Spatial Transformer Networks Tutorial

Author: Ghassen HAMROUNI

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

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

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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)

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Downloading https://ossci-datasets.s3.amazonaws.com/mnist/train-labels-idx1-ubyte.gz
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Downloading https://ossci-datasets.s3.amazonaws.com/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.

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()

Train Epoch: 1 [0/60000 (0%)]   Loss: 2.315648
Train Epoch: 1 [32000/60000 (53%)]      Loss: 1.065225

Test set: Average loss: 0.2645, Accuracy: 9267/10000 (93%)

Train Epoch: 2 [0/60000 (0%)]   Loss: 0.550773
Train Epoch: 2 [32000/60000 (53%)]      Loss: 0.384869

Test set: Average loss: 0.1986, Accuracy: 9425/10000 (94%)

Train Epoch: 3 [0/60000 (0%)]   Loss: 0.527896
Train Epoch: 3 [32000/60000 (53%)]      Loss: 0.191340

Test set: Average loss: 0.1038, Accuracy: 9699/10000 (97%)

Train Epoch: 4 [0/60000 (0%)]   Loss: 0.320365
Train Epoch: 4 [32000/60000 (53%)]      Loss: 0.196119

Test set: Average loss: 0.1062, Accuracy: 9670/10000 (97%)

Train Epoch: 5 [0/60000 (0%)]   Loss: 0.237412
Train Epoch: 5 [32000/60000 (53%)]      Loss: 0.204651

Test set: Average loss: 0.1042, Accuracy: 9662/10000 (97%)

Train Epoch: 6 [0/60000 (0%)]   Loss: 0.199588
Train Epoch: 6 [32000/60000 (53%)]      Loss: 0.140868

Test set: Average loss: 0.0808, Accuracy: 9756/10000 (98%)

Train Epoch: 7 [0/60000 (0%)]   Loss: 0.141149
Train Epoch: 7 [32000/60000 (53%)]      Loss: 0.170658

Test set: Average loss: 0.0650, Accuracy: 9793/10000 (98%)

Train Epoch: 8 [0/60000 (0%)]   Loss: 0.255635
Train Epoch: 8 [32000/60000 (53%)]      Loss: 0.075549

Test set: Average loss: 0.0730, Accuracy: 9774/10000 (98%)

Train Epoch: 9 [0/60000 (0%)]   Loss: 0.071969
Train Epoch: 9 [32000/60000 (53%)]      Loss: 0.111344

Test set: Average loss: 0.0733, Accuracy: 9791/10000 (98%)

Train Epoch: 10 [0/60000 (0%)]  Loss: 0.071485
Train Epoch: 10 [32000/60000 (53%)]     Loss: 0.216117

Test set: Average loss: 0.0559, Accuracy: 9810/10000 (98%)

Train Epoch: 11 [0/60000 (0%)]  Loss: 0.149677
Train Epoch: 11 [32000/60000 (53%)]     Loss: 0.131346

Test set: Average loss: 0.0578, Accuracy: 9824/10000 (98%)

Train Epoch: 12 [0/60000 (0%)]  Loss: 0.145392
Train Epoch: 12 [32000/60000 (53%)]     Loss: 0.168325

Test set: Average loss: 0.0506, Accuracy: 9850/10000 (98%)

Train Epoch: 13 [0/60000 (0%)]  Loss: 0.097744
Train Epoch: 13 [32000/60000 (53%)]     Loss: 0.074326

Test set: Average loss: 0.0592, Accuracy: 9830/10000 (98%)

Train Epoch: 14 [0/60000 (0%)]  Loss: 0.092248
Train Epoch: 14 [32000/60000 (53%)]     Loss: 0.096911

Test set: Average loss: 0.0564, Accuracy: 9833/10000 (98%)

Train Epoch: 15 [0/60000 (0%)]  Loss: 0.045171
Train Epoch: 15 [32000/60000 (53%)]     Loss: 0.095372

Test set: Average loss: 0.0500, Accuracy: 9846/10000 (98%)

Train Epoch: 16 [0/60000 (0%)]  Loss: 0.079225
Train Epoch: 16 [32000/60000 (53%)]     Loss: 0.189480

Test set: Average loss: 0.0453, Accuracy: 9869/10000 (99%)

Train Epoch: 17 [0/60000 (0%)]  Loss: 0.237551
Train Epoch: 17 [32000/60000 (53%)]     Loss: 0.326720

Test set: Average loss: 0.0469, Accuracy: 9855/10000 (99%)

Train Epoch: 18 [0/60000 (0%)]  Loss: 0.049015
Train Epoch: 18 [32000/60000 (53%)]     Loss: 0.078695

Test set: Average loss: 0.0496, Accuracy: 9865/10000 (99%)

Train Epoch: 19 [0/60000 (0%)]  Loss: 0.082634
Train Epoch: 19 [32000/60000 (53%)]     Loss: 0.154925

Test set: Average loss: 0.0424, Accuracy: 9879/10000 (99%)

Train Epoch: 20 [0/60000 (0%)]  Loss: 0.122403
Train Epoch: 20 [32000/60000 (53%)]     Loss: 0.088256

Test set: Average loss: 0.0455, Accuracy: 9868/10000 (99%)