text:
\section{Appendix}

In this appendix, we provide the implementation details, more qualitative results, and a discussion of broader impacts of our work

\subsection{Implementation Details}

\subsubsection{Model Architectures}

\begin{figure}[h]
	\centering

	\includegraphics[width=10.5cm]{figures/generator.pdf}

	\caption{The generator architecture used in ShadeGAN.}
	\label{fig:generator}

\end{figure}

\textbf{Generator and discriminator.}
For the generator and discriminator architectures, we mainly follow the design of pi-GAN~\cite{chan2020pi}.
Specifically, the generator is an MLP formed by stacking fully-connected and FiLM-SIREN layers~\cite{perez2018film,sitzmann2020implicit} with 256 units, as shown in Fig.~\ref{fig:generator}.
The generator takes a 3D coordinate ${\bm{x}}$ and a 256d latent code ${\bm{z}}$ as inputs.
It consists of two branches to predict the volume density $\sigma$ and the albedo ${\bm{a}}$ respectively,
where the albedo is also conditioned on the ray direction ${\bm{d}}$ and the lighting condition $\bm{\mu}$.
Similar to StyleGAN~\cite{karras2019style}, the latent code ${\bm{z}}$ is sent to a mapping network with four fully-connected and ReLU layers to produce the frequency and phase factors for the FiLM-SIREN layers of the generator.
As for the discriminator, we adopt the same convolutional neural network (CNN) architecture as in \cite{chan2020pi}, which uses CoordConv layers~\cite{liu2018intriguing} and residual connections~\cite{he2016deep}.

\begin{table}[h!]
	\centering
	\begin{minipage}{0.55\linewidth}
		\centering
		\caption{Architecture of the surface tracking network. }\label{tab:surfacenet}
		\vspace{-0.1cm}
		\resizebox{7.8cm}{2.2cm}{
			\begin{tabular}{lc}
				\Xhline{2\arrayrulewidth}
				Layer & Output size \\ \hline
				Linear(4608, 256) + concat($\bm{\xi}=(\text{pitch}, \text{yaw})$) & 1 \\
				Linear(258, 256) + ReLU & 1 \\
				DeConv(256, 256, 4, 1, 0) + ReLU & 4 \\
				Conv(256, 256, 3, 1, 1) + ReLU & 4 \\
				DeConv(256, 256, 4, 2, 1) + GN(32) + ReLU & 8 \\
				Conv(256, 256, 3, 1, 1) & 8 \\
				ResBlockUp(256, 128)  & 16 \\
				ResBlockUp(128, 64)  & 32 \\
				ResBlockUp(64, 32)  & 64 \\
				ResBlockUp(32, 16) + GN(4) + ReLU  & 128 \\
				Conv(16, 1, 5, 1, 2) + Sigmoid & 128 \\
				\Xhline{2\arrayrulewidth}
			\end{tabular}
		}
	\end{minipage}
	~
	\begin{minipage}{0.42\linewidth}
		\centering
		\caption{Network architecture for the ResBlockUp($c_{in}$, $c_{out}$) in Tab.\ref{tab:surfacenet}. The output of Residual path and Identity path are added as the final output. }\label{tab:resblockup}

		\resizebox{6.0cm}{1.4cm}{
			\begin{tabular}{lc}
				\Xhline{2\arrayrulewidth}
				Residual path \\ \hline
				GN($c_{in} / 8$) + ReLU + Upsample(2) \\
				Conv($c_{in}$, $c_{out}$, 3, 1, 1) + GN($c_{out} / 8$) + ReLU \\
				Conv($c_{out}$, $c_{out}$, 3, 1, 1) \\ \hline\hline
				Identity path \\ \hline
				Upsample(2) \\
				Conv($c_{in}$, $c_{out}$, 1, 1, 0) \\
				\Xhline{2\arrayrulewidth}
			\end{tabular}
		}
	\end{minipage}
\end{table}

\textbf{Surface tracking network.}
Our surface tracking network $S$ is a decoder-style CNN as shown in Tab.~\ref{tab:surfacenet} and Tab.~\ref{tab:resblockup}.
It takes the output of the mapping network and a camera pose $\bm{\xi}$ as inputs and outputs a $128 \times 128$ resolution depth map, where the camera pose $\bm{\xi}$ refers to pitch and yaw angles in this case.
The abbreviations for the network layers are described below:

Conv($c_{in}, c_{out}, k, s, p$): a convolution layer with $c_{in}$ input channels, $c_{out}$ output channels, kernel size $k$, stride $s$, and padding $p$.

Deconv($c_{in}, c_{out}, k, s, p$): a deconvolution layer with $c_{in}$ input channels, $c_{out}$ output channels, kernel size $k$, stride $s$, and padding $p$.

GN($n$): a group normalization layer~\cite{wu2018group} with $n$ groups.

BN and ReLU: the batch normalization layer~\cite{ioffe2015batch} and the rectified linear unit.

Upsample($s$): a nearest-neighbor upsampling layer with a scale of $s$.

ResBlockUp($c_{in}, c_{out}$) and ResBlock($c_{in}, c_{out}, stride$): residual blocks as defined in Tab.\ref{tab:resblockup} and Tab.\ref{tab:resblock}.

\textbf{Depth-predicting CNN.}
In our quantitative study on the BFM dataset, we train an additional CNN to predict the depth map of an input image, as described in Line 253-255 of the main paper.
Here we provide the architecture of the depth-predicting CNN in Tab.~\ref{tab:depthnet}, Tab.~\ref{tab:resblockup} and Tab.~\ref{tab:resblock}.
It is trained using Adam~\cite{kingma2014adam} for 30 epochs with a learning rate of 1e-4.

\begin{table}[h!]
	\centering
	\begin{minipage}{0.55\linewidth}
		\centering
		\caption{Architecture of the depth-predicting CNN. The input image is resized to $64 \times 64$ resolution. ResBlockUp is the same as Tab.~\ref{tab:resblockup} except that GNs are replaced by BNs. }\label{tab:depthnet}
		\vspace{-0.1cm}
		\resizebox{7.0cm}{1.9cm}{
			\begin{tabular}{lc}
				\Xhline{2\arrayrulewidth}
				Layer & Output size \\ \hline
				Conv(3, 64, 4, 2, 1) & 32 \\
				ResBlock(64, 128, 2)  & 16 \\
				ResBlock(128, 256, 2)  & 8 \\
				ResBlock(256, 512, 1)  & 8 \\
				ResBlock(512, 512, 1)  & 8 \\
				ResBlockUp(512, 256)  & 16 \\
				ResBlockUp(256, 128)  & 32 \\
				ResBlockUp(128, 64) + BN + ReLU & 64 \\
				Conv(64, 1, 5, 1, 2) + Tanh & 64 \\
				\Xhline{2\arrayrulewidth}
			\end{tabular}
		}
	\end{minipage}
	~
	\begin{minipage}{0.42\linewidth}
		\centering
		\caption{Network architecture for the ResBlock($c_{in}$, $c_{out}$, $stride$) in Tab.\ref{tab:depthnet}. The output of Residual path and Identity path are added as the final output. }\label{tab:resblock}

		\resizebox{5.8cm}{1.2cm}{
			\begin{tabular}{lc}
				\Xhline{2\arrayrulewidth}
				Residual path \\ \hline
				BN + ReLU + Conv($c_{in}$, $c_{out}$, 3, $stride$, 1) \\
				BN + ReLU + Conv($c_{out}$, $c_{out}$, 3, 1, 1) \\ \hline\hline
				Identity path \\ \hline
				Identity \quad\quad\quad\quad\quad\quad\quad if $c_{in} = c_{out}$ \\
				Conv($c_{in}$, $c_{out}$, 1, 1, 0) \quad if $c_{in} \neq c_{out}$ \\
				\Xhline{2\arrayrulewidth}
			\end{tabular}
		}
	\end{minipage}
\end{table}

\subsubsection{Training Details}

We adopt a progressive growing training strategy as in~\cite{chan2020pi}.
During training, the image resolution grows from 32 to 128, while the batchsize and learning rate decrease as listed in Tab.~\ref{tab:iterations}.
We use the Adam~\cite{kingma2014adam} optimizer with $\beta_1 = 0$, $\beta_2 = 0.9$.
Our models are trained on 8 TITAN X Pascal GPUs.
We use the same setting to train the pi-GAN~\cite{chan2020pi} baseline for fair comparison.

\begin{table}[h!]
	\centering
		\caption{Training schedule. `G\_lr' and `D\_lr' represents the learning rate for generator and discriminator respectively.}\label{tab:iterations}
		\vspace{-0.1cm}
		\resizebox{7.4cm}{1.7cm}{
	\begin{tabular}{cccccc}
		\Xhline{2\arrayrulewidth}
	Dataset                 & Iteration (k) & \hspace{-0.3cm} Batchsize & \hspace{-0.3cm} Image size & G\_lr & D\_lr \\ \hline
	\multirow{4}{*}{BFM}    & 0-20      & 96        & 32         & 2e-5  & 2e-4  \\
	& 20-40     & 48        & 64         & 2e-5  & 2e-4  \\
	& 40-50     & 48        & 64         & 1e-5  & 1e-4  \\
	& 50-80     & 16        & 128        & 2e-6  & 2e-5  \\ \hline
	\multirow{4}{*}{CelebA} & 0-30      & 104       & 32         & 2e-5  & 2e-4  \\
	& 30-70     & 64        & 64         & 2e-5  & 2e-4  \\
	& 70-100    & 64        & 64         & 1e-5  & 1e-4  \\
	& 100-150   & 16        & 128        & 2e-6  & 2e-5  \\ \hline
	Cats   & 0-20      & 128        & 64         & 6e-5  & 2e-4  \\\Xhline{2\arrayrulewidth}

	\end{tabular}
		}
\end{table}

For the camera pose $\bm{\xi}$, we follow pi-GAN~\cite{chan2020pi} and constrain the camera position to the surface of a unit sphere and keep its direction to the origin.
Thus, $\bm{\xi}$ could be determined by pitch and yaw angles, which are sampled from prior distributions.
For BFM and CelebA, $\text{pitch} \sim \mathcal{N}(\pi/2, 0.155)$ and $\text{yaw} \sim \mathcal{N}(\pi/2, 0.3)$, while for Cats, $\text{pitch} \sim \mathcal{U}(\pi/2-0.5, \pi/2+0.5)$ and $\text{yaw} \sim \mathcal{U}(\pi/2-0.4, \pi/2+0.4)$.
The lighting condition $\bm{\mu}$ consists of four factors $(k_a, k_d, l_x, l_y)$, where the lighting direction could be determined by ${\bm{l}} = (l_x, l_y, 1)^T / \sqrt{l_x^2 + l_y^2 + 1}$.
We use the multi-variate Gaussian distribution of $(2k_a-1, 2k_d-1, l_x, l_y)$ estimated using~\cite{wu2020unsupervised} as the prior distribution.
The mean and covariance matrix for different datasets are provided in Tab.~\ref{tab:lprior}.
For the results in Tab. 3 No.(5) of the main paper, we use a simple manually tuned prior: $k_a \sim \mathcal{N}(0.6, 0.2) $, $k_d \sim \mathcal{N}(0.5, 0.2) $, $l_x \sim \mathcal{N}(0, 0.2) $, $l_y \sim \mathcal{N}(0.2, 0.05) $.

