使用NeRF进行3D体素渲染

使用NeRF进行3D体素渲染的最小代码实现

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前言

在这个例子中，我们展示了文献NeRF: Representing Scenes as Neural Radiance Fields for View Synthesis的最小实现。作者提出了一种巧妙的方法，通过神经网络对体积场景函数进行建模，从而合成场景的新视图。

为了帮助您直观地理解这一点，让我们从以下问题开始：是否可以将图像中像素的位置提供给神经网络，并要求网络预测该位置的颜色？

　　　　　　图 1：给定图像坐标作为神经网络作的输入并要求预测坐标处的颜色

神经网络会假设记忆（过拟合）图像。这意味着我们的神经网络会将整个图像编码为其权重。我们可以用每个位置查询神经网络，它最终会重建整个图像。

　　　　　　　　　　　图 2：经过训练的神经网络从头开始重新创建图像。

现在出现了一个问题，我们如何扩展这个想法来学习 3D 体素场景？实现与上述类似的过程需要了解每个体素（体积像素）。事实证明，这是一项非常具有挑战性的任务。

该论文的作者提出了一种使用场景的一些图像来学习 3D 场景的最小而优雅的方法。他们放弃使用体素进行训练。使用网络学习对体积场景进行建模，从而生成模型在训练时未显示的 3D 场景的新视图（图像）。

为了充分理解这一过程，需要了解一些先决条件。我们以这样一种方式构建示例，以便您在开始实施之前拥有所有必需的知识。

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一、设置

# Setting random seed to obtain reproducible results.
import tensorflow as tf

tf.random.set_seed(42)

import os
import glob
import imageio
import numpy as np
from tqdm import tqdm
from tensorflow import keras
from tensorflow.keras import layers
import matplotlib.pyplot as plt

# Initialize global variables.
AUTO = tf.data.AUTOTUNE
BATCH_SIZE = 5
NUM_SAMPLES = 32
POS_ENCODE_DIMS = 16
EPOCHS = 20

二、下载并载入数据

npz 数据文件包含图像、相机姿势和焦距。这些图像是从多个摄像机角度拍摄的，如图 3 所示：

　　　　　　　　　　　　　　　图 3：多个摄像机角度

要理解这种情况下的相机姿势，我们必须首先让自己认为相机是现实世界和二维图像之间的映射。

　　　　　　　　　　　　图 4：通过相机将 3-D 世界映射到 2-D 图像
考虑以下等式：

其中 x 是 2-D 图像点，X 是 3-D 世界点，P 是相机矩阵。 P 是一个 3 x 4 矩阵，在将现实世界对象映射到图像平面上起着至关重要的作用。

相机矩阵是一个仿射变换矩阵，它与 3 x 1 列 [图像高度、图像宽度、焦距] 连接以生成姿势矩阵。该矩阵的尺寸为 3 x 5，其中第一个 3 x 3 块位于相机的视点中。轴是 [down, right, backwards] 或 [-y, x, z]，其中相机面向前方 -z。

　　　　　　　　　　　　　　　　　图 5：仿射变换。
　　　　　　　
COLMAP 帧是 [right, down, forwards] 或 [x, -y, -z]。在此处阅读有关 COLMAP 的更多信息。

# Download the data if it does not already exist.
file_name = "tiny_nerf_data.npz"
url = "https://people.eecs.berkeley.edu/~bmild/nerf/tiny_nerf_data.npz"
if not os.path.exists(file_name):
    data = keras.utils.get_file(fname=file_name, origin=url)

data = np.load(data)
images = data["images"]
im_shape = images.shape
(num_images, H, W, _) = images.shape
(poses, focal) = (data["poses"], data["focal"])

# Plot a random image from the dataset for visualization.
plt.imshow(images[np.random.randint(low=0, high=num_images)])
plt.show()

Downloading data from https://people.eecs.berkeley.edu/~bmild/nerf/tiny_nerf_data.npz
12730368/12727482 [==============================] - 0s 0us/step

