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.

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)

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 STN the 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: 2.297115
Train Epoch: 1 [32000/60000 (53%)]      Loss: 0.948902

Test set: Average loss: 0.2371, Accuracy: 9323/10000 (93%)

Train Epoch: 2 [0/60000 (0%)]   Loss: 0.435741
Train Epoch: 2 [32000/60000 (53%)]      Loss: 0.272999

Test set: Average loss: 0.1215, Accuracy: 9641/10000 (96%)

Train Epoch: 3 [0/60000 (0%)]   Loss: 0.256528
Train Epoch: 3 [32000/60000 (53%)]      Loss: 0.497887

Test set: Average loss: 0.1254, Accuracy: 9612/10000 (96%)

Train Epoch: 4 [0/60000 (0%)]   Loss: 0.182472
Train Epoch: 4 [32000/60000 (53%)]      Loss: 0.285030

Test set: Average loss: 0.0778, Accuracy: 9749/10000 (97%)

Train Epoch: 5 [0/60000 (0%)]   Loss: 0.333017
Train Epoch: 5 [32000/60000 (53%)]      Loss: 0.195107

Test set: Average loss: 0.1506, Accuracy: 9523/10000 (95%)

Train Epoch: 6 [0/60000 (0%)]   Loss: 0.166007
Train Epoch: 6 [32000/60000 (53%)]      Loss: 0.267899

Test set: Average loss: 0.0646, Accuracy: 9786/10000 (98%)

Train Epoch: 7 [0/60000 (0%)]   Loss: 0.129741
Train Epoch: 7 [32000/60000 (53%)]      Loss: 0.166837

Test set: Average loss: 0.0571, Accuracy: 9811/10000 (98%)

Train Epoch: 8 [0/60000 (0%)]   Loss: 0.098625
Train Epoch: 8 [32000/60000 (53%)]      Loss: 0.283886

Test set: Average loss: 0.0532, Accuracy: 9832/10000 (98%)

Train Epoch: 9 [0/60000 (0%)]   Loss: 0.232190
Train Epoch: 9 [32000/60000 (53%)]      Loss: 0.056998

Test set: Average loss: 0.0548, Accuracy: 9835/10000 (98%)

Train Epoch: 10 [0/60000 (0%)]  Loss: 0.098180
Train Epoch: 10 [32000/60000 (53%)]     Loss: 0.173006

Test set: Average loss: 0.0512, Accuracy: 9843/10000 (98%)

Train Epoch: 11 [0/60000 (0%)]  Loss: 0.198763
Train Epoch: 11 [32000/60000 (53%)]     Loss: 0.082556

Test set: Average loss: 0.0452, Accuracy: 9863/10000 (99%)

Train Epoch: 12 [0/60000 (0%)]  Loss: 0.125281
Train Epoch: 12 [32000/60000 (53%)]     Loss: 0.041822

Test set: Average loss: 0.0558, Accuracy: 9822/10000 (98%)

Train Epoch: 13 [0/60000 (0%)]  Loss: 0.220886
Train Epoch: 13 [32000/60000 (53%)]     Loss: 0.296830

Test set: Average loss: 0.0401, Accuracy: 9869/10000 (99%)

Train Epoch: 14 [0/60000 (0%)]  Loss: 0.034315
Train Epoch: 14 [32000/60000 (53%)]     Loss: 0.145938

Test set: Average loss: 0.0480, Accuracy: 9854/10000 (99%)

Train Epoch: 15 [0/60000 (0%)]  Loss: 0.024913
Train Epoch: 15 [32000/60000 (53%)]     Loss: 0.040974

Test set: Average loss: 0.0416, Accuracy: 9864/10000 (99%)

Train Epoch: 16 [0/60000 (0%)]  Loss: 0.099197
Train Epoch: 16 [32000/60000 (53%)]     Loss: 0.189908

Test set: Average loss: 0.0518, Accuracy: 9845/10000 (98%)

Train Epoch: 17 [0/60000 (0%)]  Loss: 0.154701
Train Epoch: 17 [32000/60000 (53%)]     Loss: 0.212819

Test set: Average loss: 0.0473, Accuracy: 9857/10000 (99%)

Train Epoch: 18 [0/60000 (0%)]  Loss: 0.061061
Train Epoch: 18 [32000/60000 (53%)]     Loss: 0.025670

Test set: Average loss: 0.0394, Accuracy: 9877/10000 (99%)

Train Epoch: 19 [0/60000 (0%)]  Loss: 0.110355
Train Epoch: 19 [32000/60000 (53%)]     Loss: 0.065720

Test set: Average loss: 0.0371, Accuracy: 9879/10000 (99%)

Train Epoch: 20 [0/60000 (0%)]  Loss: 0.068162
Train Epoch: 20 [32000/60000 (53%)]     Loss: 0.101386

Test set: Average loss: 0.0402, Accuracy: 9884/10000 (99%)

Total running time of the script: ( 1 minutes 16.176 seconds)

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