\begin{table}[h!]
	\centering
	\caption{Parameters of the lighting prior distributions.}\label{tab:lprior}
	\vspace{-0.1cm}
	\resizebox{13.2cm}{1.0cm}{
	\begin{tabular}{c|cccc|cccc|cccc}
		\Xhline{2\arrayrulewidth}
		Dataset & \multicolumn{4}{c|}{BFM}         & \multicolumn{4}{c|}{CelebA}       & \multicolumn{4}{c}{Cats}        \\ \hline
		mean                        & 0.058  & 0.141 & -0.02 & 0.251  & 0.214  & 0.352 & -0.006 & 0.389  & -0.155 & 0.300  & 0.003 & 0.080 \\ \hline
		\multirow{4}{*}{covariance} & 0.077  & 0.032 & 0     & -0.002 & 0.081  & 0.004 & 0      & -0.007 & 0.161  & -0.008 & 0     & 0.006 \\
		& 0.032  & 0.058 & 0     & 0.004  & 0.004  & 0.031 & 0      & 0.003  & -0.008 & 0.043  & 0     & 0     \\
		& 0      & 0     & 0.062 & 0      & 0      & 0     & 0.079  & 0      & 0      & 0      & 0.093 & 0     \\
		& -0.002 & 0.004 & 0     & 0.006  & -0.007 & 0.003 & 0      & 0.006  & 0.006  & 0      & 0     & 0.009 \\ \Xhline{2\arrayrulewidth}
	\end{tabular}
	}
\end{table}

In the volume rendering process, we sample $m$ points within the near and far bounds $t_n$ and $t_f$ with a hierarchical sampling strategy as in NeRF~\cite{mildenhall2020nerf}.
For BFM and CelebA, $m=24$, $t_n=0.88$, and $t_f=1.12$, while for Cats, $m=40$, $t_n=0.80$, and $t_f=1.20$.
In experiments with the surface tracking network, the ray sampling interval $\Delta_i$ and the number of sampling points $m_i$ are gradually reduced as the training iteration $i$ grows.
We start to adopt this strategy after training for 5000 iterations.
Specifically, we start with a large interval $\Delta_{max}$ and decrease to $\Delta_{min}$ with an exponential schedule as $\Delta_i = \Delta_{min} + \text{exp}(-i \beta) (\Delta_{max} - \Delta_{min})$, where $\beta$ controls the decay.
$m_i$ is defined similarly as $m_i = \lfloor m_{min} + \text{exp}(-i \beta) (m_{max} - m_{min}) \rceil$.
In our experiments, we set $\Delta_{max}=0.24$, $\Delta_{min}=0.06$, $m_{max}=m$, and $m_{min}=m/2$.
$\beta$ is set to 5.5e-5, 3e-5, and 1e-4 for BFM, CelebA, and Cats datasets respectively.

\subsubsection{Datasets}
Here we provide more information on the datasets used in our experiments.

\textbf{BFM}~\cite{paysan20093d} is a synthetic human face dataset generated via the Basel face model.
It consists of 160k images for training, 20k images for validation, and 20k images for testing.
For each image, there is a corresponding ground-truth depth map.
This dataset is released along with the code of Unsup3d~\cite{wu2020unsupervised,unsup3d}, which is protected under the MIT License.

\textbf{CelebA}~\cite{liu2015deep} is a large-scale face attributes dataset with more than 200k images of human faces.
According to the agreement on its official website~\cite{celeba}, this dataset is available for non-commercial research purposes.

\textbf{Cats} dataset~\cite{zhang2008cat} contains 6444 images of cat heads.
According to the official website~\cite{cats}, this dataset is available for research purposes.

All these datasets are obtained from their corresponding website mentioned above.
These datasets do not contain personally identifiable information or offensive content, as they are ray images without identity labels.

\subsubsection{GAN Inversion}
With a pretrained ShadeGAN, we can perform GAN inversion for real image editing as shown in Fig. 9 of the main paper.
Specifically, we revise the discriminator to be an encoder $E$ by adding an additional fully-connected layer on top of the final feature.
We randomly sample latent codes ${\bm{z}}$, camera poses $\bm{\xi}$, lighting conditions $\bm{\mu}$, and generate their corresponding images ${\bm{I}}_g$ via the generator.
These data are used to train the encoder $E$ to predict $\bm{\xi}$, $\bm{\mu}$, and the frequency and phase factors of the mapping network.
The training of $E$ takes 10k iterations with a learning rate of 2e-4.
Given a real target image, we first obtain the initial $\bm{\xi}$, $\bm{\mu}$, frequency and phase factors via the trained encoder, and then finetune them by minimizing the image reconstruction error in the form of mean-squared-error
During finetuning, we jointly optimize $\bm{\xi}$, $\bm{\mu}$, frequency and phase factors with the Adam optimizer for 400 iterations.
The learning rate is initialized to 0.005, decaying by a half at 200, 300, and 350 iterations.

\section{Qualitative Results}

\begin{figure}[h!]
	\centering
	\vspace{-0.2cm}
	\includegraphics[width=13.8cm]{figures/qualitative_supp.pdf}
	\vspace{-0.2cm}
	\caption{More qualitative examples of (a) pi-GAN~\cite{chan2020pi} and (b) our ShadeGAN.}
	\label{fig:qualitative_supp}

\end{figure}

\begin{figure}[h!]
	\centering
	\vspace{-0.2cm}
	\includegraphics[width=13.2cm]{figures/afhq_cats.pdf}
	\vspace{-0.2cm}
	\caption{Qualitative results of ShadeGAN on the AFHQ dataset.}
	\label{fig:afhqcats}

\end{figure}

In this section, we provide more qualitative results of our method.
In Fig.~\ref{fig:qualitative_supp}, we provide more qualitative comparisons between pi-GAN~\cite{chan2020pi} and our ShadeGAN.
We also show the results of our method on the AFHQ Cat dataset~\cite{choi2020starganv2} in Fig.~\ref{fig:afhqcats}.
Fig.~\ref{fig:view_compare} shows the effects of view conditioning in our model.
The model without view conditioning looks slightly better in general, but would have slightly worse FID score as indicated in Tab.~\ref{tab:ablation}.
Fig.~\ref{fig:3drecon} provides a qualitative comparison of the 3D shape reconstruction results corresponding to Tab. 1 of the main paper.
Fig.~\ref{fig:normal} compares different ways of calculating normal directions, which shows that ours as described in Eq. 3 of the main paper is better.
It is observed that our method predicts more accurate 3D shapes than GRAF~\cite{schwarz2020graf} and pi-GAN~\cite{chan2020pi}.
Fig.~\ref{fig:interpolate} illustrates the effects of linearly interpolating the latent codes and lighting conditions, which creates a continuous image and shape morphing effect.
We further show more examples on image relighting effects of ShadeGAN in Fig.~\ref{fig:supp_relight}.

\begin{figure}[h!]
	\centering
	\vspace{-0.2cm}
	\includegraphics[width=13.2cm]{figures/view_compare.pdf}
	\vspace{-0.2cm}
	\caption{Qualitative results of our method with and without view conditioning.}
	\label{fig:view_compare}

\end{figure}

\begin{figure}[t!]
	\centering
	\includegraphics[width=13.5cm]{figures/3drecon.pdf}

	\caption{Qualitative results of 3D shape reconstruction corresponding to Tab. 1 of the main paper. We visualize the shapes and normals predicted by the depth-predicting CNNs. Our results are closer to the ground truth shapes than other baselines. }
	\label{fig:3drecon}

\end{figure}

\begin{figure}[t!]
	\centering
	\vspace{-0.3cm}
	\includegraphics[width=\linewidth]{figures/normal.pdf}
	\vspace{-0.6cm}
	\caption{Comparisons of different normal direction calculation methods. `Local normal' represents the alternative normal calculation method described in "Discussion" of Sec 3.2 in the main paper, which normalizes the normal direction at each local points on a ray. `Ours' corresponds to Eq. 3 of the main paper. It can be observed that our results have less artifacts. }
	\label{fig:normal}
	\vspace{-0.5cm}
\end{figure}

\begin{figure}[t!]
	\centering

	\includegraphics[width=12.5cm]{figures/interpolate.pdf}
	\vspace{-0.2cm}
	\caption{Linearly interpolating between two latent vectors and lighting conditions achieves continuous morphing on both images and shapes. }
	\label{fig:interpolate}
	\vspace{-0.5cm}
\end{figure}

\begin{figure}[t!]
	\centering

	\includegraphics[width=12.5cm]{figures/supp_relight.pdf}
	\vspace{-0.2cm}
	\caption{More image relighting examples produced by ShadeGAN.}
	\label{fig:supp_relight}
	\vspace{-0.6cm}
\end{figure}

\subsection{Broader Impacts}

This work provides a new approach for 3D-aware image synthesis.
It could not only synthesize novel views of an instance in a 3D-consistent manner, but also generate the corresponding 3D shape that is more accurate than those produced by previous methods.
The applications of our approach mainly lie in those related to 3D content creation, like augmented reality, virtual reality, and computer games.
Besides, it could be used to edit 2D images, including those of human portraits.
It could also possibly be extended for malicious use like deep fakes.
Thus, any application or research that uses our approach has to strictly respect personality rights and privacy regulations.

\end{document}

\section{Experiments}\label{sec:experiments}

In this section, we evaluate the proposed ShadeGAN on 3D-aware image synthesis.
We also show that ShadeGAN learns much more accurate 3D shapes than previous methods,
and in the meantime allows explicit control over lighting conditions.
The datasets used include CelebA~\cite{liu2015deep}, BFM~\cite{paysan20093d}, and Cats~\cite{zhang2008cat},
all of which contain only unconstrained 2D RGB images.

\textbf{Implementation.}
In terms of model architectures, we adopt a SIREN-based MLP~\cite{sitzmann2020implicit} as the generator and a convolutional neural network as the discriminator following~\cite{chan2020pi}.
For the prior distribution of lighting conditions, we use Unsup3d~\cite{wu2020unsupervised} to estimate the lighting conditions of real data and subsequently fit a multivariate Gaussian distribution of $\bm{\mu} = ({\bm{l}}, k_a, k_d)$ as the prior.
A hand-crafted prior distribution is also included in the ablation study.
In quantitative study, we let the pre-cosine color ${\bm{a}}$ be conditioned on the lighting condition $\bm{\mu}$ as well as the viewing direction ${\bm{d}}$ unless otherwise stated.
In qualitative study, we observe that removing view conditioning achieves slightly better 3D shapes for CelebA and BFM datasets.
Thus, we show results without view conditioning for these two datasets in the main paper, and put those with view conditioning in Fig.~\ref{fig:view_compare} of the appendix.
Other implementation details are provided in the appendix.

\begin{figure}[t!]
	\centering
	\includegraphics[width=\linewidth]{figures/qualitative.pdf}
	\vspace{-0.25cm}
	\caption{\textbf{Qualitative comparison} on BFM (top), CelebA (middle), and Cats (bottom) datasets. "Albedo" refers to the pre-cosine color that approximates albedo. Our approach synthesizes more accurate 3D shapes than pi-GAN and GRAF, and also learns to disentangle shading with albedo. }
	\label{fig:qualitative}
\end{figure}

\textbf{Comparison with baselines.}
We compare ShadeGAN with two state-of-the-art generative implicit models, namely GRAF~\cite{schwarz2020graf} and pi-GAN~\cite{chan2020pi}.
Specifically,
Fig.~\ref{fig:qualitative} includes both synthesized images as well as their corresponding 3D meshes,
which are obtained by performing marching cubes on the volume density $\sigma$.
While GRAF and pi-GAN could synthesize images with controllable poses, their learned 3D shapes are inaccurate and noisy.
In contrast, our approach not only synthesizes photorealistic 3D-consistent images,
but also learns much more accurate 3D shapes and surface normals,
indicating the effectiveness of the proposed multi-lighting constraint as a regularization.
More synthesized images and their corresponding shapes are included in Fig.\ref{fig:samples}.
Besides more accurate 3D shapes,
ShadeGAN can also learn the albedo and diffuse shading components inherently.
As shown in Fig.~\ref{fig:qualitative},
although not perfect, ShadeGAN has managed to disentangle shading and albedo with satisfying quality,
as such disentanglement is a natural solution to the multi-lighting constraint.