三、数据处理流程

现在您已经了解了相机矩阵的概念以及从 3D 场景到 2D 图像的映射，让我们来谈谈逆映射，即从 2D 图像到 3D 场景。

我们需要讨论使用光线投射和追踪的体素渲染，这是常见的计算机图形技术。本节将帮助您快速掌握这些技术。

考虑具有 N 个像素的图像。我们通过每个像素射出一条射线，并在射线上采样一些点。射线通常由方程 r(t) = o + td 参数化，其中 t 是参数，o 是原点，d 是单位方向矢量，如图 6 所示。

　　　　　　　　　　　　　图 6：r(t) = o + td 其中 t 为 3

在图 7 中，我们考虑一条射线，并在射线上采样一些随机点。这些样本点每个都有一个唯一的位置（x、y、z），并且射线有一个视角（theta、phi），关于该视角，可以参考下面的示意图。

　　　　　　　　　　　　　　　　视线角度示意图

视角特别有趣，因为我们可以通过许多不同的方式通过单个像素拍摄光线，每种方式都有独特的视角。这里要注意的另一件有趣的事情是添加到采样过程中的噪声。我们为每个样本添加均匀的噪声，使样本对应于连续分布。在图 7 中，蓝点是均匀分布的样本，白点（t1、t2、t3）随机放置在样本之间。

　　　　　　　　　　　　　　　　图 7：从射线中采样点。
　　　　　　　　　　　　　　　　　
图 8 以 3D 形式展示了整个采样过程，您可以在其中看到从白色图像发出的光线。这意味着每个像素都有其对应的光线，并且每条光线都将在不同的点进行采样。

　　　　　　　　　　　　　图 8：从 3-D 图像的所有像素发射光线

这些采样点作为 NeRF 模型的输入。然后要求模型预测该点的 RGB 颜色和体积密度。

　　　　　　　　　　　　　　　　图 9：数据管道

def encode_position(x):
    """Encodes the position into its corresponding Fourier feature.

    Args:
        x: The input coordinate.

    Returns:
        Fourier features tensors of the position.
    """
    positions = [x]
    for i in range(POS_ENCODE_DIMS):
        for fn in [tf.sin, tf.cos]:
            positions.append(fn(2.0 ** i * x))
    return tf.concat(positions, axis=-1)


def get_rays(height, width, focal, pose):
    """Computes origin point and direction vector of rays.

    Args:
        height: Height of the image.
        width: Width of the image.
        focal: The focal length between the images and the camera.
        pose: The pose matrix of the camera.

    Returns:
        Tuple of origin point and direction vector for rays.
    """
    # Build a meshgrid for the rays.
    i, j = tf.meshgrid(
        tf.range(width, dtype=tf.float32),
        tf.range(height, dtype=tf.float32),
        indexing="xy",
    )

    # Normalize the x axis coordinates.
    transformed_i = (i - width * 0.5) / focal

    # Normalize the y axis coordinates.
    transformed_j = (j - height * 0.5) / focal

    # Create the direction unit vectors.
    directions = tf.stack([transformed_i, -transformed_j, -tf.ones_like(i)], axis=-1)

    # Get the camera matrix.
    camera_matrix = pose[:3, :3]
    height_width_focal = pose[:3, -1]

    # Get origins and directions for the rays.
    transformed_dirs = directions[..., None, :]
    camera_dirs = transformed_dirs * camera_matrix
    ray_directions = tf.reduce_sum(camera_dirs, axis=-1)
    ray_origins = tf.broadcast_to(height_width_focal, tf.shape(ray_directions))

    # Return the origins and directions.
    return (ray_origins, ray_directions)


def render_flat_rays(ray_origins, ray_directions, near, far, num_samples, rand=False):
    """Renders the rays and flattens it.

    Args:
        ray_origins: The origin points for rays.
        ray_directions: The direction unit vectors for the rays.
        near: The near bound of the volumetric scene.
        far: The far bound of the volumetric scene.
        num_samples: Number of sample points in a ray.
        rand: Choice for randomising the sampling strategy.

