政安晨：【Keras机器学习示例演绎】（七）—— 利用 NeRF 进行 3D 体积渲染

import os

os.environ["KERAS_BACKEND"] = "tensorflow"

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

tf.random.set_seed(42)

import keras
from keras import layers

import os
import glob
import imageio.v2 as imageio
import numpy as np
from tqdm import tqdm
import matplotlib.pyplot as plt

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

下载并加载数据

npz 数据文件包含图像、相机姿势和焦距。如下图所示，图像是从多个摄像机角度拍摄的。

（下图：多角度拍摄）

要在这种情况下理解摄像机的姿势，我们必须首先让自己认为，摄像机是真实世界和二维图像之间的映射。

请看下面的等式：

其中 x 是二维图像点，X 是三维世界点，P 是摄像机矩阵。P 是一个 3 x 4 矩阵，在将现实世界中的物体映射到图像平面上起着至关重要的作用。

摄像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]相连接，从而产生姿态矩阵。

该矩阵的尺寸为 3 x 5，其中第一个 3 x 3 块为摄像机视角。轴线为[向下、向右、向后]或[-y、x、z]，其中摄像机朝向前方-z。

（下图：仿射变换）

COLMAP 框架为 [右、下、前] 或 [x、-y、-z]。点击此处了解更多有关 COLMAP 的信息。

# Download the data if it does not already exist.
url = (
    "http://cseweb.ucsd.edu/~viscomp/projects/LF/papers/ECCV20/nerf/tiny_nerf_data.npz"
)
data = keras.utils.get_file(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()

数据管道

在了解了摄像机矩阵的概念以及三维场景到二维图像的映射之后，我们来谈谈反向映射，即从二维图像到三维场景的映射。

我们需要讨论使用光线投射和追踪进行体积渲染的问题，这些都是常见的计算机图形技术。本节将帮助你快速掌握这些技术。

考虑一幅有 N 个像素的图像。我们用光线穿过每个像素，并对光线上的一些点进行采样。如下图所示，射线的参数方程通常为 r(t) = o + td，其中 t 为参数，o 为原点，d 为单位方向向量。

（下图：r(t) = o + td，其中 t 为 3）

在下图中，我们考虑了一条射线，并对射线上的一些随机点进行了采样。

这些采样点都有一个唯一的位置（x、y、z），射线有一个视角（theta、phi）。视角尤其有趣，因为我们可以用多种不同的方式将光线射穿一个像素，每种方式都有一个独特的视角。

另一个值得注意的地方是采样过程中添加的噪声。

我们在每个样本中都添加了均匀的噪声，这样样本就对应于一个连续的分布。在下图中，蓝色的点是均匀分布的样本，白色的点（t1、t2、t3）是随机放置在样本之间的。

（下图：从射线中采样点。）

下图展示了整个三维采样过程，可以看到射线从白色图像中射出。

这意味着每个像素都会有相应的光线，而每条光线都会在不同的点上采样。

（下图：从三维图像的所有像素射出光线）

**这些采样点是 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。

（下图：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)
)

NeRF 模型

该模型为多层感知器（MLP），以 ReLU 作为非线性。

某论文节选：

"我们通过限制网络仅预测体积密度 sigma 与位置 x 的函数关系，同时允许预测 RGB 颜色 c 与位置和观察方向的函数关系，从而使表示法与多视角一致。为此，MLP 首先使用 8 个全连接层（每层使用 ReLU 激活和 256 个通道）处理输入的 3D 坐标 x，并输出 sigma 和 256 维特征向量。然后，将该特征向量与摄像机光线的观察方向连接起来，并传递给另外一个全连接层（使用 ReLU 激活和 128 个通道），该层输出与视图相关的 RGB 颜色"。

在这里，我们采用了最小化的实现方式，使用了 64 个密集单元，而不是论文中提到的 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 `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)

训练

训练步骤是作为自定义 keras.Model 子类的一部分实现的，这样我们就可以使用 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.utils.array_to_img(test_recons_images[0]))
        ax[0].set_title(f"Predicted Image: {epoch:03d}")

        ax[1].imshow(keras.utils.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()],
)


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")

演绎展示：

Epoch 1/20
  1/16 ━[37m━━━━━━━━━━━━━━━━━━━  3:54 16s/step - loss: 0.0948 - psnr: 10.6234

WARNING: All log messages before absl::InitializeLog() is called are written to STDERR
I0000 00:00:1699908753.457905   65271 device_compiler.h:187] Compiled cluster using XLA!  This line is logged at most once for the lifetime of the process.

