Third Time's the Charm? Image and Video Editing with StyleGAN3
Yuval Alaluf*, Or Patashnik*, Zongze Wu, Asif Zamir, Eli Shechtman, Dani Lischinski, Daniel Cohen-Or
*Denotes equal contributionStyleGAN is arguably one of the most intriguing and well-studied generative models, demonstrating impressive performance in image generation, inversion, and manipulation. In this work, we explore the recent StyleGAN3 architecture, compare it to its predecessor, and investigate its unique advantages, as well as drawbacks. In particular, we demonstrate that while StyleGAN3 can be trained on unaligned data, one can still use aligned data for training, without hindering the ability to generate unaligned imagery. Next, our analysis of the disentanglement of the different latent spaces of StyleGAN3 indicates that the commonly used W/W+ spaces are more entangled than their StyleGAN2 counterparts, underscoring the benefits of using the StyleSpace for fine-grained editing. Considering image inversion, we observe that existing encoder-based techniques struggle when trained on unaligned data. We therefore propose an encoding scheme trained solely on aligned data, yet can still invert unaligned images. Finally, we introduce a novel video inversion and editing workflow that leverages the capabilities of a fine-tuned StyleGAN3 generator to reduce texture sticking and expand the field of view of the edited video.
Using the recent StyleGAN3 generator, we edit unaligned input images across various domains using off-the-shelf editing techniques. Using a trained StyleGAN3 encoder, these techniques can likewise be used to edit real images and videos.
Description
Official implementation of our StyleGAN3 paper "Third Time's the Charm?" where we analyze the recent StyleGAN3 generator and explore its advantages over previous style-based generators. We evaluate StyleGAN3's latent spaces, explore their editability, and introduce an encoding scheme for inverting and editing real images and videos.
Table of Contents
- Getting Started
- Preparing Your Data
- StyleGAN3 Encoder
- Editing
- StyleGAN-NADA
- Acknowledgments
- Citation
Table of contents generated with markdown-toc
Getting Started
Prerequisites
- Linux or macOS
- NVIDIA GPU + CUDA CuDNN (CPU may be possible with some modifications, but is not inherently supported)
- Python 3
During the building of this repository, we decided to replace all uses of argparse
with dataclasses
and pyrallis
. Using dataclasses
provides useful features such as type hints and code completion. We believe this has helped make the code cleaner and we hope you enjoy just as much as we do!
To learn more, check out the pyrallis repository.
Installation
- Dependencies: We recommend running this repository using Anaconda.
All dependencies for defining the environment are provided inenvironment/sg3_env.yaml
.
Inference Notebook
Check out our inference notebook for inverting and editing real images with StyleGAN3.
Preparing Your Data
In this repo, we work with images that are both aligned and cropped (unaligned). Given a directory of raw images, you can prepare your data by running the script prepare_data/preparing_faces_parallel.py
. For example, for preparing your aligned data, you can run:
python prepare_data/preparing_faces_parallel.py \
--mode align \
--root_path /path/to/raw/images
Similarly, to obtain unaligned data, you can run:
python prepare_data/preparing_faces_parallel.py \
--mode crop \
--root_path /path/to/raw/images \
--random_shift 0.05
Given the aligned and unaligned images, we can then compute the transformations between each pair of images.
To compute these landmarks, you can run the following command:
python prepare_data/compute_landmarks_transforms.py \
--raw_root /path/to/root/data \
--aligned_root /path/to/aligned/data \
--cropped_root /path/to/unaligned/data \
--output_root /path/to/directory/to/save/transforms/to/
The aligned data, unaligned data, and landmarks-based transforms will be used in various applications such as inverting unaligned images and editing unaligned images.
StyleGAN3 Encoder
We provide our pretrained StyleGAN3 encoder trained over ReStyle-pSp and ReStyle-e4e using the FFHQ dataset. The models can be downloaded from the following links:
Path | Description |
---|---|
ReStyle-pSp Human Faces | ReStyle-pSp trained on the FFHQ dataset over the StyleGAN3 generator. |
ReStyle-e4e Human Faces | ReStyle-e4e trained on the FFHQ dataset over the StyleGAN3 generator.. |
In addition, we provide various auxiliary models needed for training your own encoders models from scratch.
This includes the StyleGAN generators converted to .pt
format and pre-trained models used for loss computation and encoder backbone.
Path | Description |
---|---|
FFHQ Aligned StyleGAN3 | StyleGAN3 model trained on FFHQ with 1024x1024 output resolution and saved as .pt file. |
FFHQ Unaligned StyleGAN3 | StyleGAN3 model trained on FFHