model(data)
        loss = F.nll_loss(output, target)
        loss.backward()
        optimizer.step()
        if batch_idx % 500 == 0:
            print('Train Epoch: {} [{}/{} ({:.0f}%)]\tLoss: {:.6f}'.format(
                epoch, batch_idx * len(data), len(train_loader.dataset),
                100. * batch_idx / len(train_loader), loss.item()))
#
# A simple test procedure to measure the STN performances on MNIST.
#


def test():
    with torch.no_grad():
        model.eval()
        test_loss = 0
        correct = 0
        for data, target in test_loader:
            data, target = data.to(device), target.to(device)
            output = model(data)

            # sum up batch loss
            test_loss += F.nll_loss(output, target, size_average=False).item()
            # get the index of the max log-probability
            pred = output.max(1, keepdim=True)[1]
            correct += pred.eq(target.view_as(pred)).sum().item()

        test_loss /= len(test_loader.dataset)
        print('\nTest set: Average loss: {:.4f}, Accuracy: {}/{} ({:.0f}%)\n'
              .format(test_loss, correct, len(test_loader.dataset),
                      100. * correct / len(test_loader.dataset)))

Visualizing the STN results

Now, we will inspect the results of our learned visual attention mechanism.

We define a small helper function in order to visualize the transformations while training.

def convert_image_np(inp):
    """Convert a Tensor to numpy image."""
    inp = inp.numpy().transpose((1, 2, 0))
    mean = np.array([0.485, 0.456, 0.406])
    std = np.array([0.229, 0.224, 0.225])
    inp = std * inp + mean
    inp = np.clip(inp, 0, 1)
    return inp

# We want to visualize the output of the spatial transformers layer
# after the training, we visualize a batch of input images and
# the corresponding transformed batch using STN.


def visualize_stn():
    with torch.no_grad():
        # Get a batch of training data
        data = next(iter(test_loader))[0].to(device)

        input_tensor = data.cpu()
        transformed_input_tensor = model.stn(data).cpu()

        in_grid = convert_image_np(
            torchvision.utils.make_grid(input_tensor))

        out_grid = convert_image_np(
            torchvision.utils.make_grid(transformed_input_tensor))

        # Plot the results side-by-side
        f, axarr = plt.subplots(1, 2)
        axarr[0].imshow(in_grid)
        axarr[0].set_title('Dataset Images')

        axarr[1].imshow(out_grid)
        axarr[1].set_title('Transformed Images')

for epoch in range(1, 20 + 1):
    train(epoch)
    test()

# Visualize the STN transformation on some input batch
visualize_stn()

plt.ioff()
plt.show()
Dataset Images, Transformed Images
/opt/conda/lib/python3.10/site-packages/torch/nn/functional.py:4289: UserWarning:

Default grid_sample and affine_grid behavior has changed to align_corners=False since 1.3.0. Please specify align_corners=True if the old behavior is desired. See the documentation of grid_sample for details.

/opt/conda/lib/python3.10/site-packages/torch/nn/functional.py:4227: UserWarning:

Default grid_sample and affine_grid behavior has changed to align_corners=False since 1.3.0. Please specify align_corners=True if the old behavior is desired. See the documentation of grid_sample for details.

Train Epoch: 1 [0/60000 (0%)]   Loss: 2.332839
Train Epoch: 1 [32000/60000 (53%)]      Loss: 0.864555
/opt/conda/lib/python3.10/site-packages/torch/nn/_reduction.py:42: UserWarning:

size_average and reduce args will be deprecated, please use reduction='sum' instead.


Test set: Average loss: 0.2621, Accuracy: 9281/10000 (93%)

Train Epoch: 2 [0/60000 (0%)]   Loss: 0.466716
Train Epoch: 2 [32000/60000 (53%)]      Loss: 0.522560

Test set: Average loss: 0.1155, Accuracy: 9635/10000 (96%)

Train Epoch: 3 [0/60000 (0%)]   Loss: 0.305918
Train Epoch: 3 [32000/60000 (53%)]      Loss: 0.219244

Test set: Average loss: 0.0911, Accuracy: 9723/10000 (97%)

Train Epoch: 4 [0/60000 (0%)]   Loss: 0.207619
Train Epoch: 4 [32000/60000 (53%)]      Loss: 0.251243

Test set: Average loss: 0.0782, Accuracy: 9758/10000 (98%)

Train Epoch: 5 [0/60000 (0%)]   Loss: 0.181567
Train Epoch: 5 [32000/60000 (53%)]      Loss: 0.183908

Test set: Average loss: 0.1179, Accuracy: 9636/10000 (96%)

Train Epoch: 6 [0/60000 (0%)]   Loss: 0.209384
Train Epoch: 6 [32000/60000 (53%)]      Loss: 0.121687

Test set: Average loss: 0.0676, Accuracy: 9796/10000 (98%)

Train Epoch: 7 [0/60000 (0%)]   Loss: 0.173014
Train Epoch: 7 [32000/60000 (53%)]      Loss: 0.152269

Test set: Average loss: 0.0592, Accuracy: 9817/10000 (98%)

Train Epoch: 8 [0/60000 (0%)]   Loss: 0.115667
Train Epoch: 8 [32000/60000 (53%)]      Loss: 0.164522

Test set: Average loss: 0.0518, Accuracy: 9826/10000 (98%)

Train Epoch: 9 [0/60000 (0%)]   Loss: 0.123830
Train Epoch: 9 [32000/60000 (53%)]      Loss: 0.071623

Test set: Average loss: 0.0501, Accuracy: 9845/10000 (98%)

Train Epoch: 10 [0/60000 (0%)]  Loss: 0.036666
Train Epoch: 10 [32000/60000 (53%)]     Loss: 0.245215

Test set: Average loss: 0.0523, Accuracy: 9842/10000 (98%)

Train Epoch: 11 [0/60000 (0%)]  Loss: 0.121718
Train Epoch: 11 [32000/60000 (53%)]     Loss: 0.056175

Test set: Average loss: 0.0588, Accuracy: 9820/10000 (98%)

Train Epoch: 12 [0/60000 (0%)]  Loss: 0.197022
Train Epoch: 12 [32000/60000 (53%)]     Loss: 0.161486

Test set: Average loss: 0.0425, Accuracy: 9866/10000 (99%)

Train Epoch: 13 [0/60000 (0%)]  Loss: 0.035945
Train Epoch: 13 [32000/60000 (53%)]     Loss: 0.054246

Test set: Average loss: 0.0513, Accuracy: 9845/10000 (98%)

Train Epoch: 14 [0/60000 (0%)]  Loss: 0.023802
Train Epoch: 14 [32000/60000 (53%)]     Loss: 0.218162

Test set: Average loss: 0.0490, Accuracy: 9852/10000 (99%)

Train Epoch: 15 [0/60000 (0%)]  Loss: 0.103968
Train Epoch: 15 [32000/60000 (53%)]     Loss: 0.048652

Test set: Average loss: 0.0408, Accuracy: 9881/10000 (99%)

Train Epoch: 16 [0/60000 (0%)]  Loss: 0.039995
Train Epoch: 16 [32000/60000 (53%)]     Loss: 0.053690

Test set: Average loss: 0.0397, Accuracy: 9882/10000 (99%)

Train Epoch: 17 [0/60000 (0%)]  Loss: 0.056825
Train Epoch: 17 [32000/60000 (53%)]     Loss: 0.122102

Test set: Average loss: 0.0403, Accuracy: 9876/10000 (99%)

Train Epoch: 18 [0/60000 (0%)]  Loss: 0.074200
Train Epoch: 18 [32000/60000 (53%)]     Loss: 0.109606

Test set: Average loss: 0.0413, Accuracy: 9867/10000 (99%)

Train Epoch: 19 [0/60000 (0%)]  Loss: 0.024249
Train Epoch: 19 [32000/60000 (53%)]     Loss: 0.190879

Test set: Average loss: 0.0448, Accuracy: 9860/10000 (99%)

Train Epoch: 20 [0/60000 (0%)]  Loss: 0.063989
Train Epoch: 20 [32000/60000 (53%)]     Loss: 0.081831

Test set: Average loss: 0.0448, Accuracy: 9864/10000 (99%)

Total running time of the script: ( 3 minutes 22.120 seconds)

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