    Returns:
       Tuple of flattened rays and sample points on each rays.
    """
    # Compute 3D query points.
    # Equation: r(t) = o+td -> Building the "t" here.
    t_vals = tf.linspace(near, far, num_samples)
    if rand:
        # Inject uniform noise into sample space to make the sampling
        # continuous.
        shape = list(ray_origins.shape[:-1]) + [num_samples]
        noise = tf.random.uniform(shape=shape) * (far - near) / num_samples
        t_vals = t_vals + noise

    # Equation: r(t) = o + td -> Building the "r" here.
    rays = ray_origins[..., None, :] + (
        ray_directions[..., None, :] * t_vals[..., None]
    )
    rays_flat = tf.reshape(rays, [-1, 3])
    rays_flat = encode_position(rays_flat)
    return (rays_flat, t_vals)


def map_fn(pose):
    """Maps individual pose to flattened rays and sample points.

    Args:
        pose: The pose matrix of the camera.

    Returns:
        Tuple of flattened rays and sample points corresponding to the
        camera pose.
    """
    (ray_origins, ray_directions) = get_rays(height=H, width=W, focal=focal, pose=pose)
    (rays_flat, t_vals) = render_flat_rays(
        ray_origins=ray_origins,
        ray_directions=ray_directions,
        near=2.0,
        far=6.0,
        num_samples=NUM_SAMPLES,
        rand=True,
    )
    return (rays_flat, t_vals)


# Create the training split.
split_index = int(num_images * 0.8)

# Split the images into training and validation.
train_images = images[:split_index]
val_images = images[split_index:]

# Split the poses into training and validation.
train_poses = poses[:split_index]
val_poses = poses[split_index:]

# Make the training pipeline.
train_img_ds = tf.data.Dataset.from_tensor_slices(train_images)
train_pose_ds = tf.data.Dataset.from_tensor_slices(train_poses)
train_ray_ds = train_pose_ds.map(map_fn, num_parallel_calls=AUTO)
training_ds = tf.data.Dataset.zip((train_img_ds, train_ray_ds))
train_ds = (
    training_ds.shuffle(BATCH_SIZE)
    .batch(BATCH_SIZE, drop_remainder=True, num_parallel_calls=AUTO)
    .prefetch(AUTO)
)

# Make the validation pipeline.
val_img_ds = tf.data.Dataset.from_tensor_slices(val_images)
val_pose_ds = tf.data.Dataset.from_tensor_slices(val_poses)
val_ray_ds = val_pose_ds.map(map_fn, num_parallel_calls=AUTO)
validation_ds = tf.data.Dataset.zip((val_img_ds, val_ray_ds))
val_ds = (
    validation_ds.shuffle(BATCH_SIZE)
    .batch(BATCH_SIZE, drop_remainder=True, num_parallel_calls=AUTO)
    .prefetch(AUTO)
)

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四、NeRF模型

该模型是一个多层感知器 (MLP)，以 ReLU 作为其非线性激活函数。

论文摘录：

“我们通过限制网络将体积密度 sigma 预测为仅位置 x 的函数，来使得这个表征是多视图一致的，同时允许将 RGB 颜色 c 预测为位置和视角的函数。为了实现这些功能，MLP 首先使用 8 个全连接层（使用 ReLU 激活和每层 256 个通道）处理输入 3D 坐标 x，并输出 sigma 和 256 维特征向量。然后将该特征向量与相机光线视线连接，并输入到一个额外的全连接层（使用 ReLU 激活和 128 个通道），输出与视图相关（view-dependent）的 RGB 颜色。”

在这里，我们进行了最小化实现，并使用了 64 个 Dense 单元，而不是本文中提到的 256 个。

def get_nerf_model(num_layers, num_pos):
    """Generates the NeRF neural network.

    Args:
        num_layers: The number of MLP layers.
        num_pos: The number of dimensions of positional encoding.

    Returns:
        The [`tf.keras`](https://www.tensorflow.org/api_docs/python/tf/keras) model.
    """
    inputs = keras.Input(shape=(num_pos, 2 * 3 * POS_ENCODE_DIMS + 3))
    x = inputs
    for i in range(num_layers):
        x = layers.Dense(units=64, activation="relu")(x)
        if i % 4 == 0 and i > 0:
            # Inject residual connection.
            x = layers.concatenate([x, inputs], axis=-1)
    outputs = layers.Dense(units=4)(x)
    return keras.Model(inputs=inputs, outputs=outputs)


def render_rgb_depth(model, rays_flat, t_vals, rand=True, train=True):
    """Generates the RGB image and depth map from model prediction.

