# ARF-Plus: Controlling Perceptual Factors in Artistic Radiance Fields for 3D
Scene Stylization

Wenzhao Li1, Tianhao Wu1, Fangcheng Zhong1 Cengiz Oztireli1, 2

###### Abstract

The radiance fields style transfer is an emerging field that has recently
gained popularity as a means of 3D scene stylization, thanks to the
outstanding performance of neural radiance fields in 3D reconstruction and
view synthesis. We highlight a research gap in radiance fields style transfer,
the lack of sufficient perceptual controllability, motivated by the existing
concept in the 2D image style transfer. In this paper, we present ARF-Plus, a
3D neural style transfer framework offering manageable control over perceptual
factors, to systematically explore the perceptual controllability in 3D scene
stylization. Four distinct types of controls - color preservation control,
(style pattern) scale control, spatial (selective stylization area) control,
and depth enhancement control - are proposed and integrated into this
framework. Results from real-world datasets, both quantitative and
qualitative, show that the four types of controls in our ARF-Plus framework
successfully accomplish their corresponding perceptual controls when stylizing
3D scenes. These techniques work well for individual style inputs as well as
for the simultaneous application of multiple styles within a scene. This
unlocks a realm of limitless possibilities, allowing customized modifications
of stylization effects and flexible merging of the strengths of different
styles, ultimately enabling the creation of novel and eye-catching stylistic
effects on 3D scenes.

##  1 Introduction

The neural style transfer technique (Gatys, Ecker, and Bethge 2016) unravels
the mysteries of the artist. With the aid of this technology, a photograph may
look to have been produced by a well-known artist. Video style transfer
(Ruder, Dosovitskiy, and Brox 2018) extends the original neural style transfer
from the 2D image domain to the temporal domain as well. 3D scene style
transfer further extends it to the spatial-temporal domain, offering enhanced
artistic transformations and immersive aesthetic experiences.

Figure 1: An overview of ARF-Plus framework. It facilitates the control of
various perceptual factors and permits the use of multiple style images as
input, resulting in perceptual flexibility in 3D scene stylization.

Nonetheless, 3D scene style transfer is not an easy task due to the domain gap
between 2D and 3D. Traditional 3D scene stylization techniques (Huang et al.
2021; Mu et al. 2022; Yin et al. 2021; Höllein, Johnson, and Nießner 2022) are
often based on mesh or point-cloud representations. The limited reconstruction
accuracy and discrete geometric representation in these models constrain the
stylization performance, resulting in observable artifacts in challenging
real-world circumstances (Zhang et al. 2022). The Neural Radiance Fields
(NeRF) (Mildenhall et al. 2021) represents the optics of the 3D scene without
explicit geometry which is inherently discontinuous. With its superior
performance in 3D reconstruction and view synthesis, many researchers have
attempted to perform 3D stylization based on radiance fields (Chiang et al.
2022; Huang et al. 2021, 2022; Zhang et al. 2022). However, they have focused
on optimizing a unified style transfer across the whole scene, neglecting the
control of perceptual factors that influence visual perception.

Color preservation control (Gatys et al. 2016), stroke size control (Jing et
al. 2018; Reimann et al. 2022), spatial control (Castillo et al. 2017; Yu, Wu,
and Wang 2019; Gatys et al. 2017), and other types of perceptual controls have
been widely applied in the image domain style transfer. The research gap in
the radiance fields style transfer hinders the diversity of choices and
potential applications in 3D scene style transfer. In certain application
scenarios, users may desire to selectively apply an abstract art style only to
the scene’s background, while keeping the main objects (e.g., people) in a
realistic appearance. Alternatively, users may wish to add unique aesthetic
effects to specific objects to create cartoon-like characters. Moreover, users
might prefer to retain the original colors of the scene while applying
transferred patterns and textures from a given style. Furthermore, users may
have a preference to adjust the size of patterns or brushstrokes in the
stylized outcomes for aesthetic adjustments. All these diverse 3D radiance
fields style transfer requirements and numerous promising application
scenarios are yet to be fully realized.

Hence, exploring perceptual control in 3D stylization on radiance fields and
developing algorithms that offer perceptual-feature-aware controls hold
promising potential for meeting application-level demands. We introduce ARF-
Plus, a framework that enables the manipulation of four perceptual factors in
3D stylization, namely, color preservation, stroke scale, selective spatial
area, and depth-aware perception. Our main contributions are listed as
follows:

  * •

We introduce ARF-Plus, a framework to _simultaneously_ manipulate the
influence of various perceptual factors on 3D stylization. To the best of our
knowledge, we are the _first_ to explore the control of various perceptual
factors in the stylization of 3D models based on radiance fields.

  * •

We demonstrate the effectiveness of ARF-Plus in controlling the aforementioned
perceptual factors on 3D stylization through a series of qualitative and
quantitative evaluations.

##  2 Background and Related Work

3D style transfer entails applying a reference style’s visual characteristics
to a target 3D scene while maintaining the 3D structure itself. Due to the
exceptional 3D reconstruction capabilities of radiance fields, radiance fields
style transfer has emerged as a promising approach to enhance the outcomes of
3D style transfer. Recent studies (Chiang et al. 2022; Fan et al. 2022; Huang
et al. 2022; Nguyen-Phuoc, Liu, and Xiao 2022; Zhang et al. 2022; Chen et al.
2022b) have shown that style features can be transferred from a given style to
an entire real 3D scene represented by radiance fields.

Zhang Kai et al. (Zhang et al. 2022) present the Artistic Radiance Fields
(ARF) approach, which is highly effective at capturing style characteristics
while preserving multi-view consistency. They present and implement a nearest
neighbour-based feature matching (NNFM) loss, which can produce a consistent
multi-view visual experience and achieve state-of-the-art visual quality.
Additionally, their approach is independent of the radiance fields
representation, making it applicable to a wider range of systems, including
Plenoxels (Yu et al. 2021), NeRF (Mildenhall et al. 2021), TensoRF (Chen et
al. 2022a), and others. We choose ARF as the basis of our architecture for two
primary reasons. Firstly, ARF is currently one of the best-performing state-
of-the-art methods. It captures style details while maintaining multi-view
consistency and produces more convincing outcomes than other state-of-the-art
techniques such as Huang et al. (Huang et al. 2022) and Chiang et al. (Chiang
et al. 2022). Secondly, the ARF method is versatile and adaptable to various
radiance fields representations. As a result, our ARF-Plus can benefit from
ARF’s exceptional performance and inherit ARF’s broad applicability.

Based on our best knowledge, the concept of perceptual control has not been
well utilized in the radiance fields style transfer. NeRF-Art (Wang et al.
2023) achieves text-driven neural radiance fields stylization, by addressing
the mapping between a text prompt and a particular given style or aesthetic
pattern. However, its matched stylized result with a given text prompt is
still a uniformly stylized scene. Ref-NPR (Zhang et al. 2023) proposes a ray
registration process, in order to maintain cross-view consistency and
establish semantic correspondence in transferring style across the entire
stylized scene. While Ref-NPR mentioned the concept of “controllable”, its
notion of controllability pertains to semantic correspondence and
geometrically consistent stylizations. This differs from the user-level
controllability discussed in this paper, where we aim to offer enhanced
flexibility, enabling individuals to effectively customize controlled
stylization. Nevertheless, similar to the demand for customized and diverse 2D
image style transfer, there exists a substantial market for radiance field
style transfer with personalized and varied characteristics. Therefore, our
primary objective is to fill this research gap, and the subsequent sections
will present our initial endeavours and discoveries.

##  3 Methodology

As illustrated in Figure 1, ARF-Plus involves the conversion of a photo-
realistic radiance field, reconstructed from photographs of a real-world
scene, into an artistic style radiance fields with a variety of perceptual
factors controls. Initially, we reconstruct photo-realistic radiance fields
from multiple photographs to represent a 3D scene. Next, with the given style
image(s), we stylize the photo-realistic radiance fields in a fine-tuning
process. The style transfer process of radiance fields is formulated as a
problem of optimisation. Images are rendered from the radiance fields across
different viewpoints in a differentiable manner. A variety of loss functions
and gradient updating strategies are employed based on the selected perceptual
controls. After the stylization process is completed, we achieve the stylized
3D scene radiance fields and can generate free-viewpoint and consistent
stylized renderings from it.

###  3.1 Color Preservation Control

The general radiance fields style transfer algorithms convert the photo-
realistic radiance fields, which depict a real 3D scene, to match the style of
a specified style image. Once the stylization process is complete, the color
distribution of the style reference is also transferred. However, in some
cases, one may prefer to retain the colors of the photo-realistic 3D scene and
only learn the painting patterns, while ensuring that stylization does not
result in unnatural colors (e.g., the sky turning green or the grass becoming
red).

Our method is inspired by the luminance-only algorithm proposed by Gatys et
al. (Gatys et al. 2016). Their work is based on the utilization of the $YIQ$
color space, which effectively separates luminance in $\mathit{Y}$, and color
information in $\mathit{I}$ and $\mathit{Q}$. As shown in Equation 1, we
extract the luminance channel in the rendered view $\hat{\mathbf{X}^{Y}}$ and
the luminance channel of the style image $\mathbf{X}_{\text{style}}^{Y}$ for
style loss $\mathcal{L}_{\text{style}}$ calculation, while keeping the RGB
channels for the content loss $\mathcal{L}_{\text{content}}$ calculation.

$\begin{split}\scalebox{0.9}{$\mathcal{L}_{\text{total}}=\
$}&\scalebox{0.9}{$\alpha\cdot\mathcal{L}_{\text{style}}(F_{\ell_{s}}(\hat{\mathbf{X}^{Y}}),F_{l_{s}}(\mathbf{X}_{\text{style}}^{Y}))$}\\\
&\scalebox{0.9}{$+\
\beta\cdot\mathcal{L}_{\text{content}}(F_{\ell_{c}}(\hat{\mathbf{X}}),F_{\ell_{c}}(\mathbf{X}_{\text{content}}))+\gamma\cdot\mathcal{L}_{\text{tv}}$}\end{split}$
(1)

The style loss $\mathcal{L}_{\text{style}}$ enables the radiance fields to
focus on the luminance variations (of pattern shapes) present in the style
image, without explicitly learning its color. The content loss
$\mathcal{L}_{\text{content}}$ quantifies the RGB color differences between
the rendered view $\hat{\mathbf{X}}$ and the photo-realistic ground truth
$\mathbf{X}_{\text{content}}$ at the level of content features.
$\mathcal{L}_{\text{tv}}$ is the total variation regularizer. $F_{\ell_{c}}$
and $F_{\ell_{s}}$ stand for the representation of content features and style
features, respectively. $\alpha$, $\beta$ and $\gamma$ are scalar weights.