The quality of learned 3D shapes is quantitatively evaluated on the BFM dataset.
Specifically,
we use each of the generative implicit models to generate 50k images and their corresponding depth maps.
Image-depth pairs from each model are used as training data to train an additional convolutional neural network (CNN) that learns to predict the depth map of an input image.
We then test each trained CNN on the BFM test set
and compare its predictions to the ground-truth depth maps as a measurement of the quality of learned 3D shapes.
Following \cite{wu2020unsupervised},
we report the scale-invariant depth error (SIDE) and mean angle deviation (MAD) metrics.
The results are included in Tab.~\ref{tab:synface},
where ShadeGAN significantly outperforms GRAF and pi-GAN.
Besides, ShadeGAN also outperforms other advanced unsupervised 3D shape learning approaches including Unsup3d~\cite{wu2020unsupervised} and GAN2Shape~\cite{pan2020gan2shape},
demonstrating its large potential in unsupervised 3D shapes learning.
In terms of image quality,
Tab.~\ref{tab:synface} includes the FID~\cite{heusel2017gans} scores of images synthesized by different models,
where the FID score of ShadeGAN is slightly inferior to pi-GAN in BFM and CelebA.
Intuitively, this is caused by the gap between our approximated shading (\textit{i.e.}~Lambertian shading) and the real illumination,
which can be potentially avoided by adopting more realistic shading models and improving the lighting prior.

\begin{figure}[t!]
	\centering
	\begin{minipage}{0.62\linewidth}
		\centering
		\includegraphics[width=8.9cm]{figures/samples.pdf}
		\vspace{-0.6cm}
		\caption{Generated face images and their 3D meshes. }
		\vspace{-0.1cm}
		\label{fig:samples}
	\end{minipage}
	\hfill
	\begin{minipage}{0.34\linewidth}
		\centering
		\includegraphics[width=4.7cm]{figures/ablation.pdf}
		\vspace{-0.6cm}
		\caption{\textbf{Qualitative ablation.} See the main text for discussions. }
		\vspace{-0.2cm}
		\label{fig:ablation}
	\end{minipage}
	\vspace{-0.1cm}
\end{figure}

\begin{table}[t!]
	\centering
	\begin{minipage}{0.48\linewidth}
		\centering
		\caption{\textbf{Comparisons on the BFM dataset.} We report FID ($128^2$) for image synthesis, and SIDE ($\times 10^{-2}$) and MAD (deg.) for the accuracy of 3D shapes. `-' indicates not available. Results of pi-GAN and Ours are averaged over 5 runs.}\label{tab:synface}
		\vspace{-0.2cm}
		\resizebox{6.7cm}{1.4cm}{
			\begin{tabular}{lccc}
				\Xhline{2\arrayrulewidth}
				Method    & FID $\downarrow$ & SIDE $\downarrow$ & MAD $\downarrow$ \\ \hline\hline
				Supervised & -  & 0.410 & 10.78 \\ \hline
				Unsup3d~\cite{wu2020unsupervised}   &  -  & 0.793 &  16.51 \\
				GAN2Shape~\cite{pan2020gan2shape} \hspace{-0.5cm} &  -  & 0.756 & 14.81  \\ \hline
				GRAF~\cite{schwarz2020graf}      &  53.4 & 1.857  & 26.60 \\
				pi-GAN~\cite{chan2020pi}    &  16.7{\scriptsize $\pm 0.2$}\hspace{-0.2cm} & 0.727{\scriptsize $\pm 0.012$}\hspace{-0.2cm} & 20.09{\scriptsize $\pm 0.23$}\hspace{-0.2cm} \\
				Ours      &  17.7{\scriptsize $\pm 0.2$}\hspace{-0.2cm} & 0.607{\scriptsize $\pm 0.007$}\hspace{-0.2cm} & 14.52{\scriptsize $\pm 0.11$}\hspace{-0.2cm} \\ \Xhline{2\arrayrulewidth}
			\end{tabular}
		}
	\end{minipage}
	\hfill
	\begin{minipage}{0.48\linewidth}
		\centering
		\caption{\textbf{Comparisons on the CelebA and Cats datasets.} The image resolution is $128^2$. }\label{tab:celebacat}
		\vspace{-0.2cm}
		\resizebox{5.4cm}{1.4cm}{
		\begin{tabular}{llcc}
			\Xhline{2\arrayrulewidth}
			Dataset                 & Method & FID $\downarrow$ & MAD $\downarrow$ \\ \hline\hline
			\multirow{3}{*}{CelebA} & GRAF   &  43.0  &  30.48   \\
			& pi-GAN & 15.7 & 27.22  \\
			& Ours   & 16.2  & 20.49  \\ \hline
			\multirow{3}{*}{Cats}    & GRAF   &  30.3    &  65.47   \\
			& pi-GAN &  10.7   &  33.48  \\
			& Ours   &  10.3   &  25.47   \\ \Xhline{2\arrayrulewidth}
		\end{tabular}
		}
	\end{minipage}
	\vspace{-0.2cm}
\end{table}

\begin{table}[t!]
	\centering
	\begin{minipage}{0.48\linewidth}
		\centering
		\caption{\textbf{Ablation study on the BFM dataset.}}\label{tab:ablation}
		\vspace{-0.2cm}
		\resizebox{6.5cm}{1.3cm}{
			\begin{tabular}{llccc}
				\Xhline{2\arrayrulewidth}
				No. & Method       & FID $\downarrow$ & SIDE $\downarrow$ & MAD $\downarrow$ \\ \hline\hline
				(1) & ShadeGAN     & 17.7 & 0.607 & 14.52 \\
				(2) & local shading & 30.1 & 0.754 & 18.18 \\
				(3) & w/o light    & 19.2 & 0.618  & 14.53  \\
				(4) & w/o view     & 18.6 & 0.622 & 14.88 \\
				(5) & manual prior & 20.2 & 0.643 & 15.38  \\
				(6) & +efficient    & 18.2 & 0.673 & 14.72 \\ \Xhline{2\arrayrulewidth}
			\end{tabular}
		}
	\end{minipage}
	\hfill
	\begin{minipage}{0.48\linewidth}
		\centering
		\caption{\textbf{Training and inference time cost on CelebA.} The efficient volume rendering significantly improves training and inference speed. }\label{tab:efficient}
		\vspace{-0.2cm}
		\resizebox{5.4cm}{0.95cm}{
			\begin{tabular}{llccc}
				\Xhline{2\arrayrulewidth}
				Method & \hspace{-0.3cm} Train (h) \hspace{-0.3cm} & Inference (s) \hspace{-0.3cm} & FID \\ \hline\hline
				 ShadeGAN   & 92.3 & 0.343 &  16.4 \\
		         +efficient & 70.2 &  0.179  &  16.2 \\ \hline
				 pi-GAN      & 56.8 & 0.204 &  15.7   \\
				 +efficient & 46.9 & 0.114  &  15.9    \\ \Xhline{2\arrayrulewidth}
			\end{tabular}
		}
	\end{minipage}
	\vspace{-0.2cm}
\end{table}

In Tab.~\ref{tab:celebacat},
we also show the quantitative results of different models on CelebA and Cats.
To evaluate the learned shape, we use each generative implicit model to generate 2k front-view images and their corresponding depth maps.
While these datasets do not have ground truth depth, we report MAD obtained by testing pretrained Unsup3d models~\cite{wu2020unsupervised} on these generated image-depth pairs as a reference.
As we can observe,
results on CelebA and Cat are consistent with those on the BFM dataset.

\textbf{Ablation studies.}
We further study the effects of several design choices in ShadeGAN.
First, we perform local points-specific shading as mentioned in the discussion of Sec.~\ref{ShadeGAN}.
As Tab.~\ref{tab:ablation} No.(2) and Fig.~\ref{fig:ablation} (b) show,
the results of such a local shading strategy are notably worse than the original one,
which indicates that taking the magnitude of $\nabla_{\bm{x}}\sigma$ into account is beneficial.
Besides, the results of Tab.~\ref{tab:ablation} No.(3) and No.(4) imply that
removing ${\bm{a}}$'s dependence on the lighting $\bm{\mu}$ or the viewpoint ${\bm{d}}$ could lead to a slight performance drop.
The results of using a simple manually tuned lighting prior are provided in Tab.~\ref{tab:ablation} No.(5) and Fig.~\ref{fig:ablation} (c),
which are only moderately worse than the results of using a data-driven prior,
and the generated shapes are still significantly better than the ones produced by existing approaches.

To verify the effectiveness of the proposed efficient volume rendering technique,
we include its effects on image quality and training/inference time in Tab.~\ref{tab:ablation} No.(6) and Tab.~\ref{tab:efficient}.
It is observed that the efficient volume rendering has marginal effects on the performance,
but significantly reduces the training and inference time by 24\% and 48\% for ShadeGAN.
Moreover,
in Fig.~\ref{fig:depth}
we visualize the depth maps predicted by our surface tracking network and those obtained via volume rendering.
It is shown that under varying identities and camera poses,
the surface tracking network could consistently predict depth values that are quite close to the real surface positions,
so that we can sample points near the predicted surface for rendering without sacrificing image quality.

\textbf{Illumination-aware image synthesis.}
As ShadeGAN models the shading process, it by design allows explicit control over the lighting condition.
We provide such illumination-aware image synthesis results in Fig.\ref{fig:religthing}, where ShadeGAN generates promising images under different lighting directions.
We also show that in cases where the predicted ${\bm{a}}$ is conditioned on the lighting condition $\bm{\mu}$,
${\bm{a}}$ would slightly change \textit{w.r.t.}~the lighting condition, \textit{e.g.}, it would be brighter in areas having a overly dim shading in order to make the final image more natural.
Besides, we could optionally add a specular term $k_s \text{max}({0, {\bm{h}} \cdot {\bm{n}}})^p$ in Eq.~\ref{eq:shading} (\textit{i.e.}, Blinn-Phong shading~\cite{phong1975illumination}, where ${\bm{h}}$ is the bisector of the angle between the viewpoint and the lighting direction) to create specular highlight effects, as shown in Fig.\ref{fig:religthing} (c).

