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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

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)

Out:

Downloading http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz
Downloading http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz to ./MNIST/raw/train-images-idx3-ubyte.gz
Extracting ./MNIST/raw/train-images-idx3-ubyte.gz to ./MNIST/raw

Downloading http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz
Downloading http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz to ./MNIST/raw/train-labels-idx1-ubyte.gz
Extracting ./MNIST/raw/train-labels-idx1-ubyte.gz to ./MNIST/raw

Downloading http://yann.lecun.com/exdb/mnist/t10k-images-idx3-ubyte.gz
Downloading http://yann.lecun.com/exdb/mnist/t10k-images-idx3-ubyte.gz to ./MNIST/raw/t10k-images-idx3-ubyte.gz
Extracting ./MNIST/raw/t10k-images-idx3-ubyte.gz to ./MNIST/raw

Downloading http://yann.lecun.com/exdb/mnist/t10k-labels-idx1-ubyte.gz
Downloading http://yann.lecun.com/exdb/mnist/t10k-labels-idx1-ubyte.gz to ./MNIST/raw/t10k-labels-idx1-ubyte.gz
Extracting ./MNIST/raw/t10k-labels-idx1-ubyte.gz to ./MNIST/raw

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()
../_images/sphx_glr_spatial_transformer_tutorial_001.png

Out:

Train Epoch: 1 [0/60000 (0%)]   Loss: 2.331719
Train Epoch: 1 [32000/60000 (53%)]      Loss: 1.119794

Test set: Average loss: 0.2525, Accuracy: 9316/10000 (93%)

Train Epoch: 2 [0/60000 (0%)]   Loss: 0.590933
Train Epoch: 2 [32000/60000 (53%)]      Loss: 0.404964

Test set: Average loss: 0.1147, Accuracy: 9655/10000 (97%)

Train Epoch: 3 [0/60000 (0%)]   Loss: 0.332403
Train Epoch: 3 [32000/60000 (53%)]      Loss: 0.279093

Test set: Average loss: 0.0929, Accuracy: 9724/10000 (97%)

Train Epoch: 4 [0/60000 (0%)]   Loss: 0.452063
Train Epoch: 4 [32000/60000 (53%)]      Loss: 0.301581

Test set: Average loss: 0.0729, Accuracy: 9776/10000 (98%)

Train Epoch: 5 [0/60000 (0%)]   Loss: 0.144024
Train Epoch: 5 [32000/60000 (53%)]      Loss: 0.288892

Test set: Average loss: 0.0663, Accuracy: 9790/10000 (98%)

Train Epoch: 6 [0/60000 (0%)]   Loss: 0.174932
Train Epoch: 6 [32000/60000 (53%)]      Loss: 0.208320

Test set: Average loss: 0.0599, Accuracy: 9807/10000 (98%)

Train Epoch: 7 [0/60000 (0%)]   Loss: 0.250342
Train Epoch: 7 [32000/60000 (53%)]      Loss: 0.103497

Test set: Average loss: 0.0571, Accuracy: 9819/10000 (98%)

Train Epoch: 8 [0/60000 (0%)]   Loss: 0.162338
Train Epoch: 8 [32000/60000 (53%)]      Loss: 0.164818

Test set: Average loss: 0.0715, Accuracy: 9770/10000 (98%)

Train Epoch: 9 [0/60000 (0%)]   Loss: 0.141136
Train Epoch: 9 [32000/60000 (53%)]      Loss: 0.072598

Test set: Average loss: 0.0633, Accuracy: 9797/10000 (98%)

Train Epoch: 10 [0/60000 (0%)]  Loss: 0.250712
Train Epoch: 10 [32000/60000 (53%)]     Loss: 0.038168

Test set: Average loss: 0.0599, Accuracy: 9812/10000 (98%)

Train Epoch: 11 [0/60000 (0%)]  Loss: 0.119506
Train Epoch: 11 [32000/60000 (53%)]     Loss: 0.148927

Test set: Average loss: 0.0547, Accuracy: 9834/10000 (98%)

Train Epoch: 12 [0/60000 (0%)]  Loss: 0.042774
Train Epoch: 12 [32000/60000 (53%)]     Loss: 0.111541

Test set: Average loss: 0.0562, Accuracy: 9817/10000 (98%)

Train Epoch: 13 [0/60000 (0%)]  Loss: 0.250342
Train Epoch: 13 [32000/60000 (53%)]     Loss: 0.083750

Test set: Average loss: 0.0470, Accuracy: 9848/10000 (98%)

Train Epoch: 14 [0/60000 (0%)]  Loss: 0.101970
Train Epoch: 14 [32000/60000 (53%)]     Loss: 0.065355

Test set: Average loss: 0.0528, Accuracy: 9846/10000 (98%)

Train Epoch: 15 [0/60000 (0%)]  Loss: 0.087602
Train Epoch: 15 [32000/60000 (53%)]     Loss: 0.078070

Test set: Average loss: 0.5046, Accuracy: 8576/10000 (86%)

Train Epoch: 16 [0/60000 (0%)]  Loss: 0.717720
Train Epoch: 16 [32000/60000 (53%)]     Loss: 0.110259

Test set: Average loss: 0.0390, Accuracy: 9884/10000 (99%)

Train Epoch: 17 [0/60000 (0%)]  Loss: 0.064517
Train Epoch: 17 [32000/60000 (53%)]     Loss: 0.074407

Test set: Average loss: 0.0389, Accuracy: 9884/10000 (99%)

Train Epoch: 18 [0/60000 (0%)]  Loss: 0.070490
Train Epoch: 18 [32000/60000 (53%)]     Loss: 0.060189

Test set: Average loss: 0.0401, Accuracy: 9883/10000 (99%)

Train Epoch: 19 [0/60000 (0%)]  Loss: 0.059528
Train Epoch: 19 [32000/60000 (53%)]     Loss: 0.096162

Test set: Average loss: 0.0467, Accuracy: 9864/10000 (99%)

Train Epoch: 20 [0/60000 (0%)]  Loss: 0.231828
Train Epoch: 20 [32000/60000 (53%)]     Loss: 0.168997

Test set: Average loss: 0.0392, Accuracy: 9873/10000 (99%)

Total running time of the script: ( 1 minutes 46.881 seconds)

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