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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
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
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
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
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: 2.336866
Train Epoch: 1 [32000/60000 (53%)]      Loss: 0.814886

Test set: Average loss: 0.3071, Accuracy: 9068/10000 (91%)

Train Epoch: 2 [0/60000 (0%)]   Loss: 0.557080
Train Epoch: 2 [32000/60000 (53%)]      Loss: 0.381781

Test set: Average loss: 0.1180, Accuracy: 9629/10000 (96%)

Train Epoch: 3 [0/60000 (0%)]   Loss: 0.296376
Train Epoch: 3 [32000/60000 (53%)]      Loss: 0.264963

Test set: Average loss: 0.1223, Accuracy: 9602/10000 (96%)

Train Epoch: 4 [0/60000 (0%)]   Loss: 0.321433
Train Epoch: 4 [32000/60000 (53%)]      Loss: 0.406383

Test set: Average loss: 0.0960, Accuracy: 9691/10000 (97%)

Train Epoch: 5 [0/60000 (0%)]   Loss: 0.445196
Train Epoch: 5 [32000/60000 (53%)]      Loss: 0.183014

Test set: Average loss: 0.2185, Accuracy: 9310/10000 (93%)

Train Epoch: 6 [0/60000 (0%)]   Loss: 0.592106
Train Epoch: 6 [32000/60000 (53%)]      Loss: 0.197823

Test set: Average loss: 0.0643, Accuracy: 9800/10000 (98%)

Train Epoch: 7 [0/60000 (0%)]   Loss: 0.052501
Train Epoch: 7 [32000/60000 (53%)]      Loss: 0.141110

Test set: Average loss: 0.0738, Accuracy: 9764/10000 (98%)

Train Epoch: 8 [0/60000 (0%)]   Loss: 0.082228
Train Epoch: 8 [32000/60000 (53%)]      Loss: 0.122326

Test set: Average loss: 0.0548, Accuracy: 9830/10000 (98%)

Train Epoch: 9 [0/60000 (0%)]   Loss: 0.149040
Train Epoch: 9 [32000/60000 (53%)]      Loss: 0.102508

Test set: Average loss: 0.0547, Accuracy: 9822/10000 (98%)

Train Epoch: 10 [0/60000 (0%)]  Loss: 0.060701
Train Epoch: 10 [32000/60000 (53%)]     Loss: 0.072134

Test set: Average loss: 0.0548, Accuracy: 9828/10000 (98%)

Train Epoch: 11 [0/60000 (0%)]  Loss: 0.085643
Train Epoch: 11 [32000/60000 (53%)]     Loss: 0.161989

Test set: Average loss: 0.0461, Accuracy: 9844/10000 (98%)

Train Epoch: 12 [0/60000 (0%)]  Loss: 0.095720
Train Epoch: 12 [32000/60000 (53%)]     Loss: 0.055991

Test set: Average loss: 0.0445, Accuracy: 9866/10000 (99%)

Train Epoch: 13 [0/60000 (0%)]  Loss: 0.072131
Train Epoch: 13 [32000/60000 (53%)]     Loss: 0.155747

Test set: Average loss: 0.0646, Accuracy: 9794/10000 (98%)

Train Epoch: 14 [0/60000 (0%)]  Loss: 0.083187
Train Epoch: 14 [32000/60000 (53%)]     Loss: 0.064047

Test set: Average loss: 0.0475, Accuracy: 9839/10000 (98%)

Train Epoch: 15 [0/60000 (0%)]  Loss: 0.136927
Train Epoch: 15 [32000/60000 (53%)]     Loss: 0.134590

Test set: Average loss: 0.0458, Accuracy: 9858/10000 (99%)

Train Epoch: 16 [0/60000 (0%)]  Loss: 0.113448
Train Epoch: 16 [32000/60000 (53%)]     Loss: 0.049741

Test set: Average loss: 0.0403, Accuracy: 9880/10000 (99%)

Train Epoch: 17 [0/60000 (0%)]  Loss: 0.059517
Train Epoch: 17 [32000/60000 (53%)]     Loss: 0.067672

Test set: Average loss: 0.0397, Accuracy: 9874/10000 (99%)

Train Epoch: 18 [0/60000 (0%)]  Loss: 0.119261
Train Epoch: 18 [32000/60000 (53%)]     Loss: 0.211020

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

Train Epoch: 19 [0/60000 (0%)]  Loss: 0.026400
Train Epoch: 19 [32000/60000 (53%)]     Loss: 0.117536

Test set: Average loss: 0.0625, Accuracy: 9821/10000 (98%)

Train Epoch: 20 [0/60000 (0%)]  Loss: 0.116775
Train Epoch: 20 [32000/60000 (53%)]     Loss: 0.038554

Test set: Average loss: 0.0596, Accuracy: 9838/10000 (98%)

Total running time of the script: ( 1 minutes 43.886 seconds)

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