\textbf{GAN inversion.}
ShadeGAN could also be used to reconstruct a given target image by performing GAN inversion.
As shown in Fig.~\ref{fig:inversion} such inversion allows us to obtain several factors of the image, including the 3D shape, surface normal, approximated albedo, and shading.
Besides, we can further perform view synthesis and relighting by changing the viewpoint and lighting condition.
The implementation of GAN inversion is provided in the appendix.

\begin{figure}[t!]
	\centering
	\begin{minipage}{0.32\linewidth}
		\centering
		\includegraphics[width=4.2cm]{figures/depth.pdf}
		\vspace{-0.2cm}
		\caption{Visualization of depths predicted by our depth tracking network and those calculated via volume rendering. }

		\label{fig:depth}
	\end{minipage}

	~
	\begin{minipage}{0.66\linewidth}
		\centering
		\includegraphics[width=9.0cm]{figures/relighting.pdf}
		\vspace{-0.3cm}
		\caption{\textbf{Illumination-aware image synthesis.} ShadeGAN allows explicit control over the lighting.
		The pre-cosine color (albedo) is independent of lighting in (a) and is conditioned on lighting in (b). We show results of adding a specular term in (c). }

		\label{fig:religthing}
	\end{minipage}
	\vspace{-0.4cm}
\end{figure}

\begin{figure}[t!]
	\centering
	\includegraphics[width=\linewidth]{figures/inversion.pdf}
	\vspace{-0.7cm}
	\caption{\textbf{GAN inversion for real image editing}.}
	\vspace{-0.6cm}
	\label{fig:inversion}
\end{figure}

\textbf{Discussions.}
As the Lambertian shading we used is an approximation to the real illumination,
the albedo learned by ShadeGAN is not perfectly disentangled.
Our approach does not consider the spatially-varying material properties of objects as well.
In the future, we intend to incorporate more sophisticated shading models to learn better disentangled generative reflectance fields.

\section{Related Work}

\noindent\textbf{Neural volume rendering.}
Starting from the seminal work of neural radiance fields (NeRF) \cite{mildenhall2020nerf}, neural volume rendering has gained much popularity in representing 3D scenes and synthesizing novel views.
By integrating coordinate-based neural networks with volume rendering, NeRF performs high-fidelity view synthesis in a 3D consistent manner.
Several attempts have been proposed to extend or improve NeRF.
For instance, \cite{boss2020nerd,bi2020neural,srinivasan2021nerv} further model illumination, and learn to disentangle reflectance with shading given well-aligned multi-view and multi-lighting images.
Besides, many studies accelerate the rendering of static scenes from the perspective of spatial sparsity \cite{liu2020neural,yu2021plenoctrees}, architectural design \cite{reiser2021kilonerf,garbin2021fastnerf}, or efficient rendering \cite{lindell2020autoint,neff2021donerf}.
However, it is not trivial to apply these illumination and acceleration techniques to volume rendering-based generative models \cite{schwarz2020graf,chan2020pi},
as they typically learn from unposed and unpaired images, and represent dynamic scenes that change with respect to the input latent codes.

In this work, we take the first attempt to model illumination in volume rendering-based generative models, which serves as a regularization for accurate 3D shape learning.
We further devise an efficient rendering technique for our approach, which shares similar insight with \cite{neff2021donerf}, but does not rely on ground truth depth for training and it is not limited to a small viewpoint range.

\noindent\textbf{Generative 3D-aware image synthesis.}
Generative adversarial networks (GANs) \cite{goodfellow2014generative} are capable of generating photorealistic images of high-resolution, but lack explicit control over camera viewpoint.
In order to enable them to synthesis images in a 3D-aware manner, many recent approaches investigate how 3D representations could be incorporated into GANs \cite{wu2016learning,alhaija2018geometric,chen2021ngp,zhu2018visual,nguyen2019hologan,BlockGAN2020,liao2020towards,henzler2019escaping,szabo2019unsupervised,schwarz2020graf,chan2020pi,Niemeyer2020GIRAFFE,tewari2020stylerig,yenamandra2020i3dmm}.
While some works directly learn from 3D data \cite{wu2016learning,alhaija2018geometric,chen2021ngp,zhu2018visual,yenamandra2020i3dmm}, in this work we focus on approaches that only have access to unconstrained 2D images, which is a more practical setting.
Several attempts \cite{nguyen2019hologan,BlockGAN2020,liao2020towards} adopt 3D voxel features with learned neural rendering. These methods produce realistic 3D-aware synthesis, but the 3D voxels are not interpretable, \textit{i.e.}, they cannot be transferred to 3D shapes.
By leveraging differentiable renderer, \cite{henzler2019escaping} and \cite{szabo2019unsupervised} learn interpretable 3D voxels and meshes respectively, but \cite{henzler2019escaping} suffers from limited visual quality due to low voxel resolution while the learned 3D shapes of \cite{szabo2019unsupervised} exhibit noticeable distortions.
The success of NeRF has motivated researchers to use radiance fields as the intermediate 3D representation in GANs \cite{schwarz2020graf,chan2020pi,Niemeyer2020GIRAFFE}.
While achieving impressive 3D-aware image synthesis with multi-view consistency, the extracted 3D shapes of these approaches are often imprecise and noisy.
Our main goal in this work is to address the inaccurate shape by explicitly modeling illumination in the rendering process. This innovation helps achieve better 3D-aware image synthesis with broader applications.

\noindent\textbf{Unsupervised 3D shape learning from 2D images.}
Our work is also related to unsupervised approaches that learn 3D object shapes from unconstrained, monocular view 2D images.
While several approaches use external 3D shape templates or 2D key-points as weak supervisions to facilitate learning \cite{tulsiani2020implicit,goel2020shape,tran2018nonlinear,kanazawa2018learning,kanazawa2018end,sanyal2019learning,shang2020self}, in this work we consider the harder setting where only 2D images are available.
To tackle this problem, most approaches adopt an ``analysis-by-synthesis'' paradigm \cite{sahasrabudhe2019lifting,wu2020unsupervised,li2020self}.
Specifically, they design photo-geometric autoencoders to infer the 3D shape and viewpoint of each image with a reconstruction loss.
While succeed in learning the 3D shapes for some object categories, these approaches typically rely on certain regularization to prevent trivial solutions, like the commonly used symmetry assumption on object shapes \cite{wu2020unsupervised,li2020self,tulsiani2020implicit,goel2020shape}.
Such assumption tends to produce symmetric results that may overlook the asymmetric aspects of objects.
Recently, GAN2Shape \cite{pan2020gan2shape} shows that it is possible to recover 3D shapes for images generated by 2D GANs. This method, however, requires inefficient instance-specific training, and recovers depth maps instead of full 3D representations.

The proposed 3D-aware generative model also serves as a powerful approach for unsupervised 3D shape learning.
Compared with aforementioned autoencoder-based methods, our GAN-based approach avoids the need to infer the viewpoint of each image, and does not rely on strong regularizations.
In experiments, we demonstrate superior performance over recent state-of-the-art approaches Unsup3d \cite{wu2020unsupervised} and GAN2Shape \cite{pan2020gan2shape}.
\section{Methodology}

We consider the problem of 3D-aware image synthesis by learning from a collection of unconstrained  and unlabeled 2D images.
We argue that modeling shading, \textit{i.e.}, the interaction of illumination and shape, in a generative implicit model enables unsupervised learning of more accurate 3D object shapes.
In the following, we first provide some preliminaries on neural radiance fields (NeRF)~\cite{mildenhall2020nerf}, and then introduce our shading-guided generative implicit model.

\subsection{Preliminaries on Neural Radiance Fields}

As a deep implicit model, NeRF~\cite{mildenhall2020nerf} uses an MLP network to represent a 3D scene as a radiance field.
The MLP $f_\theta : ({\bm{x}}, {\bm{d}}) \rightarrow (\sigma, {\bm{c}})$ takes a 3D coordinate ${\bm{x}} \in \mathbb{R}^3 $ and a viewing direction ${\bm{d}} \in \mathbb{S}^2$ as inputs, and outputs a volume density $\sigma \in \mathbb{R}^+$ and a color ${\bm{c}} \in \mathbb{R}^3 $.
To render an image under a given camera pose, each pixel color ${\bm{C}}$ of the image is obtained via volume rendering along its corresponding camera ray ${\bm{r}}(t) = {\bm{o}} + t{\bm{d}}$ with near and far bounds $t_n$ and $t_f$ as below:
\begin{align}
{\bm{C}}({\bm{r}}) = \int_{t_n}^{t_f} T(t) \sigma({\bm{r}}(t)) {\bm{c}}({\bm{r}}(t), {\bm{d}}) dt, ~
\text{where} ~~ T(t) = \text{exp}(-\int_{t_n}^{t}\sigma({\bm{r}}(s)) ds).
 \label{eq:nerf}
\end{align}
In practice, this volume rendering is implemented with a discretized form using stratified and hierarchical sampling.
As this rendering process is differentiable, NeRF could be directly optimized via posed images of a static scene.
After training, NeRF allows the rendering of images under new camera poses, achieving high-quality novel view synthesis.

\begin{figure}[t!]
	\centering
	\includegraphics[width=13cm]{figures/method.pdf}
	\vspace{-0.15cm}
	\caption{\textbf{Method overview}. Our generator $g_\theta$ models a relightable color field conditioned on a latent code ${\bm{z}} \sim p_z$. To synthesis an image, it performs volume rendering under a random camera pose $\bm{\xi} \sim p_\xi$. The rendering process also performs shading with a randomly sampled lighting condition $\bm{\mu} \sim p_\mu$. The discriminator learns to distinguish the synthesized images with real images from the training dataset, and the whole model is trained with a GAN loss. Although our model is trained from unconstrained 2D images, it allows explicit control over camera pose and lighting condition during inference. }
	\vspace{-0.2cm}
	\label{fig:method}
\end{figure}

\subsection{Shading-Guided Generative Implicit Model}\label{ShadeGAN}

In this work, we are interested in developing a generative implicit model that explicitly models the shading process for 3D-aware image synthesis.
To achieve this, we make two extensions to the MLP network in NeRF.
First, similar to most deep generative models, it is further conditioned on a latent code ${\bm{z}}$ sampled from a prior distribution $\mathcal{N}(0, I)^{d}$.
Second, instead of directly outputting the color ${\bm{c}}$, it outputs a relightable pre-cosine color term ${\bm{a}} \in \mathbb{R}^3$, which is conceptually similar to albedo in the way that it could be shaded under a given lighting condition.
While albedo is viewpoint-independent, in this work we do not strictly enforce such independence for ${\bm{a}}$ in order to account for dataset bias.
Thus, our generator $g_\theta : ({\bm{x}}, {\bm{d}}, {\bm{z}}) \rightarrow (\sigma, {\bm{a}})$ takes a coordinate ${\bm{x}}$, a viewing direction ${\bm{d}}$, and a latent code ${\bm{z}}$ as inputs, and outputs a volume density $\sigma$ and a pre-cosine color ${\bm{a}}$.
Note that here $\sigma$ is independent of ${\bm{d}}$, while the dependence of ${\bm{a}}$ on ${\bm{d}}$ is optional.
To obtain the color ${\bm{C}}$ of a camera ray ${\bm{r}}(t) = {\bm{o}} + t{\bm{d}}$ with near and far bounds $t_n$ and $t_f$, we calculate the final pre-cosine color ${\bm{A}}$ via:
\begin{align}
{\bm{A}}({\bm{r}}, {\bm{z}}) = \int_{t_n}^{t_f} T(t, {\bm{z}}) \sigma({\bm{r}}(t), {\bm{z}}) {\bm{a}}({\bm{r}}(t),
{\bm{d}}, {\bm{z}}) dt, ~
\text{where} ~~ T(t, {\bm{z}}) = \text{exp}(-\int_{t_n}^{t}\sigma({\bm{r}}(s), {\bm{z}}) ds).
\label{eq:albedo}
\end{align}
We also calculate the normal direction ${\bm{n}}$ with:
\begin{align}
\bm{n}({\bm{r}}, {\bm{z}}) = \bm{\hat{n}}({\bm{r}}, {\bm{z}}) / \| \bm{\hat{n}}({\bm{r}}, {\bm{z}}) \|_2, ~
\text{where} ~ \bm{\hat{n}}({\bm{r}}, {\bm{z}}) = - \int_{t_n}^{t_f} T(t, {\bm{z}}) \sigma({\bm{r}}(t), {\bm{z}}) \nabla_{{\bm{r}}(t)}\sigma({\bm{r}}(t), {\bm{z}}) dt,
\label{eq:normal}
\end{align}
where $\nabla_{{\bm{r}}(t)}\sigma({\bm{r}}(t), {\bm{z}})$ is the derivative of volume density $\sigma$ with respect to its input coordinate, which naturally captures the local normal direction, and could be calculated via back-propagation.
Then the final color ${\bm{C}}$ is obtained via Lambertian shading as:
\begin{align}
{\bm{C}}({\bm{r}}, {\bm{z}}) = {\bm{A}}({\bm{r}}, {\bm{z}}) (k_a + k_d \text{max}({0, {\bm{l}} \cdot {\bm{n}}({\bm{r}}, {\bm{z}})})),
\label{eq:shading}
\end{align}
where ${\bm{l}} \in \mathbb{S}^2$ is the lighting direction, $k_a$ and $k_d$ are the ambient and diffuse coefficients.
We provide more discussions on this shading formulation at the end of this subsection.

