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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: 2.319473
Train Epoch: 1 [32000/60000 (53%)]      Loss: 0.757302

Test set: Average loss: 0.2108, Accuracy: 9399/10000 (94%)

Train Epoch: 2 [0/60000 (0%)]   Loss: 0.499661
Train Epoch: 2 [32000/60000 (53%)]      Loss: 0.353140

Test set: Average loss: 0.0897, Accuracy: 9730/10000 (97%)

Train Epoch: 3 [0/60000 (0%)]   Loss: 0.283170
Train Epoch: 3 [32000/60000 (53%)]      Loss: 0.399784

Test set: Average loss: 0.0707, Accuracy: 9774/10000 (98%)

Train Epoch: 4 [0/60000 (0%)]   Loss: 0.166782
Train Epoch: 4 [32000/60000 (53%)]      Loss: 0.163742

Test set: Average loss: 0.0789, Accuracy: 9755/10000 (98%)

Train Epoch: 5 [0/60000 (0%)]   Loss: 0.254818
Train Epoch: 5 [32000/60000 (53%)]      Loss: 0.115249

Test set: Average loss: 0.0765, Accuracy: 9762/10000 (98%)

Train Epoch: 6 [0/60000 (0%)]   Loss: 0.406405
Train Epoch: 6 [32000/60000 (53%)]      Loss: 0.095131

Test set: Average loss: 0.0527, Accuracy: 9841/10000 (98%)

Train Epoch: 7 [0/60000 (0%)]   Loss: 0.113807
Train Epoch: 7 [32000/60000 (53%)]      Loss: 0.363093

Test set: Average loss: 0.0438, Accuracy: 9865/10000 (99%)

Train Epoch: 8 [0/60000 (0%)]   Loss: 0.186867
Train Epoch: 8 [32000/60000 (53%)]      Loss: 0.283391

Test set: Average loss: 0.0439, Accuracy: 9871/10000 (99%)

Train Epoch: 9 [0/60000 (0%)]   Loss: 0.121729
Train Epoch: 9 [32000/60000 (53%)]      Loss: 0.109074

Test set: Average loss: 0.0432, Accuracy: 9865/10000 (99%)

Train Epoch: 10 [0/60000 (0%)]  Loss: 0.126931
Train Epoch: 10 [32000/60000 (53%)]     Loss: 0.156093

Test set: Average loss: 0.0437, Accuracy: 9870/10000 (99%)

Train Epoch: 11 [0/60000 (0%)]  Loss: 0.024541
Train Epoch: 11 [32000/60000 (53%)]     Loss: 0.185332

Test set: Average loss: 0.0380, Accuracy: 9888/10000 (99%)

Train Epoch: 12 [0/60000 (0%)]  Loss: 0.040363
Train Epoch: 12 [32000/60000 (53%)]     Loss: 0.078249

Test set: Average loss: 0.0453, Accuracy: 9871/10000 (99%)

Train Epoch: 13 [0/60000 (0%)]  Loss: 0.272843
Train Epoch: 13 [32000/60000 (53%)]     Loss: 0.045672

Test set: Average loss: 0.0497, Accuracy: 9849/10000 (98%)

Train Epoch: 14 [0/60000 (0%)]  Loss: 0.184226
Train Epoch: 14 [32000/60000 (53%)]     Loss: 0.077563

Test set: Average loss: 0.0398, Accuracy: 9882/10000 (99%)

Train Epoch: 15 [0/60000 (0%)]  Loss: 0.045182
Train Epoch: 15 [32000/60000 (53%)]     Loss: 0.104022

Test set: Average loss: 0.0541, Accuracy: 9842/10000 (98%)

Train Epoch: 16 [0/60000 (0%)]  Loss: 0.090529
Train Epoch: 16 [32000/60000 (53%)]     Loss: 0.026285

Test set: Average loss: 0.0326, Accuracy: 9899/10000 (99%)

Train Epoch: 17 [0/60000 (0%)]  Loss: 0.090091
Train Epoch: 17 [32000/60000 (53%)]     Loss: 0.257354

Test set: Average loss: 0.0416, Accuracy: 9888/10000 (99%)

Train Epoch: 18 [0/60000 (0%)]  Loss: 0.182133
Train Epoch: 18 [32000/60000 (53%)]     Loss: 0.048632

Test set: Average loss: 0.0358, Accuracy: 9896/10000 (99%)

Train Epoch: 19 [0/60000 (0%)]  Loss: 0.046735
Train Epoch: 19 [32000/60000 (53%)]     Loss: 0.122107

Test set: Average loss: 0.0339, Accuracy: 9902/10000 (99%)

Train Epoch: 20 [0/60000 (0%)]  Loss: 0.072014
Train Epoch: 20 [32000/60000 (53%)]     Loss: 0.025843

Test set: Average loss: 0.0472, Accuracy: 9853/10000 (99%)

Total running time of the script: ( 2 minutes 4.725 seconds)

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