 1/1 ━━━━━━━━━━━━━━━━━━━━ 1s 924ms/step

 16/16 ━━━━━━━━━━━━━━━━━━━━ 29s 889ms/step - loss: 0.1091 - psnr: 9.8283 - val_loss: 0.0753 - val_psnr: 11.5686
Epoch 2/20
 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 477ms/step

 16/16 ━━━━━━━━━━━━━━━━━━━━ 16s 926ms/step - loss: 0.0633 - psnr: 12.4819 - val_loss: 0.0657 - val_psnr: 12.1781
Epoch 3/20
 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 474ms/step

 16/16 ━━━━━━━━━━━━━━━━━━━━ 16s 921ms/step - loss: 0.0589 - psnr: 12.6268 - val_loss: 0.0637 - val_psnr: 12.3413
Epoch 4/20
 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 470ms/step

 16/16 ━━━━━━━━━━━━━━━━━━━━ 15s 915ms/step - loss: 0.0573 - psnr: 12.8150 - val_loss: 0.0617 - val_psnr: 12.4789
Epoch 5/20
 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 477ms/step

 16/16 ━━━━━━━━━━━━━━━━━━━━ 15s 918ms/step - loss: 0.0552 - psnr: 12.9703 - val_loss: 0.0594 - val_psnr: 12.6457
Epoch 6/20
 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 476ms/step

 16/16 ━━━━━━━━━━━━━━━━━━━━ 15s 894ms/step - loss: 0.0538 - psnr: 13.0895 - val_loss: 0.0533 - val_psnr: 13.0049
Epoch 7/20
 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 473ms/step

 16/16 ━━━━━━━━━━━━━━━━━━━━ 16s 940ms/step - loss: 0.0436 - psnr: 13.9857 - val_loss: 0.0381 - val_psnr: 14.4764
Epoch 8/20
 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 475ms/step

 16/16 ━━━━━━━━━━━━━━━━━━━━ 15s 919ms/step - loss: 0.0325 - psnr: 15.1856 - val_loss: 0.0294 - val_psnr: 15.5187
Epoch 9/20
 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 478ms/step

 16/16 ━━━━━━━━━━━━━━━━━━━━ 16s 927ms/step - loss: 0.0276 - psnr: 15.8105 - val_loss: 0.0259 - val_psnr: 16.0297
Epoch 10/20
 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 474ms/step

 16/16 ━━━━━━━━━━━━━━━━━━━━ 16s 952ms/step - loss: 0.0251 - psnr: 16.1994 - val_loss: 0.0252 - val_psnr: 16.0842
Epoch 11/20
 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 474ms/step

16/16 ━━━━━━━━━━━━━━━━━━━━ 15s 909ms/step - loss: 0.0239 - psnr: 16.3749 - val_loss: 0.0228 - val_psnr: 16.5269
Epoch 12/20
 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 474ms/step

 16/16 ━━━━━━━━━━━━━━━━━━━━ 19s 1s/step - loss: 0.0215 - psnr: 16.8117 - val_loss: 0.0186 - val_psnr: 17.3930
Epoch 13/20
 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 474ms/step

 16/16 ━━━━━━━━━━━━━━━━━━━━ 16s 923ms/step - loss: 0.0188 - psnr: 17.3916 - val_loss: 0.0174 - val_psnr: 17.6570
Epoch 14/20
 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 476ms/step

 16/16 ━━━━━━━━━━━━━━━━━━━━ 16s 973ms/step - loss: 0.0175 - psnr: 17.6871 - val_loss: 0.0172 - val_psnr: 17.6644
Epoch 15/20
 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 468ms/step

 16/16 ━━━━━━━━━━━━━━━━━━━━ 15s 919ms/step - loss: 0.0172 - psnr: 17.7639 - val_loss: 0.0161 - val_psnr: 18.0313
Epoch 16/20
 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 477ms/step

