在 Google Colab 中執行# Copyright (c) Meta Platforms, Inc. and affiliates. All rights reserved.
本教學課程會說明如何使用可微隱式函數渲染，以根據場景的一組視圖擬合神經體場。
更具體來說，本教學課程將說明如何
請注意，提供的隱式模型是 NeRF 的簡化版本
Ben Mildenhall, Pratul P. Srinivasan, Matthew Tancik, Jonathan T. Barron, Ravi Ramamoorthi, Ren Ng: NeRF: Representing Scenes as Neural Radiance Fields for View Synthesis, ECCV 2020。
簡化包括
確保已安裝 torch 和 torchvision。如果未安裝 pytorch3d，請使用以下儲存格安裝
import os
import sys
import torch
need_pytorch3d=False
try:
import pytorch3d
except ModuleNotFoundError:
need_pytorch3d=True
if need_pytorch3d:
if torch.__version__.startswith("2.2.") and sys.platform.startswith("linux"):
# We try to install PyTorch3D via a released wheel.
pyt_version_str=torch.__version__.split("+")[0].replace(".", "")
version_str="".join([
f"py3{sys.version_info.minor}_cu",
torch.version.cuda.replace(".",""),
f"_pyt{pyt_version_str}"
])
!pip install fvcore iopath
!pip install --no-index --no-cache-dir pytorch3d -f https://dl.fbaipublicfiles.com/pytorch3d/packaging/wheels/{version_str}/download.html
else:
# We try to install PyTorch3D from source.
!pip install 'git+https://github.com/facebookresearch/pytorch3d.git@stable'
# %matplotlib inline
# %matplotlib notebook
import os
import sys
import time
import json
import glob
import torch
import math
import matplotlib.pyplot as plt
import numpy as np
from PIL import Image
from IPython import display
from tqdm.notebook import tqdm
# Data structures and functions for rendering
from pytorch3d.structures import Volumes
from pytorch3d.transforms import so3_exp_map
from pytorch3d.renderer import (
FoVPerspectiveCameras,
NDCMultinomialRaysampler,
MonteCarloRaysampler,
EmissionAbsorptionRaymarcher,
ImplicitRenderer,
RayBundle,
ray_bundle_to_ray_points,
)
# obtain the utilized device
if torch.cuda.is_available():
device = torch.device("cuda:0")
torch.cuda.set_device(device)
else:
print(
'Please note that NeRF is a resource-demanding method.'
+ ' Running this notebook on CPU will be extremely slow.'
+ ' We recommend running the example on a GPU'
+ ' with at least 10 GB of memory.'
)
device = torch.device("cpu")
!wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/plot_image_grid.py
!wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/generate_cow_renders.py
from plot_image_grid import image_grid
from generate_cow_renders import generate_cow_renders
或是在本機執行時，取消下方的註解並執行以下儲存格
# from utils.generate_cow_renders import generate_cow_renders
# from utils import image_grid
以下儲存格會產生我們的訓練資料。它會從教學課程 fit_textured_mesh.ipynb 的 cow mesh 渲染多個視點並傳回
注意: 為了本教學課程的目的，目標是說明隱式渲染的詳細資訊，我們不會說明實作在 generate_cow_renders 函數中的網格渲染如何運作。請參閱 fit_textured_mesh.ipynb，以瞭解網格渲染的詳細說明。
target_cameras, target_images, target_silhouettes = generate_cow_renders(num_views=40, azimuth_range=180)
print(f'Generated {len(target_images)} images/silhouettes/cameras.')
以下會初始化一個隱式渲染器，它會從目標影像中的每個畫素發出一條光線，然後沿著光線對一組間隔一致的點進行採樣。在每個光線點，都會透過查詢場景神經模型中的對應位置來取得對應的密度和顏色值 (模型會在之後的儲存格中描述並實例化)。
渲染器由 光線行進器 和 光線採樣器 組成。
MonteCarloRaysampler 用於從影像平面上隨機像素子集中產生光線。在**訓練**期間進行像素的隨機子採樣，以減少隱式模型的記憶體消耗。NDCMultinomialRaysampler 遵循標準的 PyTorch3D 座標網格慣例（+X 從右到左；+Y 從下到上；+Z 遠離使用者）。與場景的隱式模型結合使用時，NDCMultinomialRaysampler 會消耗大量的記憶體，因此僅用於在**測試**時視覺化訓練結果。EmissionAbsorptionRaymarcher，它實作標準的發射吸收光線行進演算法。# render_size describes the size of both sides of the