###  3.2 Scale Control

Stroke sizes and pattern shapes in drawing refer to two fundamental aspects of
mark-making and line creation within an artistic composition. Stroke sizes
pertain to the thickness or width of lines, brushstrokes, or marks used in a
drawing, as shown in Figure 3 (a). Pattern shapes involve the specific forms,
designs, or arrangements of strokes or marks that are repeated or used
consistently within the artwork, as shown in Figure 3 (b). Artists have their
own way of arranging strokes of different sizes and shape patterns, which
reflects unique artistic “styles”. For instance, Pablo Picasso favored simple
shapes and a limited color palette when painting objects, people, and
landscapes, whereas Claude Monet employed small, playful brush strokes to
create his impressionist works. It is worth noting that, in some cases, the
stroke and pattern sizes of the original style image may not be appropriate
for the 3D scene after the style transfer has been performed, due to the
differences (e.g. in size) between the depicted content in the style image and
the 3D scene. Therefore, adjusting the pattern scale to match the 3D scene
becomes an issue that requires attention.

#### Single Style Scale Control

Inspired by the work of Jing Y. et al. (Jing et al. 2018) on stroke-
controllable image style transfer, we take into account the two factors
mentioned in their work that influence the scale of style patterns: the
receptive field and the size of the style image.

$\mathcal{L}^{\mathcal{T}_{S}}_{\text{style}}=\sum_{l\in\left\\{l_{1},...,l_{5}\right\\}}w_{l}\cdot\mathcal{L}_{\text{style}}\left(\mathcal{F}_{l}\left(\mathcal{R}\left(\mathbf{X}_{\text{style}},\mathcal{T}^{l}_{S}\right)\right),\mathcal{F}_{l}\left(\hat{\mathbf{X}}\right)\right)$

(2)

As shown in Equation 2, $\mathcal{F}_{l}$ represents the feature map at $l$
layer blocks, where $l$ can be one of the five VGG-16 layer blocks
$\left\\{l_{1},l_{2},...,l_{5}\right\\}$. We adjust the range of the receptive
field by altering the selection of $l$. $\mathcal{R}$ denotes the resize
function for the style image. According to the specified scale
$\mathcal{T}^{l}_{S}$ for each layer block, $\mathcal{R}$ resizes the style
image for each layer block for feature extraction. The style losses from
different layer blocks are subsequently combined together to form the total
style loss $\mathcal{L}^{\mathcal{T}_{S}}_{\text{style}}$, with $w_{l}$
controlling the corresponding weight. By having the flexibility to adjust both
the size of the style image and the range of the receptive field, we are able
to attain continuous control over the scale.

$\mathcal{L}_{\text{total}}=\alpha\cdot\mathcal{L}^{\mathcal{T}_{S}}_{\text{style}}+\beta\cdot\mathcal{L}_{\text{content}}(F_{\ell_{c}}(\hat{\mathbf{X}}),F_{\ell_{c}}(\mathbf{X}_{\text{content}}))+\gamma\cdot\mathcal{L}_{\text{tv}}$

(3)

Multiple settings might be purposefully employed to highlight either the
delicate patterns or the harsh outlines within a single style image. Giving
different weights to the losses of shallow and deep layers will achieve this.
The limitless adjustment of scaling settings also allows for the creation of
innovative aesthetic patterns. The total style loss
$\mathcal{L}^{\mathcal{T}_{S}}_{\text{style}}$ is then added to the style
transfer loss function to provide scale control in 3D scene stylization, as
shown in Equation 3. There are three key aspects where our work differs from
that of Jing Y. et al. (Jing et al. 2018): 1) In contrast to 2D image style
transfer, we use the improved style transfer loss function for 3D radiance
fields style transfer, leading to a different overall model architecture. 2)
In order to ensure consistency across multi-view scenes, we utilize NNFM loss
(Zhang et al. 2022) rather than the Gram matrix to calculate the style loss.
3) We optimized their continuous size control strategy. In addition to
assigning different weights to the output feature maps, we allow alternative
style image size $\mathcal{T}^{l}_{S}$ for each VGG layer in order to produce
more adjustable results. In other words, it is possible to have different
$\mathcal{T}^{l}_{S}$ for each layer in our method.

#### Multiple Style Scale Control

There may arise a need to blend multiple styles. For instance, it may be
desirable to incorporate the fine brushstrokes of one painting with the bigger
shapes apparent in another artwork and blend them seamlessly into the 3D
scene. It allows for fusing the benefit of two styles in this way. As shown in
Equation 4 and 5, our approach can readily be extended to scenarios involving
a mixture of multiple styles.

$\mathcal{L}^{\mathcal{T}_{M}}_{\text{style}}=\sum_{i}\lambda_{i}\mathcal{L}^{\mathcal{T}_{S}}_{\text{style}_{i}}$

(4)

$\mathcal{L}_{\text{total}}=\alpha\cdot\mathcal{L}^{\mathcal{T}_{M}}_{\text{style}}+\beta\cdot\mathcal{L}_{\text{content}}(F_{\ell_{c}}(\hat{\mathbf{X}}),F_{\ell_{c}}(\mathbf{X}_{\text{content}}))+\gamma\cdot\mathcal{L}_{\text{tv}}$

(5)

The scalar weight $\lambda_{i}$ regulates the influence of each individual
style image $\mathbf{X}_{\text{style}_{i}}$. The combination loss
$\mathcal{L}^{\mathcal{T}_{M}}_{\text{style}}$ serves as the style loss term
in the style transfer loss $\mathcal{L}_{\text{total}}$.

###  3.3 Spatial Control

General 3D style transfer approaches typically apply the style globally to the
entire scene, producing a uniform stylization throughout the whole scene.
However, there are circumstances where it is necessary to only stylize a
specific area or object within a scene. For instance, one may desire to create
an immersive virtual world experience by turning the background environment
into a fantasy watercolor painting effect without affecting the people or main
subjects of a scene. Another example is creating an augmented reality effect
by turning the primary objects of a scene into cartoon-like, abstract figures
while keeping the background intact.

#### Single Style Spatial Control

Our spatial control is integrated with the deferred back-propagation technique
in ARF (Zhang et al. 2022). During the deferred back-propagation process, the
loss and gradient of the predicted view are calculated with auto-
differentiation disabled. Each 2D predicted view is associated with a cached-
gradients map of the same size. The key aspect of our spatial control is
applying a binary spatial mask $\mathbf{T}^{r}$ to the cached-gradients map
$\hat{\mathbf{X}}_{\text{grad}}$, as shown in Equation 6, where $\circ$
denotes element-wise multiplication. Each element in $\mathbf{T}^{r}$ takes
either a value of 0 or 1. The regions in the mask with a value of 0 correspond
to the portions of the predicted view that are not subject to stylization,
while the regions with a value of 1 reflect the areas of the view that need to
be stylized. As a result, only the gradients corresponding to the chosen
regions are used in the computation throughout the optimization step where the
cached gradients are back-propagated.

$\hat{\mathbf{X}}_{\text{grad}}=\mathbf{T}^{r}\circ\hat{\mathbf{X}}_{\text{grad}}$

(6)

The source of the spatial mask is not limited and can be manually annotated.
In this paper, we employ semantic segmentation maps
$\mathbf{T}_{\text{semantic}}^{r}$ to determine the regions of specific
semantic objects within the scene.

#### Multiple Style Spatial Control

To accomplish the spatial control of multiple styles, we introduce a
corresponding method called “Combined Cached-gradients Map”, which still
utilises the concept of the cached-gradients map in ARF (Zhang et al. 2022).
Assuming the scene contains $r$ areas that need individually corresponding to
a unique style image $\mathbf{X}_{\text{style}}^{r}$. As shown in Equation 7
and 8, for each area $\mathbf{T}^{r}\circ\hat{\mathbf{X}}$ and its related
style $\mathbf{X}_{\text{style}}^{r}$, we initially determine the
corresponding cached gradients maps $\hat{\mathbf{X}}_{\text{grad}}^{r}$
according to the style transfer loss $\mathcal{L}_{\text{total}}^{r}$ with
auto-differentiation disabled. $\hat{\mathbf{X}}_{\text{grad}}^{r}$ are then
added to generate the final cached gradients maps
$\hat{\mathbf{X}}_{\text{grad}}$ applied in deferred back-propagation. As a
result, during the optimization process, each selected region is updated
according to its target style.

$\begin{split}\scalebox{0.9}{$\mathcal{L}_{\text{total}}^{r}=\
$}&\scalebox{0.9}{$\alpha\cdot\mathcal{L}_{\text{style}}(F_{\ell_{s}}(\mathbf{T}^{r}\circ\hat{\mathbf{X}}),F_{l_{s}}(\mathbf{X}_{\text{style}}^{r}))+\gamma\cdot\mathcal{L}_{\text{tv}}$}\\\
&\scalebox{0.9}{$+\
\beta\cdot\mathcal{L}_{\text{content}}(F_{\ell_{c}}(\mathbf{T}^{r}\circ\hat{\mathbf{X}}),F_{\ell_{c}}(\mathbf{T}^{r}\circ\mathbf{X}_{\text{content}}))$}\end{split}$
(7)

$\hat{\mathbf{X}}_{\text{grad}}=\sum_{r}\mathbf{T}^{r}\circ\hat{\mathbf{X}}_{\text{grad}}^{r}$

(8)

###  3.4 Depth Enhancement Control

While the style transfer technique yields impressive effects by evenly
applying style patterns across the entire scene, there are instances where it
inadvertently compromises the scene’s depth perception. According to some
research findings (Liu et al. 2017; Jing et al. 2019), stylized results are
especially unsatisfactory for situations with a large range of depths. This
happens as a result of the uncontrollable alteration of the content layout,
which obscures the line separating the foreground from the background and the
boundaries between various objects.

Our depth-aware control technique is based on the Liu et al (Liu et al.
2017)’s depth-aware approach for 2D image style transfer. They note that the
depth map serves as an effective representation of the spatial distribution
within an image, and propose to preserve the depth map of the content during
stylization. It is important to note that, to achieve smooth gradient
optimization, ARF (Zhang et al. 2022) fixes the density component in the
radiance fields during stylization. Hence, the actual depth information within
the radiance fields remains unchanged, while only the appearance of the 3D
scene is altered. However, as the style transfer is done in a 2D per-view way
without any knowledge of the scene depth or geometry, object boundaries can be
easily blurred or lost during stylization. Hence, we rely on a pre-trained
depth estimation network $\phi_{1}$ (Ranftl et al. 2020) to approximate the
perceived depth of the current stylized appearance, as the depth information
remains fixed in the radiance field. This can assist ARF-Plus in promptly
understanding the changes in stylization’s appearance and whether they would
result in harmful alterations to the visually perceived depth.