\textbf{Camera and Lighting Sampling.}
Eq.(\ref{eq:albedo} - \ref{eq:shading}) describe the process of rendering a pixel color given a camera ray ${\bm{r}}(t)$ and a lighting condition $\bm{\mu} = ({\bm{l}}, k_a, k_d)$.
Generating a full image ${\bm{I}}_g \in \mathbb{R}^{3 \times H \times W}$ requires one to sample a camera pose $\bm{\xi}$
and a lighting condition $\bm{\mu}$ in addition to the latent code ${\bm{z}}$, \textit{i.e.}, ${\bm{I}}_g = G_\theta({\bm{z}}, \bm{\xi}, \bm{\mu})$.
In our setting, the camera pose $\bm{\xi}$ could be described by pitch and yaw angles, and is sampled from a prior Gaussian or uniform distribution $p_{\xi}$, as also done in previous works \cite{chan2020pi,schwarz2020graf}.
Sampling the camera pose randomly during training would motivate the learned 3D scene to look realistic from different viewpoints.
While this \textit{multi-view constraint} is beneficial for learning a valid 3D representation, it is often insufficient to infer the accurate 3D object shape.
Thus, in our approach, we further introduce a \textit{multi-lighting constraint} by also randomly sampling a lighting condition $\bm{\mu}$ from a prior distribution $p_\mu$.
In practice, $p_\mu$ could be estimated from the dataset using existing approaches like \cite{wu2020unsupervised}.
We also show in our experiments that a simple and manually tuned prior distribution could also produce reasonable results.
As the shading process is sensitive to the normal direction due to the diffuse term $k_d \text{max}({0, {\bm{l}} \cdot {\bm{n}}({\bm{r}}, {\bm{z}})})$ in Eq.(\ref{eq:shading}), this multi-lighting constraint would regularize the model to learn more accurate 3D shapes that produce natural shading, as shown in Fig.\ref{fig:fig1} (b).

\textbf{Training.}
Our generative model follows the paradigm of GANs~\cite{goodfellow2014generative}, where the generator is trained together with a discriminator $D$ with parameters $\phi$ in an adversarial manner.
During training, the generator generates fake images ${\bm{I}}_g = G_\theta({\bm{z}}, \bm{\xi}, \bm{\mu})$ by sampling the latent code ${\bm{z}}$, camera pose $\bm{\xi}$ and lighting condition $\bm{\mu}$ from their corresponding prior distributions $p_z$, $p_\xi$, and $p_\mu$.
Let ${\bm{I}}$ denotes real images sampled from the data distribution $p_I$.
We train our model with a non-saturating GAN loss with $R_1$ regularization~\cite{mescheder2018training}:
\begin{equation}
\begin{aligned}
\mathcal{L}(\theta, \phi) = {\mathbf{E}}_{{\bm{z}} \sim p_z, \bm{\xi} \sim p_\xi, \bm{\mu} \sim p_\mu}
\left[ f \Big( D_{\phi} (G_{\theta} ({\bm{z}}, \bm{\xi}, \bm{\mu})) \Big) \right]
+ {\mathbf{E}}_{{\bm{I}} \sim p_\mathcal{D}} \left[ f(-D_{\phi}({\bm{I}})) + \lambda \|\nabla D_{\phi}({\bm{I}})\|^2 \right],
\label{eq:gan}
\end{aligned}
\end{equation}
where $f(u) = -\log(1 + \exp(-u))$, and $\lambda$ controls the strength of regularization.
More implementation details are provided in the appendix.

\textbf{Discussion.}
Note that in Eq.(\ref{eq:albedo} - \ref{eq:shading}), we perform shading after ${\bm{A}}$ and ${\bm{n}}$ are obtained via volume rendering.
An alternative way is to perform shading at each local spatial point as ${\bm{c}}({\bm{r}}(t), {\bm{d}}, {\bm{z}}) = {\bm{a}}({\bm{r}}(t), {\bm{d}}, {\bm{z}})(k_a + k_d \text{max}({0, {\bm{l}} \cdot {\bm{n}}({\bm{r}}(t), {\bm{z}})}))$, where ${\bm{n}}({\bm{r}}(t), {\bm{z}}) = - \nabla_{{\bm{r}}(t)}\sigma({\bm{r}}(t), {\bm{z}}) / \|\nabla_{{\bm{r}}(t)}\sigma({\bm{r}}(t), {\bm{z}})\|_2$ is the local normal.
Then we could perform volume rendering using ${\bm{c}}({\bm{r}}(t), {\bm{z}})$ to get the final pixel color.
In practice, we observe that this formulation obtains suboptimal results.
An intuitive reason is that in this formulation, the normal direction is normalized at each local point, neglecting the magnitude of $\nabla_{{\bm{r}}(t)}\sigma({\bm{r}}(t), {\bm{z}})$, which tends to be larger near the object surfaces.
We provide more analysis in experiments and the appendix.

The Lambertian shading we used is an approximation to the real illumination scenario.
While serving as a good regularization for improving the learned 3D shape, it could possibly introduce an additional gap between the distribution of generated images and that of real images.
To compensate for such risk, we could optionally let the predicted ${\bm{a}}$ be conditioned on the lighting condition, \textit{i.e.}, ${\bm{a}} = {\bm{a}}({\bm{r}}(t), {\bm{d}}, \bm{\mu}, {\bm{z}})$.
Thus, in cases where the lighting condition deviates from the real data distribution, the generator could learn to adjust the value of ${\bm{a}}$ and reduce the aforementioned gap.
We show the benefit of this design in the experiments.

\subsection{Efficient Volume Rendering via Surface Tracking}

Similar to NeRF, we implement volume rendering with a discretized integral, which typically requires to sample dozens of points along a camera ray, as shown in Fig.~\ref{fig:surface} (a).
In our approach, we also need to perform back-propagation across the generator in Eq.(\ref{eq:normal}) to get the normal direction for each point, which introduces additional computational cost.
To achieve more efficient volume rendering, a natural idea is to exploit spatial sparsity.
Usually, the weight $T(t, {\bm{z}}) \sigma({\bm{r}}(t), {\bm{z}})$ in volume rendering would concentrate on the object surface position during training.
Thus, if we know the rough surface position before rendering, we could sample points near the surface to save computation.
While for a static scene it is possible to store such spatial sparsity in a sparse voxel grid~\cite{liu2020neural,yu2021plenoctrees}, this technique cannot be directly applied to our generative model, as the 3D scene keeps changing with respect to the input latent code.

To achieve more efficient volume rendering in our generative implicit model, we further propose a \textit{surface tracking network} $S$ that learns to mimic the surface position conditioned on the latent code.
In particular, the volume rendering naturally allows the depth estimation of the object surface via:
\begin{align}
t_s({\bm{r}}, {\bm{z}}) = \int_{t_n}^{t_f} T(t, {\bm{z}}) \sigma({\bm{r}}(t), {\bm{z}}) t \; dt,
\label{eq:depth}
\end{align}
where $T(t, {\bm{z}})$ is defined the same way as in Eq.(\ref{eq:albedo}).
Thus, given a camera pose $\bm{\xi}$ and a latent code ${\bm{z}}$, we could render the full depth map ${\bm{t}}_s({\bm{z}}, \bm{\xi})$.
As shown in Fig.~\ref{fig:surface} (b), we mimic ${\bm{t}}_s({\bm{z}}, \bm{\xi})$ with the surface tracking network $S_\psi$, which is a light-weighted convolutional neural network that takes ${\bm{z}}$, $\bm{\xi}$ as inputs and outputs a depth map.
The depth mimic loss is:
\begin{align}
\mathcal{L}(\psi) = {\mathbf{E}}_{{\bm{z}} \sim p_z, \bm{\xi} \sim p_\xi}
\left[ \|S_\psi({\bm{z}}, \bm{\xi}) - {\bm{t}}_s({\bm{z}}, \bm{\xi})\|_1 + \text{Prec}(S_\psi({\bm{z}}, \bm{\xi}), {\bm{t}}_s( {\bm{d}}({\bm{z}}, \bm{\xi})) \right],
\end{align}
where $\text{Prec}$ is the perceptual loss that motivates $S_\psi$ to better capture edges of the surface.

\begin{figure}[t!]
	\centering
	\includegraphics[width=12.5cm]{figures/surfacetracking.pdf}
	\vspace{-0.2cm}
	\caption{(a) Conventional volume rendering samples dozens of points within a predefined near and far bounds $t_n$ and $t_f$. (b) We propose an efficient volume rendering technique via surface tracking. Before rendering, our surface tracking network $S_\psi$ predicts an initial guess of the surface position $s$ conditioned on the latent code ${\bm{z}}$ and camera pose $\xi$. Then we sample points near $s$, which requires fewer samples. Finally, we use the volume rendered depth $d$ as the ground truth to train $S_\psi$. During training, $S_\psi$ is able to predict depth $s$ that well approximates the real surface depth $d$. }
	\vspace{-0.3cm}
	\label{fig:surface}
\end{figure}

During training, $S_\psi$ is optimized jointly with the generator and the discriminator.
Thus, each time after we sample a latent code ${\bm{z}}$ and a camera pose $\bm{\xi}$, we can get an initial guess of the depth map as $S_\psi({\bm{z}}, \bm{\xi})$.
Then for a pixel with predicted depth $s$, we could perform volume rendering in Eq.(\ref{eq:albedo},\ref{eq:normal},\ref{eq:depth}) with near bound $t_n = s - \Delta_i/2$ and far bound $t_f = s + \Delta_i/2$, where $\Delta_i$ is the interval for volume rendering that decreases as the training iteration $i$ grows.
Specifically, we start with a large interval $\Delta_{max}$ and decrease to $\Delta_{min}$ with an exponential schedule.
As $\Delta_i$ decreases, the number of points used for rendering $m$ also decreases accordingly.
Note that the computational cost of our efficient surface tracking network is marginal compared to the generator, as the former only needs a single forward pass to render an image while the latter will be queried for $H\times W \times m$ times.
Thus, the reduction of $m$ would significantly accelerate the training and inference speed for ShadeGAN.