# rendered images in pixels. Since an advantage of
# Neural Radiance Fields are high quality renders
# with a significant amount of details, we render
# the implicit function at double the size of
# target images.
render_size = target_images.shape[1] * 2
# Our rendered scene is centered around (0,0,0)
# and is enclosed inside a bounding box
# whose side is roughly equal to 3.0 (world units).
volume_extent_world = 3.0
# 1) Instantiate the raysamplers.
# Here, NDCMultinomialRaysampler generates a rectangular image
# grid of rays whose coordinates follow the PyTorch3D
# coordinate conventions.
raysampler_grid = NDCMultinomialRaysampler(
image_height=render_size,
image_width=render_size,
n_pts_per_ray=128,
min_depth=0.1,
max_depth=volume_extent_world,
)
# MonteCarloRaysampler generates a random subset
# of `n_rays_per_image` rays emitted from the image plane.
raysampler_mc = MonteCarloRaysampler(
min_x = -1.0,
max_x = 1.0,
min_y = -1.0,
max_y = 1.0,
n_rays_per_image=750,
n_pts_per_ray=128,
min_depth=0.1,
max_depth=volume_extent_world,
)
# 2) Instantiate the raymarcher.
# Here, we use the standard EmissionAbsorptionRaymarcher
# which marches along each ray in order to render
# the ray into a single 3D color vector
# and an opacity scalar.
raymarcher = EmissionAbsorptionRaymarcher()
# Finally, instantiate the implicit renders
# for both raysamplers.
renderer_grid = ImplicitRenderer(
raysampler=raysampler_grid, raymarcher=raymarcher,
)
renderer_mc = ImplicitRenderer(
raysampler=raysampler_mc, raymarcher=raymarcher,
)
在此儲存格中，我們定義 NeuralRadianceField 模組，它會在場景的 3D 域中指定連續的顏色和不透明度場。
NeuralRadianceField (NeRF) 的 forward 函式接收一組參數化渲染光線束的張量作為輸入。光線束稍後會轉換為場景世界座標中的 3D 光線點。然後，各個 3D 點會使用 HarmonicEmbedding 層 (定義於下一個儲存格) 對應到諧波表現。之後，諧波嵌入會進入 NeRF 模型的顏色和不透明度分支，以便標記每個光線點為 3D 向量和 [0-1] 中的 1D 標量，它們分別定義點的 RGB 顏色和不透明度。
由於 NeRF 具有大量的記憶體使用量，所以我們也實作了 NeuralRadianceField.forward_batched 方法。該方法會將輸入光線拆分為批次，並在迴圈中為每個批次個別執行 forward 函式。這讓我們可以在不耗盡 GPU 記憶體的情況下渲染大量的な光線。標準而言，forward_batched 會用於渲染從影像中所有像素發射的光線，以產生場景的全尺寸渲染。
class HarmonicEmbedding(torch.nn.Module):
def __init__(self, n_harmonic_functions=60, omega0=0.1):
"""
Given an input tensor `x` of shape [minibatch, ... , dim],
the harmonic embedding layer converts each feature
in `x` into a series of harmonic features `embedding`
as follows:
embedding[..., i*dim:(i+1)*dim] = [
sin(x[..., i]),
sin(2*x[..., i]),
sin(4*x[..., i]),
...
sin(2**(self.n_harmonic_functions-1) * x[..., i]),
cos(x[..., i]),
cos(2*x[..., i]),
cos(4*x[..., i]),
...
cos(2**(self.n_harmonic_functions-1) * x[..., i])
]
Note that `x` is also premultiplied by `omega0` before
evaluating the harmonic functions.
"""
super().__init__()
self.register_buffer(
'frequencies',
omega0 * (2.0 ** torch.arange(n_harmonic_functions)),
)
def forward(self, x):
"""
Args:
x: tensor of shape [..., dim]
Returns:
embedding: a harmonic embedding of `x`
of shape [..., n_harmonic_functions * dim * 2]
"""
embed = (x[..., None] * self.frequencies).view(*x.shape[:-1], -1)
return torch.cat((embed.sin(), embed.cos()), dim=-1)
class NeuralRadianceField(torch.nn.Module):
def __init__(self, n_harmonic_functions=60, n_hidden_neurons=256):
super().__init__()
"""
Args:
n_harmonic_functions: The number of harmonic functions
used to form the harmonic embedding of each point.
n_hidden_neurons: The number of hidden units in the
fully connected layers of the MLPs of the model.