In order to preserve depth-aware information, we take the outputs of the pre-
trained depth estimation network $\phi_{1}$ and compute the (squared,
normalized) Euclidean distances as the
$\mathcal{L}_{\text{depth}}^{\phi_{1}}$. The photo-realistic view
${\mathbf{X}_{\text{content}}}$ and stylized view $\mathbf{\hat{X}}$ have the
same size $H\times W\times C$.

$\mathcal{L}_{\text{depth}}^{\phi_{1}}=\frac{\left\|\phi_{1}(\mathbf{\hat{X}})-\phi_{1}(\mathbf{X}_{\text{content}})\right\|_{2}}{H\times
W\times C}$

(9)

As shown in Equation 10, the depth loss
$\mathcal{L}_{\text{depth}}^{\phi_{1}}$ is incorporated into the style
transfer loss $\mathcal{L}_{\text{total}}$ , where $\delta$ is a scalar
weight. $\mathcal{L}_{\text{depth}}^{\phi_{1}}$ serves as an additional aspect
to guide and influence the stylization based on depth-aware information.

$\mathcal{L}_{\text{total}}=\alpha\cdot\mathcal{L}_{\text{style}}+\beta\cdot\mathcal{L}_{\text{content}}+\delta\cdot\mathcal{L}_{\text{depth}}^{\phi_{1}}+\gamma\cdot\mathcal{L}_{\text{tv}}$

(10)

##  4 Experiments and Evaluation

###  4.1 Experiments Design

#### Baseline

To the best of our knowledge, we are the first to systematically address the
issue of enhancing perceptual flexibility controls for radiance fields style
transfer. As such, there are no similar works in the current state-of-the-art
that can be compared to ours. Since our proposed ARF-Plus framework is based
on the ARF (Zhang et al. 2022), we choose it as the baseline for our
experimental evaluation.

#### Datasets

To guarantee comparability with the baseline and achieve more accurate
differentiation, we utilise the same datasets as those employed in ARF (Zhang
et al. 2022).
a) Artworks Dataset (Zhang et al. 2022): This dataset is made up of a variety
of images which act as given styles. It is used to assess the effectiveness of
our proposed ARF-Plus framework in learning and managing multiple styles while
adhering to specific perceptual factor controls.
b) LLFF Dataset (Mildenhall et al. 2019): This dataset contains real-world
scenes that are photographed from forward angles. It is utilized to create
photo-realistic radiance fields, representing the 3D scenes prior to
stylization.
c) Real 360 Degree Scenes Dataset (Knapitsch et al. 2017): This dataset
includes real, unbounded, 360-degree large outdoor scenes with complex
geometric layouts and camera trajectories. The scene data is also employed to
train photo-realistic radiance fields before stylization.

#### Training Settings

Identical to the baseline, in ARF-Plus, we configure the stylization
optimization to run for 10 epochs, with a learning rate that exponentially
decreases from 1e-1 to 1e-2. For single-style input, the training time of our
ARF-Plus is comparable to that of baseline, as it does not entail additional
training tasks during the stylization optimization process, which typically
takes around 20 minutes on a single GPU.

#### Implementation Details

Our ARF-Plus framework, as previously mentioned, comprises reconstructing
photo-realistic radiance fields from numerous pictures and then stylizing the
resulting reconstruction with perceptual factor choices. 1) Regarding the
first step of reconstructing a photo-realistic radiance field, our work aligns
with the baseline approach in primarily relying on Plenoxels (Yu et al. 2021)
to achieve. Plenoxels is renowned for its fast reconstruction and rendering
speed. All training settings of our method in this process remain consistent
with the baseline. 2) Although ARF (Zhang et al. 2022)’s core algorithm
achieves acceptable style transfer in both style pattern and color, its
authors introduce a recoloring strategy in the stylization process to enhance
visual quality. In ARF-Plus, we continue to employ the recoloring method for
scale control and depth enhancement control in single-style cases. However, we
choose to disable the recoloring process in scenarios where color preservation
control, spatial control, and multiple input styles are involved. In those
instances, it is inappropriate to follow the recoloring process in ARF which
uses the colors of a given style image to recolor the entire scene. To ensure
a fair comparison, when our ARF-Plus deactivates the recolor process, the
baseline ARF also disables this step accordingly. Please refer to the Appendix
for additional technical details.

###  4.2 Color Preservation Control

Figure 2 demonstrates visual comparisons between methods applied to real-world
scenes. In the context of color preservation control, our goal is to ensure
that the colors of the stylized scene remain consistent with those of the
photo-realistic radiance fields. As illustrated, our proposed color
preservation control method effectively preserves the original scene’s color
while successfully learning the desired style. Moreover, the colors and
brightness distribution of the stylized outputs achieved through our method
closely resemble those of the photo-realistic view. Please refer to the
Appendix for additional qualitative and quantitative evaluations.

Figure 2: Qualitative results of color preservation. Please refer to
supplementary materials for better visualization.

###  4.3 Scale Control

We demonstrate the effects of scale control on both single and multiple
styles. Please refer to the Appendix for additional experiments regarding the
study of influential factors of scale control.

#### Single Style Scale Control

Figure 3 illustrates the successful scaling up and scaling down of style
patterns achieved by our scale control method. In addition, this approach
provides enhanced flexibility for resizing fine strokes or coarse patterns by
selectively assigning different weights to various receptive fields and
generating diverse resized style images for each receptive field. In Figure 3
(a), by configuring the range of receptive field, specifically selecting Conv1
and Conv2 for feature extraction (setting $w_{l_{1}}=0.3,w_{l_{2}}=0.7$ and
the rest to 0 in Equation 2), style transfer places greater emphasis on
capturing fine details from the style image. It can be observed that the fine
strokes - the green and white lines - are successfully scaled up or down in
the stylized scenes. In Figure 3 (b), by selecting Conv3 and Conv4 (setting
$w_{l_{3}}=0.7,w_{l_{4}}=0.3$ and the rest to 0 to in Equation 2), style
transfer focuses more on learning coarse patterns. Different layers are then
assigned different values of the resize setting of the style image to achieve
a continuously adjustable scale. The results of the stylized scene demonstrate
that the coarse shape patterns are effectively scaled up or down.

Figure 3: Qualitative results of single style scale control. Our scale control
effectively achieves style scaling. Please refer to supplementary materials
for better visualization.

#### Multiple Style Scale Control

After analyzing how well our scale control on individual styles, we move on to
examine its effectiveness in handling multiple blended styles. We utilize
color preservation to minimize the visual influence of different colors from
multiple styles, enabling a more effective comparison of pattern scale
variations. Figure 4 illustrates how our ARF-Plus scale control method, when
applied to blended styles, effectively controls each individual style’s scale.
The noticeable changes in the size of leaf patterns are evident when scaling
up or down the coarse pattern of Style-121. When the fine pattern scale
changes for Style-122, there are observable effects on the leaves and petals.

Figure 4: Qualitative results of multiple styles scale control. For better
visualization, color is preserved by using our color preservation control. Our
ARF-Plus with scale control can selectively scale up or scale down a
particular style in stylization with blended multiple styles.

###  4.4 Spatial Control

#### Single Style Spatial Control

Figure 5 presents the results of spatial control with semantic segmentation
masks. Our method successfully stylizes the associated elements of the scene
Room, namely the chairs, table, and TV. A noteworthy observation is that,
despite the semantic segmentation masks being occasionally inaccurate or not
fully covering the objects, our method manages to effectively paint nearly
whole objects’ areas in the stylized scene. One possible explanation is
multiple training perspectives partially offset the shortcomings of semantic
segmentation. Although certain views lead to poor segmentation results,
alternative views’ semantic maps provide broader and more accurate coverage.
This enables the successful coloring of the overlapping regions across
multiple views. Ultimately, the entire area of the semantic object is
successfully stylized.

Figure 5: Qualitative results of spatial control with semantic segmentation
masks. Our ARF-Plus with spatial control effectively stylizes specific
semantic objects - chair, table, and TV - within the scene. Please refer to
supplementary materials for better visualization. Table 1: Quantitative
results of spatial control with semantic segmentation masks. Evaluation metric
ArtFID (Wright and Ommer 2022) is a combination of ContentDist and StyleFID.
Room-All represents the combined usage of three semantic masks: Chair, Table,
and TV. Results better than the baseline in the mask are in bold.

| ArtFID $\downarrow$ | ContentDist $\downarrow$ | StyleFID $\downarrow$
---|---|---|---
Style | Scene | ARF | ARF-Plus w/ | ARF | ARF-Plus w/ | ARF | ARF-Plus w/
|  |  | Spatial Control |  | Spatial Control |  | Spatial Control
|  | in Mask | in Mask | in Mask | in Mask | in Mask | in Mask
007 |  Room-Chair | 41.4614 | 39.3775 | 0.0435 | 0.0434 | 38.7340 | 36.7384
007 |  Room-Table | 43.2753 | 40.8616 | 0.0473 | 0.0489 | 40.3191 | 37.9581
007 |  Room-TV | 41.2685 | 38.4802 | 0.0195 | 0.0193 | 39.4799 | 36.7500
007 |  Room-All | 41.0287 | 37.9573 | 0.0950 | 0.0983 | 36.4707 | 33.5591

We set the number of rendered novel views $N$ to 120 and render a series of
images from the stylized radiance fields. Table 1 provides quantitative
results of the stylized scenes. In comparison to ARF in the mask, our spatial
control yields overall superior ArtFID scores (Wright and Ommer 2022), which
can be attributed to a significant enhancement in styleFID. There are
potentially two reasons behind the improvement in masked styleFID scores.
Firstly, spatial control leads to a reduction in the regions requiring
stylization within the scene. This results in fewer areas participating in
gradient back-propagation during the same training epoch, allowing for the
acquisition of more style information. Secondly, the appearance of semantic
objects (such as TV) often exhibits similar textures. The uniform texture
makes it easier for those areas to learn the style. It is also notable that in
Scene Room, for ARF-Plus, the individual use of three separate semantic masks
results in higher StyleFID values compared to the combined use of all three
masks as a single mask (Room-All). Because ArtFID integrates both ContentDist
and StyleFID, changes in StyleFID contribute to an elevated ArtFID score. This
reveals that the size of the area controlled by spatial control has an impact
on the effectiveness of style transfer. When the mask is too small, indicating
a limited stylized area, it becomes difficult for that region to encompass all
the style patterns depicted in the style image. Please refer to the Appendix
for the explanation of calculating ArtFID on specific areas and additional
qualitative evaluation.

#### Multiple Style Spatial Control

As shown in Figure 6, compared to the baseline’s unified stylization, our
proposed spatial control method effectively transfers various styles to
different regions. The modification of the loss function (in Eq. 7) may result
in minor variations in the details. More specifically, our method calculates
differences solely between a specific region and its corresponding style and
segmented photo-realistic view. In contrast, the baseline ARF (Zhang et al.
2022) computes the loss differences between the entire scene, style, and the
overall photo-realistic view. Please refer to the Appendix for intermediate
training results.

Figure 6: Qualitative results of multiple styles spatial control. Our multi-
style spatial control successfully stylizes various locations with distinct
styles. Please refer to supplementary materials for better visualization.

###  4.5 Depth-aware Control

Figure 7 presents comparisons between our depth-aware control method and the
baseline. Qualitative results demonstrate that our method can successfully
preserve perceptive depth across varying views. The foreground leaf has a more
distinct outline and stands out from the other leaves in the background. For
the Horns scene, our depth control method better preserves the nostril (hole)
located next to the horn. Please refer to the Appendix for quantitative
evaluations.

Figure 7: Qualitative results of depth-aware control. Our depth-aware control
demonstrates superior performance in preserving perceptive depth across
varying views - the forefront leaf in Leaves, and the nostril (hole) in Horns.
Please refer to supplementary materials for better visualization.

###  4.6 Combination of Controls

In Figure 8, the 3D scene has successfully been infused with distinct shapes
from two different styles. Through spatial control, the semantic object
(horse) has been adorned with regular cuboid shapes transferred by Style-007,
while the rest of the background showcases triangular patterns from Style-131.
It avoids monotony by incorporating multiple shapes from different styles.
This imbues the entire scene with an abstract sensation, particularly
noticeable in elements like the leaves of trees. Furthermore, in the ARF
baseline, the shape of the horse sculpture appeared disproportionately large,
giving the impression of significant fractures in the sculpture. With our
scale control, the patterns on the horse sculpture have been reduced to a more
suitable size, enhancing visual aesthetics. Moreover, the color preservation
feature allows us to freely select style images without excessive concern for
whether their colors match our scene. In conclusion, compared to ARF, our
control methods provide greater flexibility for 3D scene stylization, opening
up endless possibilities for the imagination.

Figure 8: Qualitative results of controls combination - Multiple Styles
Spatial Control (with Style-007 on the horse & Style-131 on the background),
Scale Control (with patterns scale-down on the horse), and Color Preservation
Control (on the whole scene). Please refer to supplementary materials for
better visualization.

##  5 Summary

In this paper, we identify a research gap - the lack of sufficient perceptual
control - in the emerging radiance fields style transfer. Both quantitative
and qualitative evaluations on real-world datasets demonstrate that ARF-Plus’s
four types of control methods effectively achieve perceptual control for 3D
scene stylization. The combination use of our proposed controls through the
ARF-Plus framework offers boundless freedom, enabling the production of novel
and eye-catching stylized 3D scene effects. We wish that our research outcomes
will encourage further studies in this novel and intriguing field.

The limitations of our work include: 1) Our spatial control method, while
generally producing the desired stylization effects, sometimes demonstrates an
issue of style leakage. This occurs because the accuracy of the semantic
segmentation output differs among views, resulting in instances where the
incomplete semantic mask fails to correctly represent object boundaries. 2)
Since different styles have varying aesthetic characteristics, in order to
achieve a visually appealing visual outcome, our scale control sometimes needs
manual tuning of the hyperparameters. For example, determining the weight
configuration for different convolution layers to emphasize finer details or
coarser patterns. For a given 3D scene, it would be desirable if the system
could automatically learn and tune the hyperparameters for each individual
style in a more intelligent manner.

## References

  * Castillo et al. (2017) Castillo, C.; De, S.; Han, X.; Singh, B.; Yadav, A. K.; and Goldstein, T. 2017.  Son of zorn’s lemma: Targeted style transfer using instance-aware semantic segmentation.  In _2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)_ , 1348–1352. IEEE.
  * Chen et al. (2022a) Chen, A.; Xu, Z.; Geiger, A.; Yu, J.; and Su, H. 2022a.  Tensorf: Tensorial radiance fields.  In _Computer Vision–ECCV 2022: 17th European Conference, Tel Aviv, Israel, October 23–27, 2022, Proceedings, Part XXXII_ , 333–350. Springer.
  * Chen et al. (2022b) Chen, Y.; Yuan, Q.; Li, Z.; Xie, Y. L. W. W. C.; Wen, X.; and Yu, Q. 2022b.  UPST-NeRF: Universal Photorealistic Style Transfer of Neural Radiance Fields for 3D Scene.  _arXiv preprint arXiv:2208.07059_.
  * Chiang et al. (2022) Chiang, P.-Z.; Tsai, M.-S.; Tseng, H.-Y.; Lai, W.-S.; and Chiu, W.-C. 2022.  Stylizing 3d scene via implicit representation and hypernetwork.  In _Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision_ , 1475–1484.
  * Fan et al. (2022) Fan, Z.; Jiang, Y.; Wang, P.; Gong, X.; Xu, D.; and Wang, Z. 2022.  Unified implicit neural stylization.  In _Computer Vision–ECCV 2022: 17th European Conference, Tel Aviv, Israel, October 23–27, 2022, Proceedings, Part XV_ , 636–654. Springer.
  * Gatys et al. (2016) Gatys, L. A.; Bethge, M.; Hertzmann, A.; and Shechtman, E. 2016.  Preserving color in neural artistic style transfer.  _arXiv preprint arXiv:1606.05897_.
  * Gatys, Ecker, and Bethge (2016) Gatys, L. A.; Ecker, A. S.; and Bethge, M. 2016.  Image style transfer using convolutional neural networks.  In _Proceedings of the IEEE conference on computer vision and pattern recognition_ , 2414–2423.
  * Gatys et al. (2017) Gatys, L. A.; Ecker, A. S.; Bethge, M.; Hertzmann, A.; and Shechtman, E. 2017.  Controlling perceptual factors in neural style transfer.  In _Proceedings of the IEEE conference on computer vision and pattern recognition_ , 3985–3993.
  * Höllein, Johnson, and Nießner (2022) Höllein, L.; Johnson, J.; and Nießner, M. 2022.  Stylemesh: Style transfer for indoor 3d scene reconstructions.  In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_ , 6198–6208.
  * Huang et al. (2021) Huang, H.-P.; Tseng, H.-Y.; Saini, S.; Singh, M.; and Yang, M.-H. 2021.  Learning to stylize novel views.  In _Proceedings of the IEEE/CVF International Conference on Computer Vision_ , 13869–13878.
  * Huang et al. (2022) Huang, Y.-H.; He, Y.; Yuan, Y.-J.; Lai, Y.-K.; and Gao, L. 2022.  StylizedNeRF: consistent 3D scene stylization as stylized NeRF via 2D-3D mutual learning.  In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_ , 18342–18352.
  * Jing et al. (2018) Jing, Y.; Liu, Y.; Yang, Y.; Feng, Z.; Yu, Y.; Tao, D.; and Song, M. 2018.  Stroke controllable fast style transfer with adaptive receptive fields.  In _Proceedings of the European Conference on Computer Vision (ECCV)_ , 238–254.
  * Jing et al. (2019) Jing, Y.; Yang, Y.; Feng, Z.; Ye, J.; Yu, Y.; and Song, M. 2019.  Neural style transfer: A review.  _IEEE transactions on visualization and computer graphics_ , 26(11): 3365–3385.
  * Knapitsch et al. (2017) Knapitsch, A.; Park, J.; Zhou, Q.-Y.; and Koltun, V. 2017.  Tanks and temples: Benchmarking large-scale scene reconstruction.  _ACM Transactions on Graphics (ToG)_ , 36(4): 1–13.
  * Liu et al. (2017) Liu, X.-C.; Cheng, M.-M.; Lai, Y.-K.; and Rosin, P. L. 2017.  Depth-aware neural style transfer.  In _Proceedings of the symposium on non-photorealistic animation and rendering_ , 1–10.
  * Mildenhall et al. (2019) Mildenhall, B.; Srinivasan, P. P.; Ortiz-Cayon, R.; Kalantari, N. K.; Ramamoorthi, R.; Ng, R.; and Kar, A. 2019.  Local light field fusion: Practical view synthesis with prescriptive sampling guidelines.  _ACM Transactions on Graphics (TOG)_ , 38(4): 1–14.
  * Mildenhall et al. (2021) Mildenhall, B.; Srinivasan, P. P.; Tancik, M.; Barron, J. T.; Ramamoorthi, R.; and Ng, R. 2021.  Nerf: Representing scenes as neural radiance fields for view synthesis.  _Communications of the ACM_ , 65(1): 99–106.
  * Mu et al. (2022) Mu, F.; Wang, J.; Wu, Y.; and Li, Y. 2022.  3d photo stylization: Learning to generate stylized novel views from a single image.  In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_ , 16273–16282.
  * Nguyen-Phuoc, Liu, and Xiao (2022) Nguyen-Phuoc, T.; Liu, F.; and Xiao, L. 2022.  Snerf: stylized neural implicit representations for 3d scenes.  _arXiv preprint arXiv:2207.02363_.
  * Ranftl et al. (2020) Ranftl, R.; Lasinger, K.; Hafner, D.; Schindler, K.; and Koltun, V. 2020.  Towards robust monocular depth estimation: Mixing datasets for zero-shot cross-dataset transfer.  _IEEE transactions on pattern analysis and machine intelligence_ , 44(3): 1623–1637.
  * Reimann et al. (2022) Reimann, M.; Buchheim, B.; Semmo, A.; Döllner, J.; and Trapp, M. 2022.  Controlling strokes in fast neural style transfer using content transforms.  _The Visual Computer_ , 1–15.
  * Ruder, Dosovitskiy, and Brox (2018) Ruder, M.; Dosovitskiy, A.; and Brox, T. 2018.  Artistic style transfer for videos and spherical images.  _International Journal of Computer Vision_ , 126(11): 1199–1219.
  * Wang et al. (2023) Wang, C.; Jiang, R.; Chai, M.; He, M.; Chen, D.; and Liao, J. 2023.  Nerf-art: Text-driven neural radiance fields stylization.  _IEEE Transactions on Visualization and Computer Graphics_.
  * Wright and Ommer (2022) Wright, M.; and Ommer, B. 2022.  Artfid: Quantitative evaluation of neural style transfer.  In _DAGM German Conference on Pattern Recognition_ , 560–576. Springer.
  * Yin et al. (2021) Yin, K.; Gao, J.; Shugrina, M.; Khamis, S.; and Fidler, S. 2021.  3dstylenet: Creating 3d shapes with geometric and texture style variations.  In _Proceedings of the IEEE/CVF International Conference on Computer Vision_ , 12456–12465.
  * Yu et al. (2021) Yu, A.; Li, R.; Tancik, M.; Li, H.; Ng, R.; and Kanazawa, A. 2021.  Plenoctrees for real-time rendering of neural radiance fields.  In _Proceedings of the IEEE/CVF International Conference on Computer Vision_ , 5752–5761.
  * Yu, Wu, and Wang (2019) Yu, Z.; Wu, Y.; and Wang, T. 2019.  A Method for Arbitrary Instance Style Transfer.  _arXiv preprint arXiv:1912.06347_.
  * Zhang et al. (2022) Zhang, K.; Kolkin, N.; Bi, S.; Luan, F.; Xu, Z.; Shechtman, E.; and Snavely, N. 2022\.  ARF: Artistic Radiance Fields.  In _European Conference on Computer Vision_ , 717–733. Springer.
  * Zhang et al. (2023) Zhang, Y.; He, Z.; Xing, J.; Yao, X.; and Jia, J. 2023.  Ref-NPR: Reference-Based Non-Photorealistic Radiance Fields for Controllable Scene Stylization.  In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_ , 4242–4251.


PSOJ247.64126+40.20269 | $20.62$ | $6.06$ | $-25.98$ | Fan et al. (2003) | Shen et al. (2019)
PSOJ293.03178+71.65233 | $20.11$ | $6.05$ | $-26.50$ | Bañados et al. (2016) | Bañados et al. (2016)
PSOJ250.34052+37.92226 | $21.09$ | $6.05$ | $-25.51$ | Willott et al. (2007) | Willott et al. (2010)
PSOJ210.72777+40.40088 | $21.00$ | $6.04$ | $-25.59$ | Bañados et al. (2016) | Bañados et al. (2016)
PSOJ313.52710-00.08733 | $20.57$ | $6.04$ | $-26.03$ | Jiang et al. (2008) | Venemans et al. (2020)
PSOJ181.90597+06.50283 | $20.15$ | $6.04$ | $-26.46$ | Jiang et al. (2015) | Decarli et al. (2018)
PSOJ196.53444+03.94065 | $20.07$ | $6.03$ | $-26.53$ | Fan et al. (2001a) | Venemans et al. (2020)
PSOJ265.92982+41.41395 | $21.32$ | $6.03$ | $-25.27$ | Banados et al. (2022) | Eilers et al. (2020)
PSOJ124.61417+17.38111 | $19.26$ | $6.02$ | $-27.34$ | Fan et al. (2006) | Carilli et al. (2010)
PSOJ194.48949+63.82699 | $20.42$ | $6.02$ | $-26.18$ | Jiang et al. (2015) | Jiang et al. (2015)
PSOJ340.20404-18.66219 | $20.39$ | $6.01$ | $-26.21$ | Bañados et al. (2014) | Bañados et al. (2016)
PSOJ174.32386+35.83245 | $19.41$ | $6.01$ | $-27.18$ | Fan et al. (2006) | Shen et al. (2019)
PSOJ007.02733+04.95712 | $20.15$ | $6.00$ | $-26.43$ |  Bañados et al. (2014),Jiang et al. (2015) | Venemans et al. (2020)
PSOJ037.97064-28.83892 | $20.58$ | $6.00$ | $-26.01$ | Bañados et al. (2014) | Bañados et al. (2016)
PSOJ182.31219+53.46335 | $21.05$ | $5.99$ | $-25.53$ | Banados et al. (2022) | Banados et al. (2022)
PSOJ029.51725-29.08868 | $19.37$ | $5.98$ | $-27.21$ | Bañados et al. (2016) | Banados et al. (2022)
PSOJ027.15681+06.00556 | $19.35$ | $5.98$ | $-27.23$ | Jiang et al. (2015) | Becker et al. (2015b)
PSOJ056.71684-16.47693 | $20.07$ | $5.97$ | $-26.50$ | Bañados et al. (2016) | Eilers et al. (2020)
PSOJ288.64769+63.24792 | $20.76$ | $5.96$ | $-25.81$ | Banados et al. (2022) | Banados et al. (2022)
PSOJ130.33131+29.08460 | $20.19$ | $5.95$ | $-26.37$ | Goto (2006) | Shen et al. (2019)
PSOJ167.47265+56.95211 | $20.62$ | $5.95$ | $-25.95$ | Bañados et al. (2016) | Bañados et al. (2016)
PSOJ267.00210+22.78120 | $21.04$ | $5.95$ | $-25.52$ | Bañados et al. (2016) | Bañados et al. (2016)
PSOJ002.10738-06.43457 | $20.29$ | $5.93$ | $-26.26$ |  Bañados et al. (2016),Jiang et al. (2015) | Bañados et al. (2016)
PSOJ076.23444-10.88780 | $20.61$ | $5.93$ | $-25.95$ | Banados et al. (2022) | Banados et al. (2022)
PSOJ139.61940+19.67919 | $20.71$ | $5.92$ | $-25.83$ | Wang et al. (2018) | Wang et al. (2018)
PSOJ213.36298-22.56173 | $19.89$ | $5.92$ | $-26.65$ | Bañados et al. (2014) | Bañados et al. (2016)
PSOJ228.68712+21.23882 | $20.60$ | $5.92$ | $-25.95$ | Bañados et al. (2016) | Bañados et al. (2016)
PSOJ328.73399-09.50762 | $20.46$ | $5.92$ | $-26.08$ | Bañados et al. (2016) | Bañados et al. (2016)
PSOJ135.87045-13.83368 | $21.01$ | $5.91$ | $-25.53$ | Bañados et al. (2016) | Bañados et al. (2016)
PSOJ194.12902+25.54761 | $21.07$ | $5.91$ | $-25.47$ | Bañados et al. (2016) | Bañados et al. (2016)
PSOJ218.39674+28.33067 | $20.45$ | $5.91$ | $-26.09$ | Banados et al. (2022) | Banados et al. (2022)
PSOJ212.79703+12.29368 | $20.10$ | $5.90$ | $-26.44$ | Fan et al. (2004) | Kurk et al. (2007)
PSOJ023.00711-02.26753 | $20.20$ | $5.90$ | $-26.35$ | Bañados et al. (2016) | Bañados et al. (2016)
PSOJ319.60403-10.93263 | $20.05$ | $5.90$ | $-26.49$ | Bañados et al. (2016) | Bañados et al. (2016)
PSOJ216.31805+32.90265 | $20.37$ | $5.89$ | $-26.16$ | Cool et al. (2006) | Carilli et al. (2010)
PSOJ042.66908-02.91745 | $20.02$ | $5.89$ | $-26.51$ | Bañados et al. (2016) | Bañados et al. (2016)
PSOJ187.30502+04.32436 | $21.09$ | $5.89$ | $-25.45$ | Bañados et al. (2014) | Bañados et al. (2014)
PSOJ075.93563-07.50613 | $20.13$ | $5.88$ | $-26.40$ | Bañados et al. (2016) | Bañados et al. (2016)
PSOJ157.90703-02.65990 | $20.26$ | $5.88$ | $-26.27$ | Bañados et al. (2016) | Bañados et al. (2016)
PSOJ210.82969+09.04750 | $20.33$ | $5.88$ | $-26.20$ |  Bañados et al. (2016),Jiang et al. (2015) | Bañados et al. (2016)
PSOJ175.42940+71.32363 | $20.62$ | $5.86$ | $-25.90$ | Banados et al. (2022) | Banados et al. (2022)
PSOJ183.29919-12.76762 | $19.22$ | $5.86$ | $-27.30$ | Bañados et al. (2014) | Bañados et al. (2014)
PSOJ025.23764-11.68319 | $19.86$ | $5.85$ | $-26.65$ | Bañados et al. (2016) | Bañados et al. (2016)
PSOJ127.28174+03.06571 | $20.73$ | $5.85$ | $-25.78$ | Bañados et al. (2016) | Bañados et al. (2016)
PSOJ190.92005+25.48995 | $20.61$ | $5.85$ | $-25.90$ |  Bañados et al. (2014),Jiang et al. (2016) | Jiang et al. (2016)
PSOJ219.04890+50.11865 | $20.20$ | $5.85$ | $-26.32$ | Fan et al. (2006) | Carilli et al. (2010)
PSOJ130.14626+56.40561 | $19.56$ | $5.84$ | $-26.95$ | Fan et al. (2006) | Wang et al. (2010)
PSOJ001.46807-00.11546 | $20.91$ | $5.84$ | $-25.59$ | Fan et al. (2004) | De Rosa et al. (2011)
PSOJ148.48293+69.18128 | $20.23$ | $5.84$ | $-26.28$ | Banados et al. (2022) | Banados et al. (2022)
PSOJ197.71978+25.53518 | $20.76$ | $5.84$ | $-25.74$ | Bañados et al. (2016) | Bañados et al. (2016)
PSOJ210.87224-12.00948 | $21.11$ | $5.84$ | $-25.40$ | Bañados et al. (2014) | Bañados et al. (2014)
PSOJ306.35128-04.82274 | $20.57$ | $5.84$ | $-25.94$ | Banados et al. (2022) | Banados et al. (2022)
PSOJ175.90977+38.14133 | $20.08$ | $5.84$ | $-26.43$ | Jiang et al. (2016) | Eilers et al. (2020)
PSOJ352.40341-15.33732 | $21.20$ | $5.83$ | $-25.30$ | Bañados et al. (2018a) | Rojas-Ruiz et al. (2021)
PSOJ212.29742-15.98660 | $20.89$ | $5.83$ | $-25.61$ | Bañados et al. (2016) | Bañados et al. (2016)
PSOJ122.72630+51.09447 | $19.86$ | $5.82$ | $-26.64$ | Jiang et al. (2016) | Bañados et al. (2016)
PSOJ235.94506+17.00789 | $20.20$ | $5.82$ | $-26.30$ | Bañados et al. (2016) | Bañados et al. (2016)
PSOJ236.29124+16.60886 | $20.83$ | $5.82$ | $-25.67$ | Bañados et al. (2016) | Bañados et al. (2016)
PSOJ000.66411+25.84303 | $19.42$ | $5.82$ | $-27.08$ | Fan et al. (2004) | Shen et al. (2019)
PSOJ129.18276+00.91479 | $19.03$ | $5.81$ | $-27.47$ | Fan et al. (2001a) | Kurk et al. (2007)
PSOJ174.79204-12.28454 | $20.23$ | $5.81$ | $-26.26$ | Bañados et al. (2016) | Bañados et al. (2016)
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PSOJ017.06916-11.99193 | $20.66$ | $5.80$ | $-25.82$ | Banados et al. (2022) | Banados et al. (2022)
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PSOJ308.48295-27.64850 | $19.90$ | $5.80$ | $-26.59$ | Bañados et al. (2016) | Bañados et al. (2016)
PSOJ021.42133-25.88228 | $19.71$ | $5.79$ | $-26.78$ | Bañados et al. (2016) | Bañados et al. (2016)
PSOJ161.13770-01.41721 | $19.32$ | $5.78$ | $-27.16$ | Fan et al. (2000) | Venemans et al. (2020)
PSOJ169.84022+01.21906 | $21.20$ | $5.78$ | $-25.27$ | Wang et al. (2018) | Wang et al. (2018)
PSOJ215.15142-16.04173 | $19.25$ | $5.78$ | $-27.23$ | Morganson et al. (2012) | Li, J. et al. 2022, in prep.
PSOJ236.46704+60.47332 | $19.13$ | $5.78$ | $-27.35$ | Wang et al. (2016a) | Wang et al. (2016a)
PSOJ243.64732+01.24579 | $19.96$ | $5.78$ | $-26.52$ | Yang et al. (2019) | Yang et al. (2019)
PSOJ000.04163-04.27391 | $20.46$ | $5.77$ | $-26.01$ | Banados et al. (2022) | Banados et al. (2022)
PSOJ172.17701+26.88666 | $20.73$ | $5.77$ | $-25.73$ | Bañados et al. (2016) | Bañados et al. (2016)
PSOJ187.10477-02.56090 | $20.83$ | $5.77$ | $-25.63$ | Bañados et al. (2016) | Bañados et al. (2016)
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PSOJ351.30935+26.47995 | $19.42$ | $5.77$ | $-27.06$ | Wang et al. (2016a) | Wang et al. (2016a)
PSOJ249.46742+02.69955 | $19.37$ | $5.76$ | $-27.10$ | Wenzl et al. (2021) | Wenzl et al. (2021)
PSOJ261.12470+37.30605 | $20.49$ | $5.76$ | $-25.97$ | Banados et al. (2022) | Banados et al. (2022)
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PSOJ201.92220+57.54400 | $20.56$ | $5.74$ | $-25.89$ | Bañados et al. (2016) | Bañados et al. (2016)
PSOJ271.44556+49.30671 | $20.59$ | $5.74$ | $-25.86$ | Banados et al. (2022) | Banados et al. (2022)
PSOJ169.14063+58.88944 | $20.44$ | $5.73$ | $-26.01$ | Banados et al. (2022) | Banados et al. (2022)
PSOJ320.87027-24.36041 | $20.37$ | $5.73$ | $-26.07$ | Bañados et al. (2016) | Bañados et al. (2016)
PSOJ030.88490+00.20813 | $20.41$ | $5.72$ | $-26.03$ | Venemans et al. (2007) | Mortlock et al. (2009)
PSOJ209.20588-26.70839 | $19.45$ | $5.72$ | $-26.99$ | Bañados et al. (2016) | Bañados et al. (2016)
PSOJ071.45075-02.33330 | $19.13$ | $5.69$ | $-27.30$ | Bañados et al. (2016) | Bañados et al. (2016)
PSOJ175.40916-20.26547 | $20.37$ | $5.69$ | $-26.05$ | Bañados et al. (2016) | Bañados et al. (2016)
PSOJ196.34762+15.38990 | $20.44$ | $5.69$ | $-25.98$ | Banados et al. (2022) | Banados et al. (2022)
PSOJ207.59836+37.80990 | $20.59$ | $5.69$ | $-25.82$ |  Banados et al. (2022),Gloudemans et al. (2022) | Banados et al. (2022)
PSOJ004.81406-24.29917 | $19.41$ | $5.68$ | $-27.02$ | Bañados et al. (2016) | Bañados et al. (2016)
PSOJ038.19141-18.57350 | $20.47$ | $5.68$ | $-25.95$ | Banados et al. (2022) | Banados et al. (2022)
PSOJ040.01591+17.54581 | $20.88$ | $5.68$ | $-25.52$ | Bañados et al. (2016) | Bañados et al. (2016)
PSOJ055.42440-00.80355 | $20.18$ | $5.68$ | $-26.24$ | Bañados et al. (2015b) | Bañados et al. (2015a)
PSOJ178.37330+28.50753 | $19.86$ | $5.68$ | $-26.56$ | Banados et al. (2022) | Banados et al. (2022)
PSOJ245.06367-00.19786 | $21.21$ | $5.68$ | $-25.20$ | Bañados et al. (2016) | Bañados et al. (2016)
PSOJ197.86749+45.80408 | $20.75$ | $5.66$ | $-25.65$ | Banados et al. (2022) | Banados et al. (2022)
PSOJ002.54292+03.06321 | $20.93$ | $5.64$ | $-25.46$ | Banados et al. (2022) | Banados et al. (2022)
PSOJ224.65067+10.21379 | $19.84$ | $5.60$ | $-26.55$ | Banados et al. (2022) | Banados et al. (2022)
PSOJ330.28172+23.64389 | $20.49$ | $5.83$ | $-26.01$ |  Gloudemans et al. (2022),Banados et al. (2022) | Gloudemans et al. (2022)