\section{Introduction}

Advanced deep generative models, \textit{e.g.},  StyleGAN \cite{karras2019style,karras2020analyzing} and BigGAN \cite{brock2018large}, have achieved great successes in natural image synthesis.
While producing impressive results, these 2D representation-based models cannot synthesize novel views of an instance in a 3D-consistent manner.
They also fall short of representing an explicit 3D object shape.
To overcome such limitations, researchers have proposed new deep generative models that represent 3D scenes as neural radiance fields~\cite{chan2020pi,schwarz2020graf}.
Such 3D-aware generative models allow explicit control of viewpoint while preserving 3D consistency during image synthesis.
Perhaps a more fascinating merit is that they have shown the great potential of learning 3D shapes in an unsupervised manner from just a collection of unconstrained 2D images.
If we could train a 3D-aware generative model that learns accurate 3D object shapes, it would broaden various downstream applications such as 3D shape reconstruction and image relighting.

Existing attempts for 3D-aware image synthesis \cite{chan2020pi,schwarz2020graf} tend to learn coarse 3D shapes that are inaccurate and noisy, as shown in Fig.\ref{fig:fig1} (a).
We found that such inaccuracy arises from an inevitable ambiguity inherent in the training strategy adopted by these methods. In particular, a form of regularization, which we refer to as \textit{"multi-view constraint"}, is used to enforce the 3D representation to look realistic from different viewpoints.
The constraint is commonly implemented by first projecting the generator's outputs (\textit{e.g.}, radiance fields \cite{mildenhall2020nerf}) to randomly sampled viewpoints, and then feeding them to a discriminator as fake images for training.
While such a constraint enables these models to synthesize images in a 3D-aware manner, it suffers from the \textit{shape-color ambiguity}, \textit{i.e.}, small variations of shape could lead to similar RGB images that look equally plausible to the discriminator, as the color of many objects is locally smooth.
Consequently, inaccurate shapes are concealed under this constraint.

\begin{figure}[t!]
	\centering
	\includegraphics[width=13.0cm]{figures/fig1.pdf}
	\vspace{-0.25cm}
	\caption{\textbf{Motivation}. \textbf{(a)} Previous methods like pi-GAN \cite{chan2020pi} resort to the \textit{"multi-view constraint"}, where the 3D representation is projected to different viewpoints as fake images to the discriminator. The extracted 3D meshes are often inaccurate due to the shape-color ambiguity. \textbf{(b)} The proposed approach ShadeGAN further adopts a \textit{"multi-lighting constraint"}, which motivates the 3D representation to look realistic under different lighting conditions. This constraint effectively addresses the ambiguity, giving rise to more natural and precise 3D shapes. }
	\vspace{-0.3cm}
	\label{fig:fig1}
\end{figure}

In this work, we propose a novel shading-guided generative implicit model (ShadeGAN) to address the aforementioned ambiguity. In particular, ShadeGAN learns more accurate 3D shapes by explicitly modeling shading, \textit{i.e.}, the interaction of illumination and shape.
We believe that an accurate 3D shape should look realistic not only from different viewpoints, but also under different lighting conditions, \textit{i.e.}, satisfying the \textit{"multi-lighting constraint"}.
This idea shares similar intuition with photometric stereo~\cite{woodham1980photometric}, which shows that accurate surface normal could be recovered from images taken under different lighting conditions.
Note that the multi-lighting constraint is feasible as real-world images used for training are often taken under various lighting conditions.
To fulfill this constraint,
ShadeGAN takes a relightable color
field as the intermediate representation,
which approximates the \textit{albedo} but does not necessarily satisfy viewpoint independence.
The color field is shaded under a randomly sampled lighting condition during rendering.
Since image appearance via such a shading process is strongly dependent on surface normals,
inaccurate 3D shape representations will be much more clearly revealed than in earlier shading-agnostic generative models.
Hence, by satisfying the multi-lighting constraint,
ShadeGAN is encouraged to infer more accurate 3D shapes as shown in Fig.\ref{fig:fig1} (b).

The above shading process requires the calculation of the normal direction via back-propagation through the generator, and such calculation needs to be repeated dozens of times for a pixel in volume rendering \cite{chan2020pi,schwarz2020graf}, introducing additional computational overhead.
Existing efficient volume rendering techniques \cite{liu2020neural,yu2021plenoctrees,reiser2021kilonerf,garbin2021fastnerf,neff2021donerf} mainly target static scenes, and could not be directly applied to generative models due to their dynamic nature.
Therefore, to improve the rendering speed of ShadeGAN,
we formulate an efficient \textit{surface tracking network} to estimate the rendered object surface conditioned on the latent code.
This enables us to save rendering computations by just querying points near the predicted surface,
leading to 24\% and 48\% reduction of training and inference time without affecting the quality of rendered images.

Comprehensive experiments are conducted across multiple datasets to verify the effectiveness of ShadeGAN.
The results show that our approach is capable of synthesizing photorealistic images while capturing more accurate underlying 3D shapes than previous generative methods.
The learned distribution of 3D shapes enables various downstream tasks like 3D shape reconstruction, where our approach significantly outperforms other baselines on the BFM dataset~\cite{paysan20093d}.
Besides, modeling the shading process enables explicit control over lighting conditions, achieving image relighting effect.
Our contributions can be summarized as follows:
1) We address the shape-color ambiguity in existing 3D-aware image synthesis methods with a shading-guided generative model that satisfies the proposed multi-lighting constraint.
In this way, ShadeGAN is able to learn more accurate 3D shapes for better image synthesis.
2) We devise an efficient rendering technique via surface tracking, which significantly saves training and inference time for volume rendering-based generative models.
3) We show that ShadeGAN learns to disentangle shading and color that well approximates the albedo, achieving natural relighting effects in image synthesis.

\section{Conclusion}

In this work, we present ShadeGAN, a new generative implicit model for shape-accurate 3D-aware image synthesis.
We have shown that the multi-lighting constraint, achieved in ShadeGAN by explicit illumination modeling, significantly helps learning accurate 3D shapes from 2D images.
ShadeGAN also allows us to control the lighting condition during image synthesis, achieving natural image relighting effects.
To reduce the computational cost, we have further devised a light-weighted surface tracking network,
which enables an efficient volume rendering technique for generative implicit models, achieving significant acceleration on both training and inference speed.
A generative model with shape-accurate 3D representation could broaden its applications in vision and graphics,
and our work has taken a solid step towards this goal.

\vspace{7pt}
\noindent\textbf{Acknowledgment.}
We would like to thank Eric R. Chan for sharing the codebase of pi-GAN.
This study is supported under the ERC Consolidator Grant 4DRepLy (770784).
This study is also supported under the RIE2020 Industry Alignment Fund – Industry Collaboration Projects (IAF-ICP) Funding Initiative, as well as cash and in-kind contribution from the industry partner(s).

redpajama_set_name: RedPajamaArXiv


Liberia's President, Ellen Johnson Sirleaf has written a heartfelt letter to the world over the Ebola crisis that hit her country. In the letter, which was read over the radio and transmitted worldwide, she likened the Ebola epidemic to the civil war her country faced eleven years ago which killed a lot of Liberians, crumbled their economy and vital institutions.
The president called on the international community to stop all theoretical explanations on the Ebola crisis and act fast to stop the spread of the deadly virus.
'In just over six months, Ebola has managed to bring my country to a standstill. We have lost over 2,000 Liberians. Some are children struck down in the prime of their youth. Some were fathers, mothers, brothers or best friends. Many were brave health workers that risked their lives to save others, or simply offer victims comfort in their final moments.
'There is no coincidence Ebola has taken hold in three fragile states – Liberia, Sierra Leone and Guinea – all battling to overcome the effects of interconnected wars. In Liberia, our civil war ended only eleven years ago. It destroyed our public infrastructure, crushed our economy and led to an exodus of educated professionals. A country that had some 3,000 qualified doctors at the start of the war was dependent by its end on barely three dozen. In the last few years, Liberia was bouncing back. We realized there was a long way to go, but the future was looking bright.
'Now, Ebola threatens to erase that hard work. Our economy was set to be larger and stronger this year, offering more jobs to Liberians and raising living standards. Ebola is not just a health crisis – across West Africa, a generation of young people risk being lost to an economic catastrophe as harvests are missed, markets are shut and borders are closed.
'The virus has been able to spread so rapidly because of the insufficient strength of the emergency, medical and military services that remain under-resourced and without the preparedness to confront such a challenge. This would have been the case whether the confrontation was with Ebola, another infectious disease, or a natural disaster.
'But one thing is clear. This is a fight in which the whole world has a stake. This disease respects no borders. The damage it is causing in West Africa, whether in public health, the economy or within communities – is already reverberating throughout the region and across the world.
'The international reaction to this crisis was initially inconsistent and lacking in clear direction or urgency. Now finally, the world has woken up. The community of nations has realized they cannot simply pull up the drawbridge and wish this situation away.
'This fight requires a commitment from every nation that has the capacity to help – whether that is with emergency funds, medical supplies or clinical expertise.
'I have every faith in our resilience as Liberians, and our capacity as global citizens, to face down this disease, beat it and rebuild. History has shown that when a people are at their darkest hour, humanity has an enviable ability to act with bravery, compassion and selflessness for the benefit of those most in need.
'From governments to international organisations, financial institutions to NGOs, politicians to ordinary people on the street in any corner of the world, we all have a stake in the battle against Ebola. It is the duty of all of us, as global citizens, to send a message that we will not leave millions of West Africans to fend for themselves against an enemy that they do not know, and against whom they have little defence.