"""
# The harmonic embedding layer converts input 3D coordinates
# to a representation that is more suitable for
# processing with a deep neural network.
self.harmonic_embedding = HarmonicEmbedding(n_harmonic_functions)
# The dimension of the harmonic embedding.
embedding_dim = n_harmonic_functions * 2 * 3
# self.mlp is a simple 2-layer multi-layer perceptron
# which converts the input per-point harmonic embeddings
# to a latent representation.
# Not that we use Softplus activations instead of ReLU.
self.mlp = torch.nn.Sequential(
torch.nn.Linear(embedding_dim, n_hidden_neurons),
torch.nn.Softplus(beta=10.0),
torch.nn.Linear(n_hidden_neurons, n_hidden_neurons),
torch.nn.Softplus(beta=10.0),
)
# Given features predicted by self.mlp, self.color_layer
# is responsible for predicting a 3-D per-point vector
# that represents the RGB color of the point.
self.color_layer = torch.nn.Sequential(
torch.nn.Linear(n_hidden_neurons + embedding_dim, n_hidden_neurons),
torch.nn.Softplus(beta=10.0),
torch.nn.Linear(n_hidden_neurons, 3),
torch.nn.Sigmoid(),
# To ensure that the colors correctly range between [0-1],
# the layer is terminated with a sigmoid layer.
)
# The density layer converts the features of self.mlp
# to a 1D density value representing the raw opacity
# of each point.
self.density_layer = torch.nn.Sequential(
torch.nn.Linear(n_hidden_neurons, 1),
torch.nn.Softplus(beta=10.0),
# Sofplus activation ensures that the raw opacity
# is a non-negative number.
)
# We set the bias of the density layer to -1.5
# in order to initialize the opacities of the
# ray points to values close to 0.
# This is a crucial detail for ensuring convergence
# of the model.
self.density_layer[0].bias.data[0] = -1.5
def _get_densities(self, features):
"""
This function takes `features` predicted by `self.mlp`
and converts them to `raw_densities` with `self.density_layer`.
`raw_densities` are later mapped to [0-1] range with
1 - inverse exponential of `raw_densities`.
"""
raw_densities = self.density_layer(features)
return 1 - (-raw_densities).exp()
def _get_colors(self, features, rays_directions):
"""
This function takes per-point `features` predicted by `self.mlp`
and evaluates the color model in order to attach to each
point a 3D vector of its RGB color.
In order to represent viewpoint dependent effects,
before evaluating `self.color_layer`, `NeuralRadianceField`
concatenates to the `features` a harmonic embedding
of `ray_directions`, which are per-point directions
of point rays expressed as 3D l2-normalized vectors
in world coordinates.
"""
spatial_size = features.shape[:-1]
# Normalize the ray_directions to unit l2 norm.
rays_directions_normed = torch.nn.functional.normalize(
rays_directions, dim=-1
)
# Obtain the harmonic embedding of the normalized ray directions.
rays_embedding = self.harmonic_embedding(
rays_directions_normed
)
# Expand the ray directions tensor so that its spatial size
# is equal to the size of features.
rays_embedding_expand = rays_embedding[..., None, :].expand(
*spatial_size, rays_embedding.shape[-1]
)
# Concatenate ray direction embeddings with
# features and evaluate the color model.
color_layer_input = torch.cat(
(features, rays_embedding_expand),
dim=-1
)
return self.color_layer(color_layer_input)
def forward(
self,
ray_bundle: RayBundle,
**kwargs,
):
"""
The forward function accepts the parametrizations of
3D points sampled along projection rays. The forward
pass is responsible for attaching a 3D vector
and a 1D scalar representing the point's
RGB color and opacity respectively.
Args:
ray_bundle: A RayBundle object containing the following variables:
origins: A tensor of shape `(minibatch, ..., 3)` denoting the
origins of the sampling rays in world coords.
directions: A tensor of shape `(minibatch, ..., 3)`
containing the direction vectors of sampling rays in world coords.
lengths: A tensor of shape `(minibatch, ..., num_points_per_ray)`
containing the lengths at which the rays are sampled.
Returns:
rays_densities: A tensor of shape `(minibatch, ..., num_points_per_ray, 1)`
denoting the opacity of each ray point.
rays_colors: A tensor of shape `(minibatch, ..., num_points_per_ray, 3)`
denoting the color of each ray point.