## References

  * Akiyama et al. (2018) Akiyama, M., He, W., Ikeda, H., et al. 2018, PASJ, 70, S34, doi: 10.1093/pasj/psx091
  * Alam et al. (2015) Alam, S., Albareti, F. D., Allende Prieto, C., et al. 2015, ApJS, 219, 12, doi: 10.1088/0067-0049/219/1/12
  * Astropy Collaboration et al. (2013) Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33, doi: 10.1051/0004-6361/201322068
  * Astropy Collaboration et al. (2018) Astropy Collaboration, Price-Whelan, A. M., Sipőcz, B. M., et al. 2018, AJ, 156, 123, doi: 10.3847/1538-3881/aabc4f
  * Avni & Bahcall (1980) Avni, Y., & Bahcall, J. N. 1980, ApJ, 235, 694, doi: 10.1086/157673
  * Bañados et al. (2018a) Bañados, E., Carilli, C., Walter, F., et al. 2018a, ApJ, 861, L14, doi: 10.3847/2041-8213/aac511
  * Bañados et al. (2015a) Bañados, E., Decarli, R., Walter, F., et al. 2015a, ApJ, 805, L8, doi: 10.1088/2041-8205/805/1/L8
  * Bañados et al. (2014) Bañados, E., Venemans, B. P., Morganson, E., et al. 2014, AJ, 148, 14, doi: 10.1088/0004-6256/148/1/14
  * Bañados et al. (2015b) —. 2015b, ApJ, 804, 118, doi: 10.1088/0004-637X/804/2/118
  * Bañados et al. (2016) Bañados, E., Venemans, B. P., Decarli, R., et al. 2016, ApJS, 227, 11, doi: 10.3847/0067-0049/227/1/11
  * Bañados et al. (2018b) Bañados, E., Venemans, B. P., Mazzucchelli, C., et al. 2018b, Nature, 553, 473, doi: 10.1038/nature25180
  * Baldwin (1977) Baldwin, J. A. 1977, ApJ, 214, 679, doi: 10.1086/155294
  * Banados et al. (2022) Banados, E., Schindler, J.-T., Venemans, B. P., et al. 2022, arXiv e-prints, arXiv:2212.04452.  https://arxiv.org/abs/2212.04452
  * Becker & Bolton (2013) Becker, G. D., & Bolton, J. S. 2013, MNRAS, 436, 1023, doi: 10.1093/mnras/stt1610
  * Becker et al. (2015a) Becker, G. D., Bolton, J. S., & Lidz, A. 2015a, PASA, 32, e045, doi: 10.1017/pasa.2015.45
  * Becker et al. (2015b) Becker, G. D., Bolton, J. S., Madau, P., et al. 2015b, MNRAS, 447, 3402, doi: 10.1093/mnras/stu2646
  * Becker et al. (2021) Becker, G. D., D’Aloisio, A., Christenson, H. M., et al. 2021, MNRAS, 508, 1853, doi: 10.1093/mnras/stab2696
  * Bischetti et al. (2022) Bischetti, M., Feruglio, C., D’Odorico, V., et al. 2022, Nature, 605, 244, doi: 10.1038/s41586-022-04608-1
  * Boroson & Green (1992) Boroson, T. A., & Green, R. F. 1992, ApJS, 80, 109, doi: 10.1086/191661
  * Bosman (2021) Bosman, S. E. I. 2021, arXiv e-prints, arXiv:2108.12446.  https://arxiv.org/abs/2108.12446
  * Boutsia et al. (2020) Boutsia, K., Grazian, A., Calderone, G., et al. 2020, arXiv e-prints, arXiv:2008.03865.  https://arxiv.org/abs/2008.03865
  * Boutsia et al. (2021) Boutsia, K., Grazian, A., Fontanot, F., et al. 2021, ApJ, 912, 111, doi: 10.3847/1538-4357/abedb5
  * Boyle et al. (2000) Boyle, B. J., Shanks, T., Croom, S. M., et al. 2000, MNRAS, 317, 1014, doi: 10.1046/j.1365-8711.2000.03730.x
  * Boyle et al. (1988) Boyle, B. J., Shanks, T., & Peterson, B. A. 1988, MNRAS, 235, 935, doi: 10.1093/mnras/235.3.935
  * Calderone et al. (2019) Calderone, G., Boutsia, K., Cristiani, S., et al. 2019, ApJ, 887, 268, doi: 10.3847/1538-4357/ab510a
  * Calverley et al. (2011) Calverley, A. P., Becker, G. D., Haehnelt, M. G., & Bolton, J. S. 2011, MNRAS, 412, 2543, doi: 10.1111/j.1365-2966.2010.18072.x
  * Cappelluti et al. (2016) Cappelluti, N., Comastri, A., Fontana, A., et al. 2016, ApJ, 823, 95, doi: 10.3847/0004-637X/823/2/95
  * Carilli et al. (2010) Carilli, C. L., Wang, R., Fan, X., et al. 2010, ApJ, 714, 834, doi: 10.1088/0004-637X/714/1/834
  * Chambers et al. (2016) Chambers, K. C., Magnier, E. A., Metcalfe, N., et al. 2016, arXiv e-prints, arXiv:1612.05560.  https://arxiv.org/abs/1612.05560
  * Cool et al. (2006) Cool, R. J., Kochanek, C. S., Eisenstein, D. J., et al. 2006, AJ, 132, 823, doi: 10.1086/505535
  * Croom et al. (2009) Croom, S. M., Richards, G. T., Shanks, T., et al. 2009, MNRAS, 399, 1755, doi: 10.1111/j.1365-2966.2009.15398.x
  * D’Aloisio et al. (2018) D’Aloisio, A., McQuinn, M., Davies, F. B., & Furlanetto, S. R. 2018, MNRAS, 473, 560, doi: 10.1093/mnras/stx2341
  * Davies et al. (2018) Davies, F. B., Hennawi, J. F., Eilers, A.-C., & Lukić, Z. 2018, ApJ, 855, 106, doi: 10.3847/1538-4357/aaaf70
  * De Rosa et al. (2011) De Rosa, G., Decarli, R., Walter, F., et al. 2011, ApJ, 739, 56, doi: 10.1088/0004-637X/739/2/56
  * Decarli et al. (2018) Decarli, R., Walter, F., Venemans, B. P., et al. 2018, ApJ, 854, 97, doi: 10.3847/1538-4357/aaa5aa
  * Di Matteo et al. (2005) Di Matteo, T., Springel, V., & Hernquist, L. 2005, Nature, 433, 604, doi: 10.1038/nature03335
  * Diamond-Stanic et al. (2009) Diamond-Stanic, A. M., Fan, X., Brandt, W. N., et al. 2009, ApJ, 699, 782, doi: 10.1088/0004-637X/699/1/782
  * Eilers et al. (2020) Eilers, A.-C., Hennawi, J. F., Decarli, R., et al. 2020, ApJ, 900, 37, doi: 10.3847/1538-4357/aba52e
  * Eilers et al. (2021) —. 2021, ApJ, 914, 74, doi: 10.3847/1538-4357/ac05c3
  * Euclid Collaboration et al. (2019) Euclid Collaboration, Barnett, R., Warren, S. J., et al. 2019, A&A, 631, A85, doi: 10.1051/0004-6361/201936427
  * Fan (1999) Fan, X. 1999, AJ, 117, 2528, doi: 10.1086/300848
  * Fan et al. (2000) Fan, X., White, R. L., Davis, M., et al. 2000, AJ, 120, 1167, doi: 10.1086/301534
  * Fan et al. (2001a) Fan, X., Narayanan, V. K., Lupton, R. H., et al. 2001a, AJ, 122, 2833, doi: 10.1086/324111
  * Fan et al. (2001b) Fan, X., Strauss, M. A., Schneider, D. P., et al. 2001b, AJ, 121, 54, doi: 10.1086/318033
  * Fan et al. (2003) —. 2003, AJ, 125, 1649, doi: 10.1086/368246
  * Fan et al. (2004) Fan, X., Hennawi, J. F., Richards, G. T., et al. 2004, AJ, 128, 515, doi: 10.1086/422434
  * Fan et al. (2006) Fan, X., Strauss, M. A., Richards, G. T., et al. 2006, AJ, 131, 1203, doi: 10.1086/500296
  * Fan et al. (2019) Fan, X., Wang, F., Yang, J., et al. 2019, ApJ, 870, L11, doi: 10.3847/2041-8213/aaeffe
  * Faucher-Giguère (2020) Faucher-Giguère, C.-A. 2020, MNRAS, 493, 1614, doi: 10.1093/mnras/staa302
  * Faucher-Giguère et al. (2008) Faucher-Giguère, C.-A., Lidz, A., Hernquist, L., & Zaldarriaga, M. 2008, ApJ, 688, 85, doi: 10.1086/592289
  * Fontanot et al. (2007) Fontanot, F., Cristiani, S., Monaco, P., et al. 2007, A&A, 461, 39, doi: 10.1051/0004-6361:20066073
  * Foreman-Mackey et al. (2013) Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013, PASP, 125, 306, doi: 10.1086/670067