    Args:
        model: The MLP model that is trained to predict the rgb and
            volume density of the volumetric scene.
        rays_flat: The flattened rays that serve as the input to
            the NeRF model.
        t_vals: The sample points for the rays.
        rand: Choice to randomise the sampling strategy.
        train: Whether the model is in the training or testing phase.

    Returns:
        Tuple of rgb image and depth map.
    """
    # Get the predictions from the nerf model and reshape it.
    if train:
        predictions = model(rays_flat)
    else:
        predictions = model.predict(rays_flat)
    predictions = tf.reshape(predictions, shape=(BATCH_SIZE, H, W, NUM_SAMPLES, 4))

    # Slice the predictions into rgb and sigma.
    rgb = tf.sigmoid(predictions[..., :-1])
    sigma_a = tf.nn.relu(predictions[..., -1])

    # Get the distance of adjacent intervals.
    delta = t_vals[..., 1:] - t_vals[..., :-1]
    # delta shape = (num_samples)
    if rand:
        delta = tf.concat(
            [delta, tf.broadcast_to([1e10], shape=(BATCH_SIZE, H, W, 1))], axis=-1
        )
        alpha = 1.0 - tf.exp(-sigma_a * delta)
    else:
        delta = tf.concat(
            [delta, tf.broadcast_to([1e10], shape=(BATCH_SIZE, 1))], axis=-1
        )
        alpha = 1.0 - tf.exp(-sigma_a * delta[:, None, None, :])

    # Get transmittance.
    exp_term = 1.0 - alpha
    epsilon = 1e-10
    transmittance = tf.math.cumprod(exp_term + epsilon, axis=-1, exclusive=True)
    weights = alpha * transmittance
    rgb = tf.reduce_sum(weights[..., None] * rgb, axis=-2)

    if rand:
        depth_map = tf.reduce_sum(weights * t_vals, axis=-1)
    else:
        depth_map = tf.reduce_sum(weights * t_vals[:, None, None], axis=-1)
    return (rgb, depth_map)

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五、训练

训练步骤作为自定义 keras.Model 子类的一部分实现，以便我们可以使用 model.fit 功能。

class NeRF(keras.Model):
    def __init__(self, nerf_model):
        super().__init__()
        self.nerf_model = nerf_model

    def compile(self, optimizer, loss_fn):
        super().compile()
        self.optimizer = optimizer
        self.loss_fn = loss_fn
        self.loss_tracker = keras.metrics.Mean(name="loss")
        self.psnr_metric = keras.metrics.Mean(name="psnr")

    def train_step(self, inputs):
        # Get the images and the rays.
        (images, rays) = inputs
        (rays_flat, t_vals) = rays

        with tf.GradientTape() as tape:
            # Get the predictions from the model.
            rgb, _ = render_rgb_depth(
                model=self.nerf_model, rays_flat=rays_flat, t_vals=t_vals, rand=True
            )
            loss = self.loss_fn(images, rgb)

        # Get the trainable variables.
        trainable_variables = self.nerf_model.trainable_variables

        # Get the gradeints of the trainiable variables with respect to the loss.
        gradients = tape.gradient(loss, trainable_variables)

        # Apply the grads and optimize the model.
        self.optimizer.apply_gradients(zip(gradients, trainable_variables))

        # Get the PSNR of the reconstructed images and the source images.
        psnr = tf.image.psnr(images, rgb, max_val=1.0)

        # Compute our own metrics
        self.loss_tracker.update_state(loss)
        self.psnr_metric.update_state(psnr)
        return {"loss": self.loss_tracker.result(), "psnr": self.psnr_metric.result()}

    def test_step(self, inputs):
        # Get the images and the rays.
        (images, rays) = inputs
        (rays_flat, t_vals) = rays

        # Get the predictions from the model.
        rgb, _ = render_rgb_depth(
            model=self.nerf_model, rays_flat=rays_flat, t_vals=t_vals, rand=True
        )
        loss = self.loss_fn(images, rgb)

