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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

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)
Downloading http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz
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Downloading https://ossci-datasets.s3.amazonaws.com/mnist/train-images-idx3-ubyte.gz
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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-images-idx3-ubyte.gz
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Failed to download (trying next):
HTTP Error 403: Forbidden

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.

../_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
Train Epoch: 1 [0/60000 (0%)]   Loss: 2.315648
Train Epoch: 1 [32000/60000 (53%)]      Loss: 1.035394

Test set: Average loss: 0.2557, Accuracy: 9279/10000 (93%)

Train Epoch: 2 [0/60000 (0%)]   Loss: 0.527344
Train Epoch: 2 [32000/60000 (53%)]      Loss: 0.347577

Test set: Average loss: 0.2630, Accuracy: 9215/10000 (92%)

Train Epoch: 3 [0/60000 (0%)]   Loss: 0.470311
Train Epoch: 3 [32000/60000 (53%)]      Loss: 0.215354

Test set: Average loss: 0.1424, Accuracy: 9555/10000 (96%)

Train Epoch: 4 [0/60000 (0%)]   Loss: 0.409373
Train Epoch: 4 [32000/60000 (53%)]      Loss: 0.176189

Test set: Average loss: 0.1044, Accuracy: 9680/10000 (97%)

Train Epoch: 5 [0/60000 (0%)]   Loss: 0.218112
Train Epoch: 5 [32000/60000 (53%)]      Loss: 0.194059

Test set: Average loss: 0.0843, Accuracy: 9739/10000 (97%)

Train Epoch: 6 [0/60000 (0%)]   Loss: 0.112562
Train Epoch: 6 [32000/60000 (53%)]      Loss: 0.121518

Test set: Average loss: 0.0809, Accuracy: 9751/10000 (98%)

Train Epoch: 7 [0/60000 (0%)]   Loss: 0.130490
Train Epoch: 7 [32000/60000 (53%)]      Loss: 0.147118

Test set: Average loss: 0.0721, Accuracy: 9786/10000 (98%)

Train Epoch: 8 [0/60000 (0%)]   Loss: 0.195880
Train Epoch: 8 [32000/60000 (53%)]      Loss: 0.067920

Test set: Average loss: 0.0648, Accuracy: 9798/10000 (98%)

Train Epoch: 9 [0/60000 (0%)]   Loss: 0.056485
Train Epoch: 9 [32000/60000 (53%)]      Loss: 0.112973

Test set: Average loss: 0.0706, Accuracy: 9803/10000 (98%)

Train Epoch: 10 [0/60000 (0%)]  Loss: 0.102115
Train Epoch: 10 [32000/60000 (53%)]     Loss: 0.289902

Test set: Average loss: 0.0611, Accuracy: 9821/10000 (98%)

Train Epoch: 11 [0/60000 (0%)]  Loss: 0.136880
Train Epoch: 11 [32000/60000 (53%)]     Loss: 0.124532

Test set: Average loss: 0.0570, Accuracy: 9842/10000 (98%)

Train Epoch: 12 [0/60000 (0%)]  Loss: 0.152176
Train Epoch: 12 [32000/60000 (53%)]     Loss: 0.063707

Test set: Average loss: 0.0573, Accuracy: 9835/10000 (98%)

Train Epoch: 13 [0/60000 (0%)]  Loss: 0.114098
Train Epoch: 13 [32000/60000 (53%)]     Loss: 0.097089

Test set: Average loss: 0.0703, Accuracy: 9794/10000 (98%)

Train Epoch: 14 [0/60000 (0%)]  Loss: 0.087669
Train Epoch: 14 [32000/60000 (53%)]     Loss: 0.110027

Test set: Average loss: 0.0547, Accuracy: 9829/10000 (98%)

Train Epoch: 15 [0/60000 (0%)]  Loss: 0.062772
Train Epoch: 15 [32000/60000 (53%)]     Loss: 0.062491

Test set: Average loss: 0.0477, Accuracy: 9861/10000 (99%)

Train Epoch: 16 [0/60000 (0%)]  Loss: 0.047836
Train Epoch: 16 [32000/60000 (53%)]     Loss: 0.417422

Test set: Average loss: 0.0493, Accuracy: 9856/10000 (99%)

Train Epoch: 17 [0/60000 (0%)]  Loss: 0.268897
Train Epoch: 17 [32000/60000 (53%)]     Loss: 0.211773

Test set: Average loss: 0.0521, Accuracy: 9840/10000 (98%)

Train Epoch: 18 [0/60000 (0%)]  Loss: 0.095129
Train Epoch: 18 [32000/60000 (53%)]     Loss: 0.106638

Test set: Average loss: 0.0606, Accuracy: 9820/10000 (98%)

Train Epoch: 19 [0/60000 (0%)]  Loss: 0.189171
Train Epoch: 19 [32000/60000 (53%)]     Loss: 0.095619

Test set: Average loss: 0.0531, Accuracy: 9838/10000 (98%)

Train Epoch: 20 [0/60000 (0%)]  Loss: 0.047276
Train Epoch: 20 [32000/60000 (53%)]     Loss: 0.069885

Test set: Average loss: 0.0599, Accuracy: 9825/10000 (98%)

Total running time of the script: ( 2 minutes 5.495 seconds)

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