  * Gehrels (1986) Gehrels, N. 1986, ApJ, 303, 336, doi: 10.1086/164079
  * Giallongo et al. (2015) Giallongo, E., Grazian, A., Fiore, F., et al. 2015, A&A, 578, A83, doi: 10.1051/0004-6361/201425334
  * Giallongo et al. (2019) —. 2019, ApJ, 884, 19, doi: 10.3847/1538-4357/ab39e1
  * Glikman et al. (2011) Glikman, E., Djorgovski, S. G., Stern, D., et al. 2011, ApJ, 728, L26, doi: 10.1088/2041-8205/728/2/L26
  * Gloudemans et al. (2022) Gloudemans, A. J., Duncan, K. J., Saxena, A., et al. 2022, arXiv e-prints, arXiv:2210.01811.  https://arxiv.org/abs/2210.01811
  * Górski et al. (2005) Górski, K. M., Hivon, E., Banday, A. J., et al. 2005, ApJ, 622, 759, doi: 10.1086/427976
  * Goto (2006) Goto, T. 2006, MNRAS, 371, 769, doi: 10.1111/j.1365-2966.2006.10702.x
  * Grazian et al. (2020) Grazian, A., Giallongo, E., Fiore, F., et al. 2020, ApJ, 897, 94, doi: 10.3847/1538-4357/ab99a3
  * Grazian et al. (2022) Grazian, A., Giallongo, E., Boutsia, K., et al. 2022, ApJ, 924, 62, doi: 10.3847/1538-4357/ac33a4
  * Haardt & Madau (1996) Haardt, F., & Madau, P. 1996, ApJ, 461, 20, doi: 10.1086/177035
  * Haardt & Madau (2012) —. 2012, ApJ, 746, 125, doi: 10.1088/0004-637X/746/2/125
  * Harris et al. (2020) Harris, C. R., Jarrod Millman, K., van der Walt, S. J., et al. 2020, arXiv e-prints, arXiv:2006.10256.  https://arxiv.org/abs/2006.10256
  * Hinton (2016) Hinton, S. R. 2016, The Journal of Open Source Software, 1, 00045, doi: 10.21105/joss.00045
  * Inayoshi et al. (2020) Inayoshi, K., Visbal, E., & Haiman, Z. 2020, ARA&A, 58, 27, doi: 10.1146/annurev-astro-120419-014455
  * Jiang et al. (2015) Jiang, L., McGreer, I. D., Fan, X., et al. 2015, AJ, 149, 188, doi: 10.1088/0004-6256/149/6/188
  * Jiang et al. (2006) Jiang, L., Fan, X., Hines, D. C., et al. 2006, AJ, 132, 2127, doi: 10.1086/508209
  * Jiang et al. (2008) Jiang, L., Fan, X., Annis, J., et al. 2008, AJ, 135, 1057, doi: 10.1088/0004-6256/135/3/1057
  * Jiang et al. (2016) Jiang, L., McGreer, I. D., Fan, X., et al. 2016, ApJ, 833, 222, doi: 10.3847/1538-4357/833/2/222
  * Jiang et al. (2022) Jiang, L., Ning, Y., Fan, X., et al. 2022, Nature Astronomy, 6, 850, doi: 10.1038/s41550-022-01708-w
  * Kaiser et al. (2002) Kaiser, N., Aussel, H., Burke, B. E., et al. 2002, in Proc. SPIE, Vol. 4836, Survey and Other Telescope Technologies and Discoveries, ed. J. A. Tyson & S. Wolff, 154–164, doi: 10.1117/12.457365
  * Kaiser et al. (2010) Kaiser, N., Burgett, W., Chambers, K., et al. 2010, in Proc. SPIE, Vol. 7733, Ground-based and Airborne Telescopes III, 77330E, doi: 10.1117/12.859188
  * Kim et al. (2015) Kim, Y., Im, M., Jeon, Y., et al. 2015, ApJ, 813, L35, doi: 10.1088/2041-8205/813/2/L35
  * Kim et al. (2020) —. 2020, ApJ, 904, 111, doi: 10.3847/1538-4357/abc0ea
  * Kormendy & Ho (2013) Kormendy, J., & Ho, L. C. 2013, ARA&A, 51, 511, doi: 10.1146/annurev-astro-082708-101811
  * Kulkarni et al. (2019) Kulkarni, G., Worseck, G., & Hennawi, J. F. 2019, MNRAS, 488, 1035, doi: 10.1093/mnras/stz1493
  * Kurk et al. (2007) Kurk, J. D., Walter, F., Fan, X., et al. 2007, ApJ, 669, 32, doi: 10.1086/521596
  * Lusso et al. (2015) Lusso, E., Worseck, G., Hennawi, J. F., et al. 2015, MNRAS, 449, 4204, doi: 10.1093/mnras/stv516
  * Lyke et al. (2020) Lyke, B. W., Higley, A. N., McLane, J. N., et al. 2020, ApJS, 250, 8, doi: 10.3847/1538-4365/aba623
  * Lyu & Rieke (2017) Lyu, J., & Rieke, G. H. 2017, ApJ, 841, 76, doi: 10.3847/1538-4357/aa7051
  * Madau & Haardt (2015) Madau, P., & Haardt, F. 2015, ApJ, 813, L8, doi: 10.1088/2041-8205/813/1/L8
  * Madau et al. (1999) Madau, P., Haardt, F., & Rees, M. J. 1999, ApJ, 514, 648, doi: 10.1086/306975
  * Magnier et al. (2020a) Magnier, E. A., Chambers, K. C., Flewelling, H. A., et al. 2020a, ApJS, 251, 3, doi: 10.3847/1538-4365/abb829
  * Magnier et al. (2020b) Magnier, E. A., Sweeney, W. E., Chambers, K. C., et al. 2020b, ApJS, 251, 5, doi: 10.3847/1538-4365/abb82c
  * Marshall et al. (1983) Marshall, H. L., Tananbaum, H., Avni, Y., & Zamorani, G. 1983, ApJ, 269, 35, doi: 10.1086/161016
  * Matsuoka et al. (2016) Matsuoka, Y., Onoue, M., Kashikawa, N., et al. 2016, ApJ, 828, 26, doi: 10.3847/0004-637X/828/1/26
  * Matsuoka et al. (2018) Matsuoka, Y., Strauss, M. A., Kashikawa, N., et al. 2018, ApJ, 869, 150, doi: 10.3847/1538-4357/aaee7a
  * McGreer et al. (2021) McGreer, I., Moustakas, J., & Schindler, J. 2021, simqso: Simulated quasar spectra generator, Astrophysics Source Code Library, record ascl:2106.008.  http://ascl.net/2106.008
  * McGreer et al. (2018) McGreer, I. D., Fan, X., Jiang, L., & Cai, Z. 2018, AJ, 155, 131, doi: 10.3847/1538-3881/aaaab4
  * McGreer et al. (2013) McGreer, I. D., Jiang, L., Fan, X., et al. 2013, ApJ, 768, 105, doi: 10.1088/0004-637X/768/2/105
  * Morganson et al. (2012) Morganson, E., De Rosa, G., Decarli, R., et al. 2012, AJ, 143, 142, doi: 10.1088/0004-6256/143/6/142
  * Mortlock et al. (2009) Mortlock, D. J., Patel, M., Warren, S. J., et al. 2009, A&A, 505, 97, doi: 10.1051/0004-6361/200811161
  * Neeleman et al. (2021) Neeleman, M., Novak, M., Venemans, B. P., et al. 2021, ApJ, 911, 141, doi: 10.3847/1538-4357/abe70f
  * Newville et al. (2014) Newville, M., Stensitzki, T., Allen, D. B., & Ingargiola, A. 2014, LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python, 0.8.0, Zenodo, doi: 10.5281/zenodo.11813
  * Niida et al. (2020) Niida, M., Nagao, T., Ikeda, H., et al. 2020, ApJ, 904, 89, doi: 10.3847/1538-4357/abbe11
  * Onken et al. (2022) Onken, C. A., Wolf, C., Bian, F., et al. 2022, MNRAS, 511, 572, doi: 10.1093/mnras/stac051
  * Pacucci & Loeb (2019) Pacucci, F., & Loeb, A. 2019, ApJ, 870, L12, doi: 10.3847/2041-8213/aaf86a
  * Page & Carrera (2000) Page, M. J., & Carrera, F. J. 2000, MNRAS, 311, 433, doi: 10.1046/j.1365-8711.2000.03105.x
  * Pan et al. (2022) Pan, Z., Jiang, L., Fan, X., Wu, J., & Yang, J. 2022, ApJ, 928, 172, doi: 10.3847/1538-4357/ac5aab
  * pandas development team (2020) pandas development team, T. 2020, pandas-dev/pandas: Pandas, latest, Zenodo, doi: 10.5281/zenodo.3509134
  * Pâris et al. (2014) Pâris, I., Petitjean, P., Aubourg, É., et al. 2014, A&A, 563, A54, doi: 10.1051/0004-6361/201322691