        # Get the PSNR of the reconstructed images and the source images.
        psnr = tf.image.psnr(images, rgb, max_val=1.0)

        # Compute our own metrics
        self.loss_tracker.update_state(loss)
        self.psnr_metric.update_state(psnr)
        return {"loss": self.loss_tracker.result(), "psnr": self.psnr_metric.result()}

    @property
    def metrics(self):
        return [self.loss_tracker, self.psnr_metric]


test_imgs, test_rays = next(iter(train_ds))
test_rays_flat, test_t_vals = test_rays

loss_list = []


class TrainMonitor(keras.callbacks.Callback):
    def on_epoch_end(self, epoch, logs=None):
        loss = logs["loss"]
        loss_list.append(loss)
        test_recons_images, depth_maps = render_rgb_depth(
            model=self.model.nerf_model,
            rays_flat=test_rays_flat,
            t_vals=test_t_vals,
            rand=True,
            train=False,
        )

        # Plot the rgb, depth and the loss plot.
        fig, ax = plt.subplots(nrows=1, ncols=3, figsize=(20, 5))
        ax[0].imshow(keras.preprocessing.image.array_to_img(test_recons_images[0]))
        ax[0].set_title(f"Predicted Image: {epoch:03d}")

        ax[1].imshow(keras.preprocessing.image.array_to_img(depth_maps[0, ..., None]))
        ax[1].set_title(f"Depth Map: {epoch:03d}")

        ax[2].plot(loss_list)
        ax[2].set_xticks(np.arange(0, EPOCHS + 1, 5.0))
        ax[2].set_title(f"Loss Plot: {epoch:03d}")

        fig.savefig(f"images/{epoch:03d}.png")
        plt.show()
        plt.close()


num_pos = H * W * NUM_SAMPLES
nerf_model = get_nerf_model(num_layers=8, num_pos=num_pos)

model = NeRF(nerf_model)
model.compile(
    optimizer=keras.optimizers.Adam(), loss_fn=keras.losses.MeanSquaredError()
)

# Create a directory to save the images during training.
if not os.path.exists("images"):
    os.makedirs("images")

model.fit(
    train_ds,
    validation_data=val_ds,
    batch_size=BATCH_SIZE,
    epochs=EPOCHS,
    callbacks=[TrainMonitor()],
    steps_per_epoch=split_index // BATCH_SIZE,
)


def create_gif(path_to_images, name_gif):
    filenames = glob.glob(path_to_images)
    filenames = sorted(filenames)
    images = []
    for filename in tqdm(filenames):
        images.append(imageio.imread(filename))
    kargs = {"duration": 0.25}
    imageio.mimsave(name_gif, images, "GIF", **kargs)


create_gif("images/*.png", "training.gif")

Epoch 1/20
16/16 [==============================] - 15s 753ms/step - loss: 0.1134 - psnr: 9.7278 - val_loss: 0.0683 - val_psnr: 12.0722

Epoch 2/20
16/16 [==============================] - 13s 752ms/step - loss: 0.0648 - psnr: 12.4200 - val_loss: 0.0664 - val_psnr: 12.1765

Epoch 3/20
16/16 [==============================] - 13s 746ms/step - loss: 0.0607 - psnr: 12.5281 - val_loss: 0.0673 - val_psnr: 12.0121

Epoch 4/20
16/16 [] - 13s 758ms/step - loss: 0.0595 - psnr: 12.7050 - val_loss: 0.0646 - val_psnr: 12.2768

Epoch 5/20
16/16 [] - 13s 755ms/step - loss: 0.0583 - psnr: 12.7522 - val_loss: 0.0613 - val_psnr: 12.5351

Epoch 6/20
16/16 [==============================] - 13s 749ms/step - loss: 0.0545 - psnr: 13.0654 - val_loss: 0.0553 - val_psnr: 12.9512

Epoch 7/20
16/16 [==============================] - 13s 744ms/step - loss: 0.0480 - psnr: 13.6313 - val_loss: 0.0444 - val_psnr: 13.7838

