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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: 2.310246
Train Epoch: 1 [32000/60000 (53%)]      Loss: 0.963255

Test set: Average loss: 0.2943, Accuracy: 9171/10000 (92%)

Train Epoch: 2 [0/60000 (0%)]   Loss: 0.888166
Train Epoch: 2 [32000/60000 (53%)]      Loss: 0.274492

Test set: Average loss: 0.1344, Accuracy: 9584/10000 (96%)

Train Epoch: 3 [0/60000 (0%)]   Loss: 0.332119
Train Epoch: 3 [32000/60000 (53%)]      Loss: 0.310127

Test set: Average loss: 0.1065, Accuracy: 9687/10000 (97%)

Train Epoch: 4 [0/60000 (0%)]   Loss: 0.353095
Train Epoch: 4 [32000/60000 (53%)]      Loss: 0.217555

Test set: Average loss: 0.1090, Accuracy: 9654/10000 (97%)

Train Epoch: 5 [0/60000 (0%)]   Loss: 0.242575
Train Epoch: 5 [32000/60000 (53%)]      Loss: 0.286949

Test set: Average loss: 0.0851, Accuracy: 9733/10000 (97%)

Train Epoch: 6 [0/60000 (0%)]   Loss: 0.349826
Train Epoch: 6 [32000/60000 (53%)]      Loss: 0.281250

Test set: Average loss: 0.0790, Accuracy: 9750/10000 (98%)

Train Epoch: 7 [0/60000 (0%)]   Loss: 0.157301
Train Epoch: 7 [32000/60000 (53%)]      Loss: 0.166657

Test set: Average loss: 0.0821, Accuracy: 9742/10000 (97%)

Train Epoch: 8 [0/60000 (0%)]   Loss: 0.049383
Train Epoch: 8 [32000/60000 (53%)]      Loss: 0.153107

Test set: Average loss: 0.1230, Accuracy: 9623/10000 (96%)

Train Epoch: 9 [0/60000 (0%)]   Loss: 0.199822
Train Epoch: 9 [32000/60000 (53%)]      Loss: 0.125766

Test set: Average loss: 0.0573, Accuracy: 9832/10000 (98%)

Train Epoch: 10 [0/60000 (0%)]  Loss: 0.099677
Train Epoch: 10 [32000/60000 (53%)]     Loss: 0.082555

Test set: Average loss: 0.0576, Accuracy: 9821/10000 (98%)

Train Epoch: 11 [0/60000 (0%)]  Loss: 0.213009
Train Epoch: 11 [32000/60000 (53%)]     Loss: 0.085521

Test set: Average loss: 0.0561, Accuracy: 9838/10000 (98%)

Train Epoch: 12 [0/60000 (0%)]  Loss: 0.040678
Train Epoch: 12 [32000/60000 (53%)]     Loss: 0.078440

Test set: Average loss: 0.0535, Accuracy: 9835/10000 (98%)

Train Epoch: 13 [0/60000 (0%)]  Loss: 0.161887
Train Epoch: 13 [32000/60000 (53%)]     Loss: 0.054764

Test set: Average loss: 0.0522, Accuracy: 9848/10000 (98%)

Train Epoch: 14 [0/60000 (0%)]  Loss: 0.206360
Train Epoch: 14 [32000/60000 (53%)]     Loss: 0.058612

Test set: Average loss: 0.0529, Accuracy: 9842/10000 (98%)

Train Epoch: 15 [0/60000 (0%)]  Loss: 0.075211
Train Epoch: 15 [32000/60000 (53%)]     Loss: 0.042702

Test set: Average loss: 0.0536, Accuracy: 9836/10000 (98%)

Train Epoch: 16 [0/60000 (0%)]  Loss: 0.055904
Train Epoch: 16 [32000/60000 (53%)]     Loss: 0.047523

Test set: Average loss: 0.0537, Accuracy: 9845/10000 (98%)

Train Epoch: 17 [0/60000 (0%)]  Loss: 0.023134
Train Epoch: 17 [32000/60000 (53%)]     Loss: 0.118878

Test set: Average loss: 0.0510, Accuracy: 9847/10000 (98%)

Train Epoch: 18 [0/60000 (0%)]  Loss: 0.068736
Train Epoch: 18 [32000/60000 (53%)]     Loss: 0.227086

Test set: Average loss: 0.0509, Accuracy: 9854/10000 (99%)

Train Epoch: 19 [0/60000 (0%)]  Loss: 0.136510
Train Epoch: 19 [32000/60000 (53%)]     Loss: 0.229261

Test set: Average loss: 0.0448, Accuracy: 9868/10000 (99%)

Train Epoch: 20 [0/60000 (0%)]  Loss: 0.139792
Train Epoch: 20 [32000/60000 (53%)]     Loss: 0.127667

Test set: Average loss: 0.0482, Accuracy: 9850/10000 (98%)

Total running time of the script: ( 2 minutes 11.973 seconds)

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