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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.

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 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 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 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 to ./MNIST/raw/t10k-labels-idx1-ubyte.gz
Extracting ./MNIST/raw/t10k-labels-idx1-ubyte.gz to ./MNIST/raw
Processing...
Done!

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: 2.380335
Train Epoch: 1 [32000/60000 (53%)]      Loss: 0.944729

Test set: Average loss: 0.2628, Accuracy: 9196/10000 (92%)

Train Epoch: 2 [0/60000 (0%)]   Loss: 0.630460
Train Epoch: 2 [32000/60000 (53%)]      Loss: 0.265266

Test set: Average loss: 0.1253, Accuracy: 9619/10000 (96%)

Train Epoch: 3 [0/60000 (0%)]   Loss: 0.291273
Train Epoch: 3 [32000/60000 (53%)]      Loss: 0.244611

Test set: Average loss: 0.1155, Accuracy: 9661/10000 (97%)

Train Epoch: 4 [0/60000 (0%)]   Loss: 0.520034
Train Epoch: 4 [32000/60000 (53%)]      Loss: 0.151760

Test set: Average loss: 0.0893, Accuracy: 9710/10000 (97%)

Train Epoch: 5 [0/60000 (0%)]   Loss: 0.178467
Train Epoch: 5 [32000/60000 (53%)]      Loss: 0.136954

Test set: Average loss: 0.1064, Accuracy: 9689/10000 (97%)

Train Epoch: 6 [0/60000 (0%)]   Loss: 0.359890
Train Epoch: 6 [32000/60000 (53%)]      Loss: 0.232079

Test set: Average loss: 0.0653, Accuracy: 9800/10000 (98%)

Train Epoch: 7 [0/60000 (0%)]   Loss: 0.109542
Train Epoch: 7 [32000/60000 (53%)]      Loss: 0.179991

Test set: Average loss: 0.0709, Accuracy: 9795/10000 (98%)

Train Epoch: 8 [0/60000 (0%)]   Loss: 0.166561
Train Epoch: 8 [32000/60000 (53%)]      Loss: 0.209908

Test set: Average loss: 0.2399, Accuracy: 9298/10000 (93%)

Train Epoch: 9 [0/60000 (0%)]   Loss: 0.557302
Train Epoch: 9 [32000/60000 (53%)]      Loss: 0.157553

Test set: Average loss: 0.0610, Accuracy: 9826/10000 (98%)

Train Epoch: 10 [0/60000 (0%)]  Loss: 0.084664
Train Epoch: 10 [32000/60000 (53%)]     Loss: 0.129301

Test set: Average loss: 0.0723, Accuracy: 9761/10000 (98%)

Train Epoch: 11 [0/60000 (0%)]  Loss: 0.077148
Train Epoch: 11 [32000/60000 (53%)]     Loss: 0.146349

Test set: Average loss: 0.0561, Accuracy: 9840/10000 (98%)

Train Epoch: 12 [0/60000 (0%)]  Loss: 0.061794
Train Epoch: 12 [32000/60000 (53%)]     Loss: 0.069933

Test set: Average loss: 0.0534, Accuracy: 9839/10000 (98%)

Train Epoch: 13 [0/60000 (0%)]  Loss: 0.145800
Train Epoch: 13 [32000/60000 (53%)]     Loss: 0.221794

Test set: Average loss: 0.0545, Accuracy: 9829/10000 (98%)

Train Epoch: 14 [0/60000 (0%)]  Loss: 0.160281
Train Epoch: 14 [32000/60000 (53%)]     Loss: 0.091294

Test set: Average loss: 0.0538, Accuracy: 9836/10000 (98%)

Train Epoch: 15 [0/60000 (0%)]  Loss: 0.167471
Train Epoch: 15 [32000/60000 (53%)]     Loss: 0.056646

Test set: Average loss: 0.0483, Accuracy: 9842/10000 (98%)

Train Epoch: 16 [0/60000 (0%)]  Loss: 0.187370
Train Epoch: 16 [32000/60000 (53%)]     Loss: 0.129717

Test set: Average loss: 0.0476, Accuracy: 9857/10000 (99%)

Train Epoch: 17 [0/60000 (0%)]  Loss: 0.147603
Train Epoch: 17 [32000/60000 (53%)]     Loss: 0.067645

Test set: Average loss: 0.1308, Accuracy: 9615/10000 (96%)

Train Epoch: 18 [0/60000 (0%)]  Loss: 0.370133
Train Epoch: 18 [32000/60000 (53%)]     Loss: 0.049101

Test set: Average loss: 0.0428, Accuracy: 9878/10000 (99%)

Train Epoch: 19 [0/60000 (0%)]  Loss: 0.038740
Train Epoch: 19 [32000/60000 (53%)]     Loss: 0.061314

Test set: Average loss: 0.0516, Accuracy: 9863/10000 (99%)

Train Epoch: 20 [0/60000 (0%)]  Loss: 0.146737
Train Epoch: 20 [32000/60000 (53%)]     Loss: 0.117933

Test set: Average loss: 0.0676, Accuracy: 9819/10000 (98%)

Total running time of the script: ( 1 minutes 57.200 seconds)

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