Epoch 8/20
16/16 [==============================] - 13s 763ms/step - loss: 0.0359 - psnr: 14.8570 - val_loss: 0.0342 - val_psnr: 14.8823

Epoch 9/20
16/16 [==============================] - 13s 758ms/step - loss: 0.0299 - psnr: 15.5374 - val_loss: 0.0287 - val_psnr: 15.6171

Epoch 10/20
16/16 [==============================] - 13s 779ms/step - loss: 0.0273 - psnr: 15.9051 - val_loss: 0.0266 - val_psnr: 15.9319

Epoch 11/20
16/16 [==============================] - 13s 736ms/step - loss: 0.0255 - psnr: 16.1422 - val_loss: 0.0250 - val_psnr: 16.1568

Epoch 12/20
16/16 [==============================] - 13s 746ms/step - loss: 0.0236 - psnr: 16.5074 - val_loss: 0.0233 - val_psnr: 16.4793

Epoch 13/20
16/16 [==============================] - 13s 755ms/step - loss: 0.0217 - psnr: 16.8391 - val_loss: 0.0210 - val_psnr: 16.8950

Epoch 14/20
16/16 [==============================] - 13s 741ms/step - loss: 0.0197 - psnr: 17.2245 - val_loss: 0.0187 - val_psnr: 17.3766

Epoch 15/20
16/16 [==============================] - 13s 739ms/step - loss: 0.0179 - psnr: 17.6246 - val_loss: 0.0179 - val_psnr: 17.5445

Epoch 16/20
16/16 [==============================] - 13s 735ms/step - loss: 0.0175 - psnr: 17.6998 - val_loss: 0.0180 - val_psnr: 17.5154

Epoch 17/20
16/16 [==============================] - 13s 741ms/step - loss: 0.0167 - psnr: 17.9393 - val_loss: 0.0156 - val_psnr: 18.1784

Epoch 18/20
16/16 [==============================] - 13s 750ms/step - loss: 0.0150 - psnr: 18.3875 - val_loss: 0.0151 - val_psnr: 18.2811

Epoch 19/20
16/16 [==============================] - 13s 755ms/step - loss: 0.0141 - psnr: 18.6476 - val_loss: 0.0139 - val_psnr: 18.6216

Epoch 20/20
16/16 [==============================] - 14s 777ms/step - loss: 0.0139 - psnr: 18.7131 - val_loss: 0.0137 - val_psnr: 18.7259

100%|██████████| 20/20 [00:00<00:00, 57.59it/s]

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六、训练步骤可视化

在这里，我们看到了训练步骤。 随着损失的减少，渲染图像和深度图越来越好。 在您的本地系统中，您将看到生成的 training.gif 文件。

---

七、推理

在本节中，我们要求模型构建场景的新颖视图。 在训练步骤中，该模型获得了 106 个场景视图。 训练图像的集合不能包含场景的每个角度。 经过训练的模型可以用一组稀疏的训练图像来表示整个 3-D 场景。

在这里，我们为模型提供不同的姿势，并要求它为我们提供与该相机视图对应的二维图像。 如果我们推断所有 360 度视图的模型，它应该提供从四面八方的整个场景的概览。

# Get the trained NeRF model and infer.
nerf_model = model.nerf_model
test_recons_images, depth_maps = render_rgb_depth(
    model=nerf_model,
    rays_flat=test_rays_flat,
    t_vals=test_t_vals,
    rand=True,
    train=False,
)

# Create subplots.
fig, axes = plt.subplots(nrows=5, ncols=3, figsize=(10, 20))

for ax, ori_img, recons_img, depth_map in zip(
    axes, test_imgs, test_recons_images, depth_maps
):
    ax[0].imshow(keras.preprocessing.image.array_to_img(ori_img))
    ax[0].set_title("Original")

    ax[1].imshow(keras.preprocessing.image.array_to_img(recons_img))
    ax[1].set_title("Reconstructed")

    ax[2].imshow(
        keras.preprocessing.image.array_to_img(depth_map[..., None]), cmap="inferno"
    )
    ax[2].set_title("Depth Map")