"""
# We first convert the ray parametrizations to world
# coordinates with `ray_bundle_to_ray_points`.
rays_points_world = ray_bundle_to_ray_points(ray_bundle)
# rays_points_world.shape = [minibatch x ... x 3]
# For each 3D world coordinate, we obtain its harmonic embedding.
embeds = self.harmonic_embedding(
rays_points_world
)
# embeds.shape = [minibatch x ... x self.n_harmonic_functions*6]
# self.mlp maps each harmonic embedding to a latent feature space.
features = self.mlp(embeds)
# features.shape = [minibatch x ... x n_hidden_neurons]
# Finally, given the per-point features,
# execute the density and color branches.
rays_densities = self._get_densities(features)
# rays_densities.shape = [minibatch x ... x 1]
rays_colors = self._get_colors(features, ray_bundle.directions)
# rays_colors.shape = [minibatch x ... x 3]
return rays_densities, rays_colors
def batched_forward(
self,
ray_bundle: RayBundle,
n_batches: int = 16,
**kwargs,
):
"""
This function is used to allow for memory efficient processing
of input rays. The input rays are first split to `n_batches`
chunks and passed through the `self.forward` function one at a time
in a for loop. Combined with disabling PyTorch gradient caching
(`torch.no_grad()`), this allows for rendering large batches
of rays that do not all fit into GPU memory in a single forward pass.
In our case, batched_forward is used to export a fully-sized render
of the radiance field for visualization purposes.
Args:
ray_bundle: A RayBundle object containing the following variables:
origins: A tensor of shape `(minibatch, ..., 3)` denoting the
origins of the sampling rays in world coords.
directions: A tensor of shape `(minibatch, ..., 3)`
containing the direction vectors of sampling rays in world coords.
lengths: A tensor of shape `(minibatch, ..., num_points_per_ray)`
containing the lengths at which the rays are sampled.
n_batches: Specifies the number of batches the input rays are split into.
The larger the number of batches, the smaller the memory footprint
and the lower the processing speed.
Returns:
rays_densities: A tensor of shape `(minibatch, ..., num_points_per_ray, 1)`
denoting the opacity of each ray point.
rays_colors: A tensor of shape `(minibatch, ..., num_points_per_ray, 3)`
denoting the color of each ray point.
"""
# Parse out shapes needed for tensor reshaping in this function.
n_pts_per_ray = ray_bundle.lengths.shape[-1]
spatial_size = [*ray_bundle.origins.shape[:-1], n_pts_per_ray]
# Split the rays to `n_batches` batches.
tot_samples = ray_bundle.origins.shape[:-1].numel()
batches = torch.chunk(torch.arange(tot_samples), n_batches)
# For each batch, execute the standard forward pass.
batch_outputs = [
self.forward(
RayBundle(
origins=ray_bundle.origins.view(-1, 3)[batch_idx],
directions=ray_bundle.directions.view(-1, 3)[batch_idx],
lengths=ray_bundle.lengths.view(-1, n_pts_per_ray)[batch_idx],
xys=None,
)
) for batch_idx in batches
]
# Concatenate the per-batch rays_densities and rays_colors
# and reshape according to the sizes of the inputs.
rays_densities, rays_colors = [
torch.cat(
[batch_output[output_i] for batch_output in batch_outputs], dim=0
).view(*spatial_size, -1) for output_i in (0, 1)
]
return rays_densities, rays_colors
在此函式中，我們定義輔助神經輻射場最佳化的函式。
def huber(x, y, scaling=0.1):
"""
A helper function for evaluating the smooth L1 (huber) loss
between the rendered silhouettes and colors.
"""
diff_sq = (x - y) ** 2
loss = ((1 + diff_sq / (scaling**2)).clamp(1e-4).sqrt() - 1) * float(scaling)
return loss
def sample_images_at_mc_locs(target_images, sampled_rays_xy):
"""
Given a set of Monte Carlo pixel locations `sampled_rays_xy`,
this method samples the tensor `target_images` at the
respective 2D locations.
This function is used in order to extract the colors from
ground truth images that correspond to the colors
rendered using `MonteCarloRaysampler`.
"""
ba = target_images.shape[0]
dim = target_images.shape[-1]
spatial_size = sampled_rays_xy.shape[1:-1]
# In order to sample target_images, we utilize
# the grid_sample function which implements a
# bilinear image sampler.
# Note that we have to invert the sign of the
# sampled ray positions to convert the NDC xy locations
# of the MonteCarloRaysampler to the coordinate
# convention of grid_sample.
images_sampled = torch.nn.functional.grid_sample(
target_images.permute(0, 3, 1, 2),
-sampled_rays_xy.view(ba, -1, 1, 2), # note the sign inversion
align_corners=True
)
return images_sampled.permute(0, 2, 3, 1).view(
ba, *spatial_size, dim
)
def show_full_render(
neural_radiance_field, camera,
target_image, target_silhouette,
loss_history_color, loss_history_sil,
):
"""
This is a helper function for visualizing the
intermediate results of the learning.
