使用mnist制作moving mnist

Moving MNIST是一个标准的序列预测数据集，它由一系列MNIST图像组成，这些图像随着时间的推移发生变化。每个时间步骤包含两个MNIST图像，一个前景图像和一个背景图像，前景图像在背景图像上运动。

以下是使用Python和Pytorch制作Moving MNIST的示例代码：

import torch
from torchvision import datasets, transforms
import numpy as np


def generate_moving_mnist(batch_size, seq_length, num_digits=2, image_size=64, digit_size=28, max_speed=1.0):
    mnist_transforms = transforms.Compose([
        transforms.Scale(digit_size),
        transforms.ToTensor(),
        transforms.Normalize((0.1307,), (0.3081,))
    ])

    mnist_dataset = datasets.MNIST('data', train=True, download=True, transform=mnist_transforms)
    mnist_data = mnist_dataset.train_data.numpy()

    # Generate random sequences
    sequences = np.zeros((batch_size, seq_length, num_digits, image_size, image_size), dtype=np.float32)
    for i in range(batch_size):
        for j in range(num_digits):
            # Choose a random digit from the MNIST dataset
            digit_idx = np.random.randint(0, len(mnist_data))
            digit = mnist_data[digit_idx]

            # Choose a random position and velocity for the digit
            x = np.random.randint(0, image_size - digit_size)
            y = np.random.randint(0, image_size - digit_size)
            dx = np.random.uniform(-max_speed, max_speed)
            dy = np.random.uniform(-max_speed, max_speed)

            # Generate the sequence for this digit
            for t in range(seq_length):
                # Compute the current position of the digit
                x += dx
                y += dy

                # If the digit goes off the edge of the image, bounce it back
                if x < 0:
                    x = 0
                    dx = -dx
                elif x + digit_size > image_size:
                    x = image_size - digit_size
                    dx = -dx
                if y < 0:
                    y = 0
                    dy = -dy
                elif y + digit_size > image_size:
                    y = image_size - digit_size
                    dy = -dy

                # Add the digit to the sequence at this time step
                sequences[i, t, j, x:x+digit_size, y:y+digit_size] = digit.numpy()

    # Normalize the sequences
    sequences -= np.mean(sequences)
    sequences /= np.std(sequences)

    # Convert to torch tensor
    sequences = torch.from_numpy(sequences)

    return sequences

上述代码使用了MNIST数据集中的样本图像，并根据随机速度和位置生成Moving MNIST序列。在此之后，对生成的序列进行标准化并转换为PyTorch张量。

可以通过调用以下代码来使用上述函数生成Moving MNIST序列：

batch_size = 16
seq_length = 20
num_digits = 2
image_size = 64
digit_size = 28
max_speed = 1.0

sequences = generate_moving_mnist(batch_size, seq_length, num_digits, image_size, digit_size, max_speed)
print(sequences.shape)

在上面的代码中，我们生成了一个大小为16x20x2x64x64的Moving MNIST序列。每个序列都包含20个时间步长和2个MNIST数字，这些数字在序列的时间步长中随机移动。