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text:
The Shape of Water [Includes Digital Copy] [4K Ultra HD Blu-ray/Blu-ray] [2017]
User rating, 4.6 out of 5 stars with 1360 reviews.
4.6(1,360 Reviews)
4K Ultra HD Blu-ray / Blu-ray
A mute cleaning lady (Sally Hawkins) working in a secret U.S. government lab in 1962 befriends an otherworldly, aquatic creature (Doug Jones) who's being held there against its will. In time, she and her friends decide to help it escape from captivity, even if it means risking the wrath of a ruthless G-man (Michael Shannon). Richard Jenkins and Octavia Spencer co-star. Directed by Guillermo del Toro (Crimson Peak, Pan's Labyrinth).~Jack Rodgers
Vanessa Taylor
Sally HawkinsElisa
Michael ShannonStrickland
Richard JenkinsGiles
Doug JonesAmphibian Man
Octavia SpencerZelda
Lauren Lee SmithElaine Strickland
Michael StuhlbargMr. Robert Hoffstetler
David HewlettFleming
Nick SearcyGeneral Hoyt
Stewart ArnottBernard
Nigel BennettMihalkov
Martin RoachBrewster Fuller
Allegra FultonYolanda
John KapelosMr. Arzoumanian
Morgan KellyPie Guy
Dru ViergeverMilitary Policeman
Wendy LyonSally (Secretary)
Diego FuentesWorker
Guillermo del ToroProducer
J. Miles DaleProducer
Guillermo del ToroScreen Story
Dan LaustsenCinematographer
Alexandre DesplatComposer (Music Score)
Sidney WolinskyEditor
Paul Denham AusterberryProduction Designer
Nigel ChurcherArt Director
Daniel KrausAssociate Producer
Luis M. SequeiraCostume Designer
Pierre HenryFirst Assistant Director
Robin D. CookCasting
Brad ZoernRe-Recording Mixer
Christian CookeRe-Recording Mixer
Dennis BerardiVisual Effects Supervisor
Glen GauthierProduction Sound Mixer
J. Miles DaleUnit Production Manager
Jordan SamuelDepartment Head Makeup
Nathan RobitailleSupervising Sound Editor
Steve LucescuStunts Coordinator
Action and Adventure,Adventure,Fantasy
Fantasy Drama,Romantic Adventure,Sci-Fi Adventure
Includes Digital Copy, 4K Ultra HD Blu-ray/Blu-ray
4K Ultra HD Blu-ray, Blu-ray
Rating 4.6 out of 5 stars with 1360 reviews
(1,360 Reviews)
Page 1 Showing 1-8 of 1,360 reviews
MovieWatcher
A Sci-Fi love story in Baltimore 1962
An alien creature has been caught by the government and being mistreated. The Russians are trying to steal the information. A blue collar worker falls in love with the creature and is able to communicate with it. Excellent movie premise with an excellent storyline and excellent actors and actresses. A five star production.
This review is from The Shape of Water [Includes Digital Copy] [Blu-ray/DVD] [2017]
PurpleNarwhal
Such A Weird Movie
I have to say, I wasn't too sure what to expect going into this movie. I ended up loving it, its so weird and quirky. It's beautifully put together and will keep you entranced throughout the whole movie. Definitely recommend buying.
RBlenheim
Another Del Toro fantasy masterpiece.
Guillermo del Toro is today's master of fantasy, having been a childhood lover of monsters growing up in Guadalajara, Mexico, before making some of the finest films of recent years -- from the ghostly horror of "The Devil's Backbone" in 2001 to his gothic horror/romance, "Crimson Peak" in 2015. Indubitably, however, his greatest film is "Pan's Labyrinth", the 2006 film many of us consider the finest fantasy film ever made. Now he's broken new ground with "The Shape of Water", one of the year's most beautiful films. Set in Baltimore in the year 1962 at the height of the Cold War, the plot follows a mute janitor at a secret government laboratory who forms a bond with a captured amphibian of the "Creature of the Black Lagoon" variety. Her name is Elisa, and Sally Hawkins plays her with an artistry that seems to reach back to the silent days of Chaplin and Keaton. Michael Shannon, with devoted viciousness, plays the right-wing Colonel Strickland, someone more interested in dissecting the creature for exploitation purposes than he is concerned over the space race with the Soviets. Del Toro saw "The Creature from the Black Lagoon" on TV at 7 years old and it changed his life. Wishing a different ending for it in which the Gill Man and co-star Julie Adams would consummate their romance and live 'happily ever after', he wrote various scripts of a remake through the years that Universal studio executives wound up rejecting. "The Shape of Water" is the result of del Toro's dream, and now today, with more permissive filmmaking allowable, he's able to deal with the previously verboten issue between fish and human. The resulting film is a worthy accomplishment not only for its production design (embodying various shades of green) and its special effects, but also for attaining the level of a genuine adult fairy tale that deals with issues of trust, tolerance, and love in the human condition -- but most of all what it's like to be an outsider (whether a lonely mute woman, gay man, overweight black woman, or an amphibious sea creature). "This is a healing movie for me," del Toro states; one likes to think it would be for viewers as well.
Bizzi
Posted 3 weeks ago .
Owned for 2 months when reviewed.
It's nice to purchase both dvd and Blu-ray in one package. This was an excellent movie. Easy to find in Best Buy as the movies are alphabetical which makes finding what you want effortless and quick so you can shop for other items.
HoratioSanz
Although deserving of praise for the value it places on authenticity and genuine concern for life, it is somewhat disconcerting and has a decidedly anti government and anti military worldview. A sort of "love in spite of the powers that be" theme, which plays off of the themes of current political movements. But very well written and well made, and definitely worth watching.
Moshii
You've already come this far.
Owned for more than 2 years when reviewed.
This was a gift. It's a very unexpected enjoyable movie about a man sleeping with a fish woman. Super bizarre but what else would you expect from a movie called " the shape of water". I don't know why it's enjoyable just like I don't know why puppies make me smile.
CapeCodIan
Del Toro Oscar winner for Best Director & Picture
Director Guillermo del Toro's best movie since Pan's Labyrinth - The Shape of Water won him a well deserved Best Director Oscar at the 90th Academy Awards and the movie won the Best Picture Oscar. Del Toro originated the idea based on childhood memories of Creature from the Black Lagoon and co-wrote the screenplay and co-produced the movie.
Khidafi
Fabulous Movie! Academy Award!
Owned for 1 year when reviewed.
This was so worth watching! It was an excellent movie that captured my attention from the beginning! I love stories that make you want to keep watching and waiting to see what happens next! I highly recommend seeing this!

redpajama_set_name: RedPajamaCommonCrawl


of each moment and being fully immersed in all that is going on each day. I've found such joy and freedom in being grateful before I get out of bed and reviewing my day at night and blessing all that has come to me. We truly are meant to be where we are. Letting go and trusting is so powerful in allowing one to be in alignment with our Higher Self.


text:
Deng Tuo (邓拓) (1912 – ) était un intellectuel, poète et journaliste chinois né en 1912

Il devient un cadre du Parti communiste chinois et éditeur en chef du Quotidien du Peuple entre 1948 et 1958, avant son suicide au début de la Révolution culturelle.

Notes et références

Poète chinois du XXe siècle
Naissance en 1912
Membre du Parti communiste chinois
Décès en mai 1966
Suicide par moyen indéterminé
Écrivain chinois du XXe siècle
Suicidé de la révolution culturelle
Écrivain suicidé
Suicide en Chine
Naissance dans la province du Fujian
Décès à Pékin

redpajama_set_name: RedPajamaWikipedia


text:
New York Teenager Helps Spread Positivity to Families in Need
Daily Point of Light # 6482 Mar 25, 2019 By Brenda Solis
Alyssa volunteers weekly at the Ronald McDonald Houses in Long Island and Westchester, NY, but has even traveled to Louisiana to volunteer at the Houses there./Courtesy Alyssa Dass
Alyssa Dass thinks everybody needs a little positivity in their lives — and she spreads much more than a little of her own positivity to the families at her local Ronald McDonald Houses. About once a week, the teenager visits the Long Island and Westchester-based houses, which are two of the hundreds of Ronald McDonald Houses across the world that provide housing and meals to families with children receiving medical treatment at nearby hospitals. During her visits, Dass cooks meals for about 100 people staying at the houses, bakes them desserts and offers a smile and an ear to the visiting families. Throughout the year, she also collects pop tabs to help the Ronald McDonald House with fundraising, as well as various other donations the families may need, from stuffed animals to socks to gift cards.
Despite the constant help she's provided to the Ronald McDonald Houses since she began volunteering five years ago, Alyssa insists its the families that are the ones helping her. She says they've given her a brighter outlook on life, helped her mature as a person and even influenced what career she wants to one day pursue — robotic cardiology, so she can help save people and give them a second chance at life.
"[The Ronald McDonald families have] given me a second chance at enjoying life and a second chance at realizing who I am," Alyssa said. "So I wanted to be able to share that with people when I get older."
For providing meals, donations and joy to families when they need it the most, Alyssa is today's Daily Point of Light Award recipient. Points of Light spoke with her to learn more about how she helps the Ronald McDonald House.
Describe your volunteer role with the Ronald McDonald House.
I started volunteering for the Ronald McDonald House about five years ago. I started volunteering there because one of my friends … got into a very bad car accident. Her family was admitted into the Ronald McDonald House. She lived all the way in Virginia and that's where they were keeping her family and treating her, and I felt I couldn't do anything so I wanted to give back in some way for everything the Ronald McDonald House was doing for her and her family. So about a couple weeks after that, I started volunteering for the Ronald McDonald House [in Long Island and Westchester, New York]. I went to all the fundraisers, I started baking and cooking. I also collect pop tabs for their Pop Tab Palooza. I just try to make sure that I'm involved in anyway that I can be, because I'm so thankful that the Ronald McDonald House does exist, because it does help many families, not only in New York but in many different states. And whether it's people that I know or not, I'm just glad that people are still feeling like they have a home during their rough times.
I volunteer at the Ronald McDonald House maybe once every week, sometimes once every two weeks. I'm there a lot and whether I'm there or not, I'm always doing stuff outside. I do bake there and cook there, but I also do clothing drives or I collect pop tabs like I said before. The pop tabs just help to fundraise, they can recycle them. I am a Girl Scout as well, so I do different drives. I'm starting to do a gift card drive for the Ronald McDonald House because the ones I work with in Long Island and Westchester, they need gift cards, sometimes toiletries. During Christmas time I collect stuffed animals or socks. Just little things because I feel it's really important to help in any way I can.
Alyssa likes to invite girls from other activities she's involved in, such as Girl Scouts and pageants, to come cook with her./Courtesy Alyssa Dass
Who exactly does the Ronald McDonald House serve?
The Ronald McDonald House serves the families of children who are hurt or injured or have been in very traumatic injuries, accidents, [or] if babies were born with some kind of deficiency. The Ronald McDonald House is a building near children's hospitals so they house families and they make them feel like they have a home and are comfortable. I find it really interesting because the Ronald McDonald House also suits the younger siblings, the older siblings, the moms, the dads. They have a lot of different rooms and comfortable places where they can just feel at home and feel comfortable. You're at the hospital all day long worrying about the person who was hurt and your loved one who is trying to get treatment, and you can still come to a place that treats you well and gives you food — breakfast, dinner, lunch, snacks, desserts — and just makes you feel comfortable at all times.
What inspires you to make the time to volunteer when you also have school and other activities?
My parents definitely inspire me to do all these things. Just knowing everything that goes on in this world, I think everybody needs a little bit of positivity. My parents always raised me to have this mindset where it's better to give than to want to receive. I think in this day and age there's so many teens who have these negative mindsets because they're going through so much and they think they're the only ones going through stuff. I think that's why the Ronald McDonald House hits so close to home, because not only does it help the children but it helps the families to feel happy in some way. It brings positivity to their life. I go in thinking that I'm helping so many families and I come out realizing they helped me more than they can realize. Because I learn so much from them when I get to talk to them. And I get to be more mature. I get to learn more about myself and other people that I don't even know, and just the way the world works.
What are the families' reactions when you come there to donate or cook a meal to them?
I truly believe that they are so thankful. Even when you just say 'Good morning' to them, or when you're just plating the food, they look so happy and so grateful. That makes me feel so good because they're going through so much and I think the least thing I can do is just cook something for them or bake cupcakes, and yet it cheers them up. When you just give them a big smile on your face and say 'Hello, how are you doing,' they automatically just feel so comfortable, so happy. They actually feel like someone wants to listen to what they have to say. And a lot of the conversations I've had with some of the families when they're going through things, I see them again and again and they're just like, 'Oh my god, thank you, I'm so happy you keep coming back and I thank you for being so young.' It makes me feel so good because I know I'm making a difference and I know that I'm helping more than one family, I'm helping so many.
What have you learned through your experiences as a volunteer?
I've learned to just live life the best way that I can. You just have to enjoy who you are and what you do because you don't know how much more time you will have. And to just always keep your head high and have hope. I was talking to a mom, and her kid was in a bit of critical condition. She told me to just stay kind and keep my head high and always have hope and I think that's always stuck with me.
Why do you think it's important for others to give back?
I think it's very important because you get to learn different things and you grow as a person and you also get to help people. I think that's the most important thing. And that helps yourself, when you're also helping others. I've always thought whether I'm helping one person, that the ripple effect will continue. You give one person a smile, they'll feel good for the rest of the day, so then they'll smile at everyone else. I think just the fact of spreading kindness, it sounds very cliche but it is so true. I think it's very important for teenagers especially, kids who are my age, especially girls who are my age, to be more appreciative of who they are and what they have and volunteering really helps you to realize that.
What do you want people to learn from your story?
I would love for people to learn to just always give back. I believe I have a heart for service. And I want people to be able to spread kindness. I think there's a lot of negativity in this world and I want people to realize that the smallest person with the biggest dream can spread the most kindness. Everyone has positivity in them, they're just scared to share it and I think you shouldn't be scared. You shouldn't be scared to live life and a part of life is having kindness and positivity.
Do you want to make a difference in your community like Alyssa? Click here to find local volunteer opportunities.
Post written by Morganne Mallon.