Since the `NeuralRadianceField` suffers from
a large memory footprint, which does not let us
render the full image grid in a single forward pass,
we utilize the `NeuralRadianceField.batched_forward`
function in combination with disabling the gradient caching.
This chunks the set of emitted rays to batches and
evaluates the implicit function on one batch at a time
to prevent GPU memory overflow.
"""
# Prevent gradient caching.
with torch.no_grad():
# Render using the grid renderer and the
# batched_forward function of neural_radiance_field.
rendered_image_silhouette, _ = renderer_grid(
cameras=camera,
volumetric_function=neural_radiance_field.batched_forward
)
# Split the rendering result to a silhouette render
# and the image render.
rendered_image, rendered_silhouette = (
rendered_image_silhouette[0].split([3, 1], dim=-1)
)
# Generate plots.
fig, ax = plt.subplots(2, 3, figsize=(15, 10))
ax = ax.ravel()
clamp_and_detach = lambda x: x.clamp(0.0, 1.0).cpu().detach().numpy()
ax[0].plot(list(range(len(loss_history_color))), loss_history_color, linewidth=1)
ax[1].imshow(clamp_and_detach(rendered_image))
ax[2].imshow(clamp_and_detach(rendered_silhouette[..., 0]))
ax[3].plot(list(range(len(loss_history_sil))), loss_history_sil, linewidth=1)
ax[4].imshow(clamp_and_detach(target_image))
ax[5].imshow(clamp_and_detach(target_silhouette))
for ax_, title_ in zip(
ax,
(
"loss color", "rendered image", "rendered silhouette",
"loss silhouette", "target image", "target silhouette",
)
):
if not title_.startswith('loss'):
ax_.grid("off")
ax_.axis("off")
ax_.set_title(title_)
fig.canvas.draw(); fig.show()
display.clear_output(wait=True)
display.display(fig)
return fig
我們在此使用可微分渲染執行輻射場擬合。
為了擬合輻射場，我們會從 target_cameras 的視點進行渲染，並將產生的渲染與觀測到的 target_images 和 target_silhouettes 進行比較。
比較是透過評估對應的 target_images/rendered_images 和 target_silhouettes/rendered_silhouettes 之間的平均 Huber（平滑-l1）誤差來完成的。
由於我們使用 MonteCarloRaysampler，因此訓練渲染器 renderer_mc 的輸出是從影像平面隨機取樣的像素顏色，而不是形成有效影像的像素格線。因此，為了將渲染顏色與真實值進行比較，我們利用隨機 MonteCarlo 像素位置在對應於渲染位置的 xy 位置取樣真實值影像/輪廓 target_silhouettes/rendered_silhouettes。這會使用之前儲存格中說明的輔助函式 sample_images_at_mc_locs 來完成。
# First move all relevant variables to the correct device.
renderer_grid = renderer_grid.to(device)
renderer_mc = renderer_mc.to(device)
target_cameras = target_cameras.to(device)
target_images = target_images.to(device)
target_silhouettes = target_silhouettes.to(device)
# Set the seed for reproducibility
torch.manual_seed(1)
# Instantiate the radiance field model.
neural_radiance_field = NeuralRadianceField().to(device)
# Instantiate the Adam optimizer. We set its master learning rate to 1e-3.
lr = 1e-3
optimizer = torch.optim.Adam(neural_radiance_field.parameters(), lr=lr)
# We sample 6 random cameras in a minibatch. Each camera
# emits raysampler_mc.n_pts_per_image rays.
batch_size = 6
# 3000 iterations take ~20 min on a Tesla M40 and lead to
# reasonably sharp results. However, for the best possible
# results, we recommend setting n_iter=20000.
n_iter = 3000
# Init the loss history buffers.
loss_history_color, loss_history_sil = [], []
# The main optimization loop.
for iteration in range(n_iter):
# In case we reached the last 75% of iterations,
# decrease the learning rate of the optimizer 10-fold.
if iteration == round(n_iter * 0.75):
print('Decreasing LR 10-fold ...')
