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 DeepMind paper

Spatial transformer networks are a generalization of differentiable attention to any spatial transformation. Spatial transformer networks (STN for short) allows a neural network to learn how to do spatial transformations to 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 CNN are not invariant to rotation and scale and more generally : affine transformations.

One of the best things about STN is the ability to simply plug it into any existing CNN with very little modifications.

# 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)

Out:

Downloading http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz
Downloading http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz
Downloading http://yann.lecun.com/exdb/mnist/t10k-images-idx3-ubyte.gz
Downloading http://yann.lecun.com/exdb/mnist/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 apply 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 froward 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: 2.316680
Train Epoch: 1 [32000/60000 (53%)]      Loss: 0.915944

Test set: Average loss: 0.2849, Accuracy: 9174/10000 (92%)

Train Epoch: 2 [0/60000 (0%)]   Loss: 0.494003
Train Epoch: 2 [32000/60000 (53%)]      Loss: 0.307739

Test set: Average loss: 0.1113, Accuracy: 9669/10000 (97%)

Train Epoch: 3 [0/60000 (0%)]   Loss: 0.324201
Train Epoch: 3 [32000/60000 (53%)]      Loss: 0.415912

Test set: Average loss: 0.0964, Accuracy: 9700/10000 (97%)

Train Epoch: 4 [0/60000 (0%)]   Loss: 0.244328
Train Epoch: 4 [32000/60000 (53%)]      Loss: 0.143516

Test set: Average loss: 0.0757, Accuracy: 9763/10000 (98%)

Train Epoch: 5 [0/60000 (0%)]   Loss: 0.371837
Train Epoch: 5 [32000/60000 (53%)]      Loss: 0.264903

Test set: Average loss: 0.0772, Accuracy: 9758/10000 (98%)

Train Epoch: 6 [0/60000 (0%)]   Loss: 0.235697
Train Epoch: 6 [32000/60000 (53%)]      Loss: 0.198383

Test set: Average loss: 0.0655, Accuracy: 9794/10000 (98%)

Train Epoch: 7 [0/60000 (0%)]   Loss: 0.141787
Train Epoch: 7 [32000/60000 (53%)]      Loss: 0.095184

Test set: Average loss: 0.0598, Accuracy: 9809/10000 (98%)

Train Epoch: 8 [0/60000 (0%)]   Loss: 0.221511
Train Epoch: 8 [32000/60000 (53%)]      Loss: 0.149709

Test set: Average loss: 0.0469, Accuracy: 9857/10000 (99%)

Train Epoch: 9 [0/60000 (0%)]   Loss: 0.396147
Train Epoch: 9 [32000/60000 (53%)]      Loss: 0.188054

Test set: Average loss: 0.0574, Accuracy: 9825/10000 (98%)

Train Epoch: 10 [0/60000 (0%)]  Loss: 0.134353
Train Epoch: 10 [32000/60000 (53%)]     Loss: 0.053522

Test set: Average loss: 0.0615, Accuracy: 9805/10000 (98%)

Train Epoch: 11 [0/60000 (0%)]  Loss: 0.091511
Train Epoch: 11 [32000/60000 (53%)]     Loss: 0.077700

Test set: Average loss: 0.0404, Accuracy: 9876/10000 (99%)

Train Epoch: 12 [0/60000 (0%)]  Loss: 0.045463
Train Epoch: 12 [32000/60000 (53%)]     Loss: 0.020756

Test set: Average loss: 0.0403, Accuracy: 9868/10000 (99%)

Train Epoch: 13 [0/60000 (0%)]  Loss: 0.019118
Train Epoch: 13 [32000/60000 (53%)]     Loss: 0.021535

Test set: Average loss: 0.0601, Accuracy: 9816/10000 (98%)

Train Epoch: 14 [0/60000 (0%)]  Loss: 0.117381
Train Epoch: 14 [32000/60000 (53%)]     Loss: 0.049683

Test set: Average loss: 0.0464, Accuracy: 9862/10000 (99%)

Train Epoch: 15 [0/60000 (0%)]  Loss: 0.030192
Train Epoch: 15 [32000/60000 (53%)]     Loss: 0.087893

Test set: Average loss: 0.0416, Accuracy: 9876/10000 (99%)

Train Epoch: 16 [0/60000 (0%)]  Loss: 0.029896
Train Epoch: 16 [32000/60000 (53%)]     Loss: 0.047947

Test set: Average loss: 0.0470, Accuracy: 9855/10000 (99%)

Train Epoch: 17 [0/60000 (0%)]  Loss: 0.146504
Train Epoch: 17 [32000/60000 (53%)]     Loss: 0.063095

Test set: Average loss: 0.0362, Accuracy: 9894/10000 (99%)

Train Epoch: 18 [0/60000 (0%)]  Loss: 0.229595
Train Epoch: 18 [32000/60000 (53%)]     Loss: 0.065047

Test set: Average loss: 0.0468, Accuracy: 9867/10000 (99%)

Train Epoch: 19 [0/60000 (0%)]  Loss: 0.117012
Train Epoch: 19 [32000/60000 (53%)]     Loss: 0.038908

Test set: Average loss: 0.1120, Accuracy: 9681/10000 (97%)

Train Epoch: 20 [0/60000 (0%)]  Loss: 0.312182
Train Epoch: 20 [32000/60000 (53%)]     Loss: 0.171513

Test set: Average loss: 0.0440, Accuracy: 9882/10000 (99%)

Total running time of the script: ( 2 minutes 54.559 seconds)

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