---

八、渲染3D场景

在这里，我们将合成新颖的 3D 视图并将它们拼接在一起以渲染包含 360 度视图的视频。

def get_translation_t(t):
    """Get the translation matrix for movement in t."""
    matrix = [
        [1, 0, 0, 0],
        [0, 1, 0, 0],
        [0, 0, 1, t],
        [0, 0, 0, 1],
    ]
    return tf.convert_to_tensor(matrix, dtype=tf.float32)


def get_rotation_phi(phi):
    """Get the rotation matrix for movement in phi."""
    matrix = [
        [1, 0, 0, 0],
        [0, tf.cos(phi), -tf.sin(phi), 0],
        [0, tf.sin(phi), tf.cos(phi), 0],
        [0, 0, 0, 1],
    ]
    return tf.convert_to_tensor(matrix, dtype=tf.float32)


def get_rotation_theta(theta):
    """Get the rotation matrix for movement in theta."""
    matrix = [
        [tf.cos(theta), 0, -tf.sin(theta), 0],
        [0, 1, 0, 0],
        [tf.sin(theta), 0, tf.cos(theta), 0],
        [0, 0, 0, 1],
    ]
    return tf.convert_to_tensor(matrix, dtype=tf.float32)


def pose_spherical(theta, phi, t):
    """
    Get the camera to world matrix for the corresponding theta, phi
    and t.
    """
    c2w = get_translation_t(t)
    c2w = get_rotation_phi(phi / 180.0 * np.pi) @ c2w
    c2w = get_rotation_theta(theta / 180.0 * np.pi) @ c2w
    c2w = np.array([[-1, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 1]]) @ c2w
    return c2w


rgb_frames = []
batch_flat = []
batch_t = []

# Iterate over different theta value and generate scenes.
for index, theta in tqdm(enumerate(np.linspace(0.0, 360.0, 120, endpoint=False))):
    # Get the camera to world matrix.
    c2w = pose_spherical(theta, -30.0, 4.0)

    #
    ray_oris, ray_dirs = get_rays(H, W, focal, c2w)
    rays_flat, t_vals = render_flat_rays(
        ray_oris, ray_dirs, near=2.0, far=6.0, num_samples=NUM_SAMPLES, rand=False
    )

    if index % BATCH_SIZE == 0 and index > 0:
        batched_flat = tf.stack(batch_flat, axis=0)
        batch_flat = [rays_flat]

        batched_t = tf.stack(batch_t, axis=0)
        batch_t = [t_vals]

        rgb, _ = render_rgb_depth(
            nerf_model, batched_flat, batched_t, rand=False, train=False
        )

        temp_rgb = [np.clip(255 * img, 0.0, 255.0).astype(np.uint8) for img in rgb]

        rgb_frames = rgb_frames + temp_rgb
    else:
        batch_flat.append(rays_flat)
        batch_t.append(t_vals)

rgb_video = "rgb_video.mp4"
imageio.mimwrite(rgb_video, rgb_frames, fps=30, quality=7, macro_block_size=None)

120it [00:12, 9.24it/s]

九、视频可视化

在这里，我们可以看到渲染的场景 360 度视图。 该模型仅在 20 个 epoch 内就通过稀疏图像集成功地学习了整个体积空间。 您可以查看本地保存的渲染视频，名为 rgb_video.mp4。

总结

我们制作了 NeRF 的最小实现，以直观地了解其核心思想和方法。 这种方法已被用于计算机图形空间的各种其他工作中。

Epochs	GIF of the training step
100
200

---

完整的代码地址

• Github
• Colab

---

前进的道路

如果有人有兴趣深入了解 NeRF，我们在 PyImageSearch 上构建了一个由 3 部分组成的博客系列。

• Prerequisites of NeRF
• Concepts of NeRF
• Implementing NeRF

---

参考

• NeRF repository：NeRF 的官方地址。
• NeRF paper：关于 NeRF 的论文。
• Manim Repository：我们使用 manim 来构建所有动画。
• Mathworks：相机校准文章相关。
• Mathew’s video：关于 NeRF 的精彩视频。

以上模型可以在Hugging Face Spaces中进行尝试。

---

最后：
以上翻译自：
https://keras.io/examples/vision/nerf/