optimizer = torch.optim.Adam(
neural_radiance_field.parameters(), lr=lr * 0.1
)
# Zero the optimizer gradient.
optimizer.zero_grad()
# Sample random batch indices.
batch_idx = torch.randperm(len(target_cameras))[:batch_size]
# Sample the minibatch of cameras.
batch_cameras = FoVPerspectiveCameras(
R = target_cameras.R[batch_idx],
T = target_cameras.T[batch_idx],
znear = target_cameras.znear[batch_idx],
zfar = target_cameras.zfar[batch_idx],
aspect_ratio = target_cameras.aspect_ratio[batch_idx],
fov = target_cameras.fov[batch_idx],
device = device,
)
# Evaluate the nerf model.
rendered_images_silhouettes, sampled_rays = renderer_mc(
cameras=batch_cameras,
volumetric_function=neural_radiance_field
)
rendered_images, rendered_silhouettes = (
rendered_images_silhouettes.split([3, 1], dim=-1)
)
# Compute the silhouette error as the mean huber
# loss between the predicted masks and the
# sampled target silhouettes.
silhouettes_at_rays = sample_images_at_mc_locs(
target_silhouettes[batch_idx, ..., None],
sampled_rays.xys
)
sil_err = huber(
rendered_silhouettes,
silhouettes_at_rays,
).abs().mean()
# Compute the color error as the mean huber
# loss between the rendered colors and the
# sampled target images.
colors_at_rays = sample_images_at_mc_locs(
target_images[batch_idx],
sampled_rays.xys
)
color_err = huber(
rendered_images,
colors_at_rays,
).abs().mean()
# The optimization loss is a simple
# sum of the color and silhouette errors.
loss = color_err + sil_err
# Log the loss history.
loss_history_color.append(float(color_err))
loss_history_sil.append(float(sil_err))
# Every 10 iterations, print the current values of the losses.
if iteration % 10 == 0:
print(
f'Iteration {iteration:05d}:'
+ f' loss color = {float(color_err):1.2e}'
+ f' loss silhouette = {float(sil_err):1.2e}'
)
# Take the optimization step.
loss.backward()
optimizer.step()
# Visualize the full renders every 100 iterations.
if iteration % 100 == 0:
show_idx = torch.randperm(len(target_cameras))[:1]
show_full_render(
neural_radiance_field,
FoVPerspectiveCameras(
R = target_cameras.R[show_idx],
T = target_cameras.T[show_idx],
znear = target_cameras.znear[show_idx],
zfar = target_cameras.zfar[show_idx],
aspect_ratio = target_cameras.aspect_ratio[show_idx],
fov = target_cameras.fov[show_idx],
device = device,
),
target_images[show_idx][0],
target_silhouettes[show_idx][0],
loss_history_color,
loss_history_sil,
)
最後，我們透過從圍繞體積 y 軸旋轉的多個視點渲染的方式來視覺化神經輻射場。
def generate_rotating_nerf(neural_radiance_field, n_frames = 50):
logRs = torch.zeros(n_frames, 3, device=device)
logRs[:, 1] = torch.linspace(-3.14, 3.14, n_frames, device=device)
Rs = so3_exp_map(logRs)
Ts = torch.zeros(n_frames, 3, device=device)
Ts[:, 2] = 2.7
frames = []
print('Rendering rotating NeRF ...')
for R, T in zip(tqdm(Rs), Ts):
camera = FoVPerspectiveCameras(
R=R[None],
T=T[None],
znear=target_cameras.znear[0],
zfar=target_cameras.zfar[0],
aspect_ratio=target_cameras.aspect_ratio[0],
fov=target_cameras.fov[0],
device=device,
)
# Note that we again render with `NDCMultinomialRaysampler`
# and the batched_forward function of neural_radiance_field.
frames.append(
renderer_grid(
cameras=camera,
volumetric_function=neural_radiance_field.batched_forward,
)[0][..., :3]
)
return torch.cat(frames)
with torch.no_grad():
rotating_nerf_frames = generate_rotating_nerf(neural_radiance_field, n_frames=3*5)
image_grid(rotating_nerf_frames.clamp(0., 1.).cpu().numpy(), rows=3, cols=5, rgb=True, fill=True)
plt.show()
在此教學課程中，我們展示了如何最佳化場景的隱式表示，以便場景從已知視點的渲染符合各視點的觀測影像。渲染使用 PyTorch3D 的隱式函式渲染器執行，該渲染器由 MonteCarloRaysampler 或 NDCMultinomialRaysampler 以及 EmissionAbsorptionRaymarcher 組成。