 16/16 ━━━━━━━━━━━━━━━━━━━━ 16s 915ms/step - loss: 0.0150 - psnr: 18.3860 - val_loss: 0.0151 - val_psnr: 18.2832
Epoch 17/20
 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 473ms/step

 16/16 ━━━━━━━━━━━━━━━━━━━━ 16s 926ms/step - loss: 0.0154 - psnr: 18.2210 - val_loss: 0.0146 - val_psnr: 18.4284
Epoch 18/20
 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 468ms/step

 16/16 ━━━━━━━━━━━━━━━━━━━━ 16s 959ms/step - loss: 0.0145 - psnr: 18.4869 - val_loss: 0.0134 - val_psnr: 18.8039
Epoch 19/20
 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 473ms/step

 16/16 ━━━━━━━━━━━━━━━━━━━━ 16s 933ms/step - loss: 0.0136 - psnr: 18.8040 - val_loss: 0.0138 - val_psnr: 18.6680
Epoch 20/20
 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 472ms/step

 16/16 ━━━━━━━━━━━━━━━━━━━━ 15s 916ms/step - loss: 0.0131 - psnr: 18.9661 - val_loss: 0.0132 - val_psnr: 18.8687

100%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 20/20 [00:00<00:00, 59.40it/s]

可视化训练步骤

在这里，我们看到了训练步骤。随着损失的减少，渲染图像和深度图的效果越来越好。在本地系统中，你将看到生成的 training.gif 文件。

推理

在本节中，我们要求模型构建新的场景视图。在训练步骤中，我们给模型提供了 106 个场景视图。训练图像集合不可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三维场景。

在这里，我们向模型提供不同的姿势，并要求它给出与该摄像机视角相对应的二维图像。如果我们推断出所有 360 度视角的模型，那么它就能从四周提供整个场景的概览。

# 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.utils.array_to_img(ori_img))
    ax[0].set_title("Original")

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

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

演绎展示：

 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 475ms/step

渲染三维场景

在这里，我们将合成新颖的 3D 视图，并将所有视图拼接在一起，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)

演绎展示：

1it [00:01,  1.02s/it]

 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 475ms/step

6it [00:03,  1.95it/s]

 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 478ms/step

11it [00:05,  2.11it/s]

 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 474ms/step

16it [00:07,  2.17it/s]

 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 477ms/step

25it [00:10,  3.05it/s]

 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 477ms/step

27it [00:12,  2.14it/s]

 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 479ms/step

31it [00:14,  2.02it/s]

 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 472ms/step

36it [00:16,  2.11it/s]

 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 474ms/step

41it [00:18,  2.16it/s]

 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 472ms/step

46it [00:21,  2.19it/s]

 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 475ms/step

51it [00:23,  2.22it/s]

 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 473ms/step

56it [00:25,  2.24it/s]

 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 464ms/step

61it [00:27,  2.26it/s]

 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 474ms/step

66it [00:29,  2.26it/s]

 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 476ms/step

71it [00:32,  2.26it/s]

 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 473ms/step

76it [00:34,  2.26it/s]

 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 475ms/step

81it [00:36,  2.26it/s]

 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 474ms/step

86it [00:38,  2.26it/s]

 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 476ms/step

91it [00:40,  2.26it/s]

 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 465ms/step

96it [00:43,  2.27it/s]

 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 473ms/step

101it [00:45,  2.28it/s]

 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 473ms/step

106it [00:47,  2.28it/s]

 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 473ms/step

111it [00:49,  2.27it/s]

 1/1 ━━━━━━━━━━━━━━━━━━━━ 0s 474ms/step

120it [00:52,  2.31it/s]
[swscaler @ 0x67626c0] Warning: data is not aligned! This can lead to a speed loss

可视化视频

在这里，我们可以看到渲染后的 360 度场景视图。该模型仅用了 20 个历时就通过稀疏图像集成功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。

结论

我们制作了一个 NeRF 的最小实现，以提供对其核心思想和方法的直观认识。这种方法已被用于计算机图形领域的其他各种工作中。

我们鼓励读者将此代码作为示例，使用超参数并观察输出结果。下面我们还提供了经过更多历时训练的模型的输出结果。

（培训步骤）