If one uses a walker on fulltime basis will require the best walker bags to carry the must-have items around the house or outdoor. Those suffering from joint pain, post-surgical operation, Alzheimer's, Parkinson's disease, handicap, and essential tremors can grab their items easily. Using the best walker bags will help them to remain independent even when there is no one around to assists.
Moreover, the best walker bags have many pockets that help the seniors and the others with walking difficulties to feel safe while carrying different items. When they have to call out for caregivers to help them to take things for them, this may be so discouraging.
The best walker bags enhance the mobility of seniors and hence increasing their will of moving about doing things for themselves. These bags are designed for easy grabs and providing a simple solution for daily activities. Caregivers should not worry about the safety of their patients because the best walker bag will carry the items while they balance the walker with two hands.
The best walker bags well sort seniors and those suffering from several health conditions that force them to a walker. These bags allow them to store personal items like medications, books, magazines, pens, and cups. They can take their medication at the right time if it's in the bag and no one around to help. A clock with day and date can remind seniors to take medicine on time.
The elderly and people with disabilities would love doing the simple things for themselves which makes them stay happy such as cooking for themselves by using a simple microwave or taking a bath by using a bath lift. A walker bag can carry all the necessary things so that seniors can do the outdoor activity and meet their old friends independently. This will help them to keep a good mood and improve their self-esteem.
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Without a walker bag or a walker tray, the seniors may struggle in balancing their walker and carrying the items whether indoor or outdoor. While trying to be stable, they could lose control and get into an accident that will cause more harm to their current condition.
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A good number of pockets will enable the seniors to carry the essential things needed regularly for daily activities. When going to the hospital or office, some document needs proper storage and not to be mixed with other things. Many pockets enable one to arrange their items well to avoid misplacing crucial things like medication.
It is essential for the walker bag is attachable to many manufacturers' models. The first walker may be destroyed and still purchase another one which is compatible with the same kits. This saves the cost of acquiring new walkers and bags every time a walker is spoiled.
Some elders need larger walker bags because they have to carry oxygen and other items. If they only need to move pill bottle, adaptive eating utensils, pens and books then just a small walker bag is required. Consider buying a walker bag with long straps that are adjustable to fit in your walker, wheelchair or rollator.
Choosing the best walker bag from the market may be difficult because of the many products available and that is the reason we have listed the best walker bags for you. These bags provide a perfect solution for those using walkers, and wheelchairs through the day. Make your seniors happy again by purchasing the best walker bag to enable them to work independently.
This walker bag is universal and fits many rollators, scooters, walkers, and wheelchairs. RMS Tote bag is designed from quality premium polyester that is water resistant and durable. It has both front and back storage pockets. The bag features 8 inches front pocket for easy reach of items and a zippered compartment for storing large things such as iPad.
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Vive water-resistant walker bag fits in our top best walker bags because it is designed to meet all types of walker styles and width. With loop fasteners that are adjustable enables it to attach easily to the front of all walker models including standard, dual-point folding and bariatric walkers. Additionally, the inner pocket is large and zippered to quick store items at hand. The bag is made from sturdy nylon and can hold vital medical supplies, change of clothes or a purse.
Again, Vive walker bag has three exterior compartments that help to carry daily activities' items such as glasses, drinks, snacks, and electronic devices. The walker bag is securely held in place by a heavy duty fastening material. This best walker bag comes with seven loops reinforced for secure attachment to any walker.
Moreover, this convenient bag is manufactured with lightweight, durable and water-resistant material that allows your items to stay dry and safe. It's machine washable with cold water and then allowed to dry. Vive provides 60 days money back guarantee, and hence customers can purchase this without fear.
Olivia & Aiden walker bag features strong adjustable Velcro loops that can easily be attached to standard walkers, bariatric walkers, and wheelchairs. Its dimension is 13 inches long, 4 inches wide and 8 inches high, that is large enough to store multiple items. The central compartment is designed with a secured zippered inner pocket, two front pockets, large mesh rear pocket, and two insulated water bottle pockets.
This best walker bag can carry tissues, reading glasses, phones, wallets, medications, keys, and snacks hence seniors can keep the essential items near. Olivia & Aiden walker bag is manufactured from a lightweight and durable material designed with a Velcro closure to quickly access details(See also velcro shoes for elderly). A 60 days refund or replacement is guaranteed if a customer is not satisfied with the product.
The comfortable attachable double-sided pouch is designed with a cup holder and comes with 8 to 9 pockets in the front and back to efficiently organize your items for quick grabbing. It can hold things like keys, water bottle, iPad, newspaper, and reading glasses.
Also, the heavy duty walker accessory has six Velcro straps to loop and hook the bag on the sides of a walker. Besides, it contains carabiner keychain clip, padded organizer pouch, and a cup holder.
This walker bag for elderly has secured six pockets and is easy to attach on the frame of all standard walker to store essential items. Secure walker bag fits our top best walker bags because it has fastening loops and multiple hooks for quick attachment on both narrow walker and wide walkers. The walker bag also sorts those having limited dexterity with an O-ring zippered large expandable pockets that can store large items.
However, best walker bag is made of durable, water-resistant nylon strong enough to withstand daily use rigor. This bag features a back and front pockets to store small items and has a one-year replacement warranty.
Pembrook walker bag is a perfect mobility device accessory that allows one to organize the items required for the day systematically. Customers have given this walker bag outstanding reviews that show that it is a fantastic product. With five pockets design, it allows a flexible arrangement of items and can be attached to backrest, armrest and on different support pieces of walkers.
Most walkers, scooters, wheelchairs, and rollators are compatible with this Pembrook walker bag that expands more than 2 inches when loaded with items. The stress points are reinforced, and it's stitched with double seams. Moreover, side walker bag fits in our list since it is designed from 70-Denier DuroTec nylon, which is water resistant. These types of best walker bags help one to keep their vital documents and medication dry. The reflective stripes it contains can be visible when 100m away.
The best walker bag enables the elderly, disabled and seniors to do things independently without seeking assistance from other people to carry items for them. Some of these best walker bags are waterproof hence your pieces are very secure. It also increases the ability to serve themselves and move around freely.
However, You could find it difficult to select the best walker bag for you or your patient since there are so many products on the market. With the list we have compiled, you will have an easy time finding the best walker bag.
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Home / Shop / PRINTS / FORMIDABLE FOES
FORMIDABLE FOES
SKU: N/A Categories: Canvas Giclées, Jim Laurier, PRINTS Tags: Defense of the Reich, FW190, Luftwaffe
500Limited Edition $185.00 Artist signed print
FORMIDABLE FOES quantity
50Giclee Canvas Proof $425.00 Ships rolled.
By the early winter of 1944 Allied bombing missions to Germany had become an almost daily occurrence. Most Luftwaffe fighters had been re-assigned to "Reich's Defense" duties in an attempt to thwart the ever-increasing destruction of German cities.
One German fighter which played a significant defensive role was the advanced Focke-Wulf Fw-190D. With its superb high altitude performance ability and heavy hitting 20mm guns, it could do severe damage to any aircraft it found in its sights. Usually three or four well-aimed 20 mm rounds could mean the end of service for a bomber.
On the other side, the B-17 Flying Fortress and B-24 Liberator were dangerous not just as bombers, but as defensive fire platforms, hence the name 'Fortress". Each bomber was equipped with about 10 -12 .50 caliber machine guns which could hit targets a mile away with accuracy and lethality.
Luftwaffe pilots didn't relish the idea of attacking the bombers streams and they calculated their odds of making it though one firing run on heavy bombers as 50:50. More than one bomber might be firing at an attacking Luftwaffe fighter and it's a wonder that the bombers didn't shoot each other down. The fact that Allied bombers destroyed more enemy fighters in WWII than all other means combined stands as stark testimony to the level of danger they represented to attacking aircraft.
Like two top predators circling each other in a contest to the death, aware of the others abilities, extreme caution and skill was necessary to ensure survival and victory was equally attainable by either side.
THE CANVAS GICLÉE EDITION
This canvas edition measures 30 x 22 inches and has been signed by the artist.
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BIRTH OF A LEGEND
GREYCAP LEADER
STORMBIRDS RISING


Take care of your clothes the right way, and they'll last longer and feel better.
Good cycling clothes are an investment--one that rubs right up against your most treasured body parts. Though care instructions from manufacturers seem to vary from the extreme "hand wash in our proprietary soap and dry with a soft lint-free towel" to the lackadaisical "machine wash, tumble dry," the truth is out there. Or, rather, it's here, in our guide to the smart way to care for your clothes and keep smelling fresh.
Use the most basic detergent you can find, without dyes, perfumes or softeners. Cycling clothes are made of high-performance fabrics meant to channel moisture away from your skin. Any residue from fancy soaps or fabric softeners will clog up the works, keeping the fabric from doing its job well.
Some manufacturers recommend against using liquid detergents--straight, concentrated detergent is potent stuff--but as long as you run water into the washer first, add the detergent, then the clothes, you'll get gentler, easier-to-rinse cleaning. A note on wool: Treat it like you would any other wool garment, using a wool-specific soap and machine washing only if the tag says it's okay.
Zip zippers and close hook-and-loop fasteners before washing--both can chew up clothes faster than skidding on loose gravel. Also, turn screenprinted or sublimated clothing inside out to protect the graphics. Before you wash, sort your clothes--your cycling gear shouldn't be mashed in with your hard-tumbling jeans or a mess of heavy towels. They're "delicates" and should be treated as such. Use the delicate cycle on your washing machine, too.
Wash in cold or lukewarm water. If your clothes still smell like detergent at the end of the cycle, run them through for an extra rinse.
Heat is used in the finishing process of most stretch fabrics, so a little hot air can give clothing a boost (unless it's wool--in which case, it's best to avoid the dryer; lay the damp clothes on a towel to dry). But high heat, or drying in a Laundromat-type commercial dryer, will lead to shrinkage--not the temporary Seinfeld kind--and damage the elastics. It could also bake in any lingering funk. Stick with low heat, and only for a little while, as high-performance fabrics dry quickly. And remember to skip the fabric-softener dryer sheets.
Line-drying nonwool clothing is fine, too, as long as the clothes are out of direct sunlight--the added UV exposure can cause fabrics to break down prematurely.
1. How often must I wash my stuff? As often as you want, as long as you follow the recommended care instructions. If you tend to sweat like a pig, wash your gear after every ride. But if your clothes still smell okay and you're all about conserving water, wash them when you feel it's necessary.
2. What if I don't wash my clothes the way the tag says? It's always best--though not always convenient--to follow the tag instructions. If you decide to ignore the manufacturer (or us) and go your own way, your clothes will still be okay. Probably. For a while. But they won't last as long or work as well as they could if you wash them with extra care.
3. Um, when it comes to washing my chamois, is there something I should know? Most chamois don't require special cleaning, unless you have an exceptionally old-fashioned pair of shorts with a real leather chamois. If you line-dry your shorts, be sure to hang them chamois-side out.