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
from torch.autograd import Variable
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.

use_cuda = torch.cuda.is_available()

# 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.fill_(0)
        self.fc_loc[2].bias.data = torch.FloatTensor([1, 0, 0, 0, 1, 0])

    # 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)


model = Net()
if use_cuda:
    model.cuda()

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):
        if use_cuda:
            data, target = data.cuda(), target.cuda()

        data, target = Variable(data), Variable(target)
        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.data[0]))
#
# A simple test procedure to measure STN the performances on MNIST.
#


def test():
    model.eval()
    test_loss = 0
    correct = 0
    for data, target in test_loader:
        if use_cuda:
            data, target = data.cuda(), target.cuda()
        data, target = Variable(data, volatile=True), Variable(target)
        output = model(data)

        # sum up batch loss
        test_loss += F.nll_loss(output, target, size_average=False).data[0]
        # get the index of the max log-probability
        pred = output.data.max(1, keepdim=True)[1]
        correct += pred.eq(target.data.view_as(pred)).cpu().sum()

    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():
    # Get a batch of training data
    data, _ = next(iter(test_loader))
    data = Variable(data, volatile=True)

    if use_cuda:
        data = data.cuda()

    input_tensor = data.cpu().data
    transformed_input_tensor = model.stn(data).cpu().data

    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: 2.328042
Train Epoch: 1 [32000/60000 (53%)]      Loss: 0.939213

Test set: Average loss: 0.2191, Accuracy: 9334/10000 (93%)

Train Epoch: 2 [0/60000 (0%)]   Loss: 0.584606
Train Epoch: 2 [32000/60000 (53%)]      Loss: 0.371455

Test set: Average loss: 0.1161, Accuracy: 9638/10000 (96%)

Train Epoch: 3 [0/60000 (0%)]   Loss: 0.306197
Train Epoch: 3 [32000/60000 (53%)]      Loss: 0.328586

Test set: Average loss: 0.0936, Accuracy: 9718/10000 (97%)

Train Epoch: 4 [0/60000 (0%)]   Loss: 0.190892
Train Epoch: 4 [32000/60000 (53%)]      Loss: 0.218988

Test set: Average loss: 0.0951, Accuracy: 9706/10000 (97%)

Train Epoch: 5 [0/60000 (0%)]   Loss: 0.339990
Train Epoch: 5 [32000/60000 (53%)]      Loss: 0.242226

Test set: Average loss: 0.0779, Accuracy: 9760/10000 (98%)

Train Epoch: 6 [0/60000 (0%)]   Loss: 0.179238
Train Epoch: 6 [32000/60000 (53%)]      Loss: 0.100567

Test set: Average loss: 0.0735, Accuracy: 9782/10000 (98%)

Train Epoch: 7 [0/60000 (0%)]   Loss: 0.186666
Train Epoch: 7 [32000/60000 (53%)]      Loss: 0.258629

Test set: Average loss: 0.0549, Accuracy: 9837/10000 (98%)

Train Epoch: 8 [0/60000 (0%)]   Loss: 0.072454
Train Epoch: 8 [32000/60000 (53%)]      Loss: 0.139633

Test set: Average loss: 0.0524, Accuracy: 9843/10000 (98%)

Train Epoch: 9 [0/60000 (0%)]   Loss: 0.035842
Train Epoch: 9 [32000/60000 (53%)]      Loss: 0.113700

Test set: Average loss: 0.0561, Accuracy: 9832/10000 (98%)

Train Epoch: 10 [0/60000 (0%)]  Loss: 0.097008
Train Epoch: 10 [32000/60000 (53%)]     Loss: 0.061220

Test set: Average loss: 0.0567, Accuracy: 9828/10000 (98%)

Train Epoch: 11 [0/60000 (0%)]  Loss: 0.087038
Train Epoch: 11 [32000/60000 (53%)]     Loss: 0.302899

Test set: Average loss: 0.0433, Accuracy: 9869/10000 (99%)

Train Epoch: 12 [0/60000 (0%)]  Loss: 0.172409
Train Epoch: 12 [32000/60000 (53%)]     Loss: 0.166645

Test set: Average loss: 0.0511, Accuracy: 9846/10000 (98%)

Train Epoch: 13 [0/60000 (0%)]  Loss: 0.039110
Train Epoch: 13 [32000/60000 (53%)]     Loss: 0.078045

Test set: Average loss: 0.0498, Accuracy: 9869/10000 (99%)

Train Epoch: 14 [0/60000 (0%)]  Loss: 0.208534
Train Epoch: 14 [32000/60000 (53%)]     Loss: 0.113415

Test set: Average loss: 0.0438, Accuracy: 9875/10000 (99%)

Train Epoch: 15 [0/60000 (0%)]  Loss: 0.098780
Train Epoch: 15 [32000/60000 (53%)]     Loss: 0.092804

Test set: Average loss: 0.0457, Accuracy: 9856/10000 (99%)

Train Epoch: 16 [0/60000 (0%)]  Loss: 0.062472
Train Epoch: 16 [32000/60000 (53%)]     Loss: 0.115080

Test set: Average loss: 0.0362, Accuracy: 9885/10000 (99%)

Train Epoch: 17 [0/60000 (0%)]  Loss: 0.058453
Train Epoch: 17 [32000/60000 (53%)]     Loss: 0.107846

Test set: Average loss: 0.0383, Accuracy: 9894/10000 (99%)

Train Epoch: 18 [0/60000 (0%)]  Loss: 0.018933
Train Epoch: 18 [32000/60000 (53%)]     Loss: 0.030990

Test set: Average loss: 0.0419, Accuracy: 9884/10000 (99%)

Train Epoch: 19 [0/60000 (0%)]  Loss: 0.047748
Train Epoch: 19 [32000/60000 (53%)]     Loss: 0.190539

Test set: Average loss: 0.0347, Accuracy: 9892/10000 (99%)

Train Epoch: 20 [0/60000 (0%)]  Loss: 0.053282
Train Epoch: 20 [32000/60000 (53%)]     Loss: 0.090556

Test set: Average loss: 0.0341, Accuracy: 9888/10000 (99%)

Total running time of the script: ( 1 minutes 1.708 seconds)

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