《Spatial Transformer Networks》

1. 研究问题

普通的CNN具有局部的平移不变性，而对于大的变换不具有不变性，这样，当新数据相对于训练数据发生大的变换时，可能会导致无法准确的预测。比如，对于分类任务来说，当测试集中的一只猫发生了平移、旋转、缩放等操作，那么很容易造成分类错误。

2. 研究方法

提出了一个可微分的spatial transformer module（空间变换模块），该模块可以嵌入CNN中，形成spatial transformer networks（空间变换网络）进行端到端的训练，从而显式地赋予CNN对输入图像以及特征图进行任意空间变换（包括仿射变换、裁剪等变换）的能力，从而简化后续的识别任务。如下图所示：

空间变换模块有三个部分组成：

• localisation network：产生一组空间变换参数
• grid generator：根据上述参数，决定变换后的图片与输入图片的坐标映射关系
• sampler：根据grid generator产生的坐标映射关系，将输入图片变换成输出图片。

注：空间变换模块是完全可微的，可以直接嵌入普通的网络中，自动学习，无需额外的监督信息

3. 实验结果

算法在三个数据集上进行了实验，分别是distorted MNIST, Street View House Numbers(SVHN), CUB-200-2011 birds。

补充实验

4. 结论

提出了一个空间变换模块，该模块可以嵌入CNN中对输入图像或特征图进行空间变换，可以在不改变原来CNN网络的条件下进行端到端的训练，从而提高网络的鲁棒性和准确度。

5. 启发

空间变换模块可以代替传统的插值算法，合并到CNN中进行训练，希望能够获得比传统的插值算法更好的效果。

6. Pytorch的STN教程

Pytorch给出了STN分类MNIST数据集的教程。

# 导入包

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

# 导入MNIST数据集

from six.moves import urllib
opener = urllib.request.build_opener()
opener.addheaders = [('User-agent', 'Mozilla/5.0')]
urllib.request.install_opener(opener)

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)  # num_workers是多线程，涉及多线程的代码必须放在if __name__=='__main__'后面
# 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)


# 构建空间变换网络
# note: 需要最新版本的Pytorch，包含affine_grid and grid_sample模块

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)

# 训练模型

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 the STN 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)))

# 可视化训练结果，包括可视化空间变换模块的输出

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')

if __name__=='__main__':
    for epoch in range(1, 5 + 1):
        train(epoch)
        test()

    # Visualize the STN transformation on some input batch
    visualize_stn()

    plt.ioff()
    plt.show()

out:

Train Epoch: 1 [0/60000 (0%)]   Loss: 2.335747
Train Epoch: 1 [32000/60000 (53%)]      Loss: 1.213178

Test set: Average loss: 0.2396, Accuracy: 9349/10000 (93%)

Train Epoch: 2 [0/60000 (0%)]   Loss: 0.656469
Train Epoch: 2 [32000/60000 (53%)]      Loss: 0.221150

Test set: Average loss: 0.1493, Accuracy: 9550/10000 (96%)

Train Epoch: 3 [0/60000 (0%)]   Loss: 0.327393
Train Epoch: 3 [32000/60000 (53%)]      Loss: 0.492515

Test set: Average loss: 0.1414, Accuracy: 9545/10000 (95%)

Train Epoch: 4 [0/60000 (0%)]   Loss: 0.682898
Train Epoch: 4 [32000/60000 (53%)]      Loss: 0.231050

Test set: Average loss: 0.0800, Accuracy: 9752/10000 (98%)

Train Epoch: 5 [0/60000 (0%)]   Loss: 0.268345
Train Epoch: 5 [32000/60000 (53%)]      Loss: 0.131333

Test set: Average loss: 0.0745, Accuracy: 9757/10000 (98%)

Train Epoch: 6 [0/60000 (0%)]   Loss: 0.197222
Train Epoch: 6 [32000/60000 (53%)]      Loss: 0.245901

Test set: Average loss: 0.0746, Accuracy: 9774/10000 (98%)

Train Epoch: 7 [0/60000 (0%)]   Loss: 0.313274
Train Epoch: 7 [32000/60000 (53%)]      Loss: 0.116866

Test set: Average loss: 0.0587, Accuracy: 9815/10000 (98%)

Train Epoch: 8 [0/60000 (0%)]   Loss: 0.115519
Train Epoch: 8 [32000/60000 (53%)]      Loss: 0.145794

Test set: Average loss: 0.0547, Accuracy: 9841/10000 (98%)

Train Epoch: 9 [0/60000 (0%)]   Loss: 0.271909
Train Epoch: 9 [32000/60000 (53%)]      Loss: 0.151952

Test set: Average loss: 0.0621, Accuracy: 9797/10000 (98%)

Train Epoch: 10 [0/60000 (0%)]  Loss: 0.141433
Train Epoch: 10 [32000/60000 (53%)]     Loss: 0.053757

Test set: Average loss: 0.0470, Accuracy: 9849/10000 (98%)

Train Epoch: 11 [0/60000 (0%)]  Loss: 0.193399
Train Epoch: 11 [32000/60000 (53%)]     Loss: 0.060293

Test set: Average loss: 0.0452, Accuracy: 9870/10000 (99%)

Train Epoch: 12 [0/60000 (0%)]  Loss: 0.137983
Train Epoch: 12 [32000/60000 (53%)]     Loss: 0.128484

Test set: Average loss: 0.0491, Accuracy: 9856/10000 (99%)

Train Epoch: 13 [0/60000 (0%)]  Loss: 0.061785
Train Epoch: 13 [32000/60000 (53%)]     Loss: 0.066256

Test set: Average loss: 0.0447, Accuracy: 9861/10000 (99%)

Train Epoch: 14 [0/60000 (0%)]  Loss: 0.032042
Train Epoch: 14 [32000/60000 (53%)]     Loss: 0.343082

Test set: Average loss: 0.0642, Accuracy: 9805/10000 (98%)

Train Epoch: 15 [0/60000 (0%)]  Loss: 0.094579
Train Epoch: 15 [32000/60000 (53%)]     Loss: 0.045928

Test set: Average loss: 0.0406, Accuracy: 9885/10000 (99%)

Train Epoch: 16 [0/60000 (0%)]  Loss: 0.048026
Train Epoch: 16 [32000/60000 (53%)]     Loss: 0.077136

Test set: Average loss: 0.0418, Accuracy: 9875/10000 (99%)

Train Epoch: 17 [0/60000 (0%)]  Loss: 0.026751
Train Epoch: 17 [32000/60000 (53%)]     Loss: 0.207613

Test set: Average loss: 0.0661, Accuracy: 9801/10000 (98%)

Train Epoch: 18 [0/60000 (0%)]  Loss: 0.204898
Train Epoch: 18 [32000/60000 (53%)]     Loss: 0.167400

Test set: Average loss: 0.0457, Accuracy: 9865/10000 (99%)

Train Epoch: 19 [0/60000 (0%)]  Loss: 0.029272
Train Epoch: 19 [32000/60000 (53%)]     Loss: 0.181033

Test set: Average loss: 0.0430, Accuracy: 9867/10000 (99%)

Train Epoch: 20 [0/60000 (0%)]  Loss: 0.065609
Train Epoch: 20 [32000/60000 (53%)]     Loss: 0.179433

Test set: Average loss: 0.0428, Accuracy: 9872/10000 (99%)

参考

Spatial Transformer Networks笔记