  * Pâris et al. (2017) Pâris, I., Petitjean, P., Ross, N. P., et al. 2017, A&A, 597, A79, doi: 10.1051/0004-6361/201527999
  * Parsa et al. (2018) Parsa, S., Dunlop, J. S., & McLure, R. J. 2018, MNRAS, 474, 2904, doi: 10.1093/mnras/stx2887
  * Pei (1995) Pei, Y. C. 1995, ApJ, 438, 623, doi: 10.1086/175105
  * Ricci et al. (2017) Ricci, F., Marchesi, S., Shankar, F., La Franca, F., & Civano, F. 2017, MNRAS, 465, 1915, doi: 10.1093/mnras/stw2909
  * Richards et al. (2006) Richards, G. T., Strauss, M. A., Fan, X., et al. 2006, AJ, 131, 2766, doi: 10.1086/503559
  * Rix et al. (2021) Rix, H.-W., Hogg, D. W., Boubert, D., et al. 2021, arXiv e-prints, arXiv:2106.07653.  https://arxiv.org/abs/2106.07653
  * Rojas-Ruiz et al. (2021) Rojas-Ruiz, S., Bañados, E., Neeleman, M., et al. 2021, ApJ, 920, 150, doi: 10.3847/1538-4357/ac1a13
  * Ross et al. (2013) Ross, N. P., McGreer, I. D., White, M., et al. 2013, ApJ, 773, 14, doi: 10.1088/0004-637X/773/1/14
  * Scaramella et al. (2021) Scaramella, R., Amiaux, J., Mellier, Y., et al. 2021, arXiv e-prints, arXiv:2108.01201.  https://arxiv.org/abs/2108.01201
  * Schindler et al. (2018) Schindler, J.-T., Fan, X., McGreer, I. D., et al. 2018, ApJ, 863, 144, doi: 10.3847/1538-4357/aad2dd
  * Schindler et al. (2019) —. 2019, ApJ, 871, 258, doi: 10.3847/1538-4357/aaf86c
  * Schlafly & Finkbeiner (2011) Schlafly, E. F., & Finkbeiner, D. P. 2011, ApJ, 737, 103, doi: 10.1088/0004-637X/737/2/103
  * Schlegel et al. (1998) Schlegel, D. J., Finkbeiner, D. P., & Davis, M. 1998, ApJ, 500, 525, doi: 10.1086/305772
  * Schmidt (1968) Schmidt, M. 1968, ApJ, 151, 393, doi: 10.1086/149446
  * Schmidt et al. (1995) Schmidt, M., Schneider, D. P., & Gunn, J. E. 1995, AJ, 110, 68, doi: 10.1086/117497
  * Schneider et al. (2010) Schneider, D. P., Richards, G. T., Hall, P. B., et al. 2010, AJ, 139, 2360, doi: 10.1088/0004-6256/139/6/2360
  * Selsing et al. (2016) Selsing, J., Fynbo, J. P. U., Christensen, L., & Krogager, J.-K. 2016, A&A, 585, A87, doi: 10.1051/0004-6361/201527096
  * Shen et al. (2020) Shen, X., Hopkins, P. F., Faucher-Giguère, C.-A., et al. 2020, MNRAS, 495, 3252, doi: 10.1093/mnras/staa1381
  * Shen & Kelly (2012) Shen, Y., & Kelly, B. C. 2012, ApJ, 746, 169, doi: 10.1088/0004-637X/746/2/169
  * Shen et al. (2019) Shen, Y., Wu, J., Jiang, L., et al. 2019, ApJ, 873, 35, doi: 10.3847/1538-4357/ab03d9
  * Shin et al. (2020) Shin, S., Im, M., Kim, Y., et al. 2020, ApJ, 893, 45, doi: 10.3847/1538-4357/ab7bde
  * Temple et al. (2021) Temple, M. J., Hewett, P. C., & Banerji, M. 2021, MNRAS, 508, 737, doi: 10.1093/mnras/stab2586
  * Tsuzuki et al. (2006) Tsuzuki, Y., Kawara, K., Yoshii, Y., et al. 2006, ApJ, 650, 57, doi: 10.1086/506376
  * van der Walt et al. (2011) van der Walt, S., Colbert, S. C., & Varoquaux, G. 2011, Computing in Science Engineering, 13, 22
  * Venemans et al. (2007) Venemans, B. P., McMahon, R. G., Warren, S. J., et al. 2007, MNRAS, 376, L76, doi: 10.1111/j.1745-3933.2007.00290.x
  * Venemans et al. (2013) Venemans, B. P., Findlay, J. R., Sutherland, W. J., et al. 2013, ApJ, 779, 24, doi: 10.1088/0004-637X/779/1/24
  * Venemans et al. (2020) Venemans, B. P., Walter, F., Neeleman, M., et al. 2020, ApJ, 904, 130, doi: 10.3847/1538-4357/abc563
  * Verner et al. (1996) Verner, D. A., Ferland, G. J., Korista, K. T., & Yakovlev, D. G. 1996, ApJ, 465, 487, doi: 10.1086/177435
  * Vestergaard & Wilkes (2001) Vestergaard, M., & Wilkes, B. J. 2001, ApJS, 134, 1, doi: 10.1086/320357
  * Virtanen et al. (2020) Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, Nature Methods, 17, 261, doi: https://doi.org/10.1038/s41592-019-0686-2
  * Vito et al. (2016) Vito, F., Gilli, R., Vignali, C., et al. 2016, MNRAS, 463, 348, doi: 10.1093/mnras/stw1998
  * Wang et al. (2019a) Wang, F., Wang, R., Fan, X., et al. 2019a, ApJ, 880, 2, doi: 10.3847/1538-4357/ab2717
  * Wang et al. (2016a) Wang, F., Wu, X.-B., Fan, X., et al. 2016a, ApJ, 819, 24, doi: 10.3847/0004-637X/819/1/24
  * Wang et al. (2017) Wang, F., Fan, X., Yang, J., et al. 2017, ApJ, 839, 27, doi: 10.3847/1538-4357/aa689f
  * Wang et al. (2018) Wang, F., Yang, J., Fan, X., et al. 2018, ApJ, 869, L9, doi: 10.3847/2041-8213/aaf1d2
  * Wang et al. (2019b) —. 2019b, ApJ, 884, 30, doi: 10.3847/1538-4357/ab2be5
  * Wang et al. (2021) —. 2021, ApJ, 907, L1, doi: 10.3847/2041-8213/abd8c6
  * Wang et al. (2010) Wang, R., Carilli, C. L., Neri, R., et al. 2010, ApJ, 714, 699, doi: 10.1088/0004-637X/714/1/699
  * Wang et al. (2011) Wang, R., Wagg, J., Carilli, C. L., et al. 2011, AJ, 142, 101, doi: 10.1088/0004-6256/142/4/101
  * Wang et al. (2016b) Wang, R., Wu, X.-B., Neri, R., et al. 2016b, ApJ, 830, 53, doi: 10.3847/0004-637X/830/1/53
  * Weigel et al. (2015) Weigel, A. K., Schawinski, K., Treister, E., et al. 2015, MNRAS, 448, 3167, doi: 10.1093/mnras/stv184
  * Wenzl et al. (2021) Wenzl, L., Schindler, J.-T., Fan, X., et al. 2021, AJ, 162, 72, doi: 10.3847/1538-3881/ac0254
  * Wes McKinney (2010) Wes McKinney. 2010, in Proceedings of the 9th Python in Science Conference, ed. Stéfan van der Walt & Jarrod Millman, 56 – 61, doi: 10.25080/Majora-92bf1922-00a
  * Willott et al. (2007) Willott, C. J., Delorme, P., Omont, A., et al. 2007, AJ, 134, 2435, doi: 10.1086/522962
  * Willott et al. (2010) Willott, C. J., Delorme, P., Reylé, C., et al. 2010, AJ, 139, 906, doi: 10.1088/0004-6256/139/3/906
  * Wu et al. (2015) Wu, X.-B., Wang, F., Fan, X., et al. 2015, Nature, 518, 512, doi: 10.1038/nature14241
  * Wyithe & Bolton (2011) Wyithe, J. S. B., & Bolton, J. S. 2011, MNRAS, 412, 1926, doi: 10.1111/j.1365-2966.2010.18030.x
  * Yang et al. (2016) Yang, J., Wang, F., Wu, X.-B., et al. 2016, ApJ, 829, 33, doi: 10.3847/0004-637X/829/1/33
  * Yang et al. (2019) Yang, J., Wang, F., Fan, X., et al. 2019, ApJ, 871, 199, doi: 10.3847/1538-4357/aaf858
  * Yang et al. (2020) —. 2020, ApJ, 897, L14, doi: 10.3847/2041-8213/ab9c26
  * Yang et al. (2021) —. 2021, ApJ, 923, 262, doi: 10.3847/1538-4357/ac2b32
  * Yue et al. (2022) Yue, M., Fan, X., Yang, J., & Wang, F. 2022, ApJ, 925, 169, doi: 10.3847/1538-4357/ac409b
  * Zonca et al. (2019) Zonca, A., Singer, L., Lenz, D., et al. 2019, Journal of Open Source Software, 4, 1298, doi: 10.21105/joss.01298
  * Zuo & Phinney (1993) Zuo, L., & Phinney, E. S. 1993, ApJ, 418, 28, doi: 10.1086/173367