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###############################################################################
#
# Inspired from Pytorch3D NeRF Tutorial
# https://github.com/facebookresearch/pytorch3d/blob/master/docs/tutorials/fit_simple_neural_radiance_field.ipynb
#
###############################################################################
#
# Copyright (c) 2021 Solal Nathan
# Author: Solal "Otthorn" Nathan <otthorn@crans.org>
# SPDX-License-Identifier: BSD-3-Clause
#
###############################################################################
import glob
import json
import math
import os
import sys
import time
import matplotlib.pyplot as plt
import numpy as np
import torch
from PIL import Image
from pytorch3d.renderer import (EmissionAbsorptionRaymarcher,
FoVPerspectiveCameras, ImplicitRenderer,
MonteCarloRaysampler, NDCGridRaysampler,
RayBundle, ray_bundle_to_ray_points)
# Data structures and functions for rendering
from pytorch3d.structures import Volumes
from pytorch3d.transforms import so3_exponential_map
from tqdm import tqdm
# add path for demo utils functions
sys.path.append(os.path.abspath(""))
from utils.generate_cow_renders import generate_cow_renders
from utils.plot_image_grid import image_grid
# Intialize CUDA gpu
device = torch.device("cuda:0")
torch.cuda.set_device(device)
# Generate dataset
target_cameras, target_images, target_silhouettes = generate_cow_renders(
num_views=40, azimuth_range=180
)
print(f"Generated {len(target_images)} images/silhouettes/cameras.")
###############################################################################
# Intitialize the implicit rendered
###############################################################################
# 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, NDCGridRaysampler generates a rectangular image
# grid of rays whose coordinates follow the PyTorch3d
# coordinate conventions.
raysampler_grid = NDCGridRaysampler(
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,
)
###############################################################################
# Define the NeRF model
###############################################################################
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 * x[..., i]),
cos(x[..., i]),
cos(2*x[..., i]),
cos(4*x[..., i]),
...
cos(2**self.n_harmonic_functions * x[..., i])
]
Note that `x` is also premultiplied by `omega0` before
evaluting 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 opacitiy 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
visualisation 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 opacitiy 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
###############################################################################
# Helper functions
###############################################################################
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,
iteration
):
"""
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 allow to 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.savefig(f"results/fullrender_{iteration:05d}.png")
#fig.show()
#display.clear_output(wait=True)
#display.display(fig)
#return fig
###############################################################################
# Fit the radiance field
###############################################################################
# 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):
tqdm.write("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 silhoutte 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:
tqdm.write(
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,
iteration,
)
###############################################################################
# Visualizing the optimized neural radiance field
###############################################################################
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_exponential_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 `NDCGridSampler`
# 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(0.0, 1.0).cpu().numpy(),
rows=3,
cols=5,
rgb=True,
fill=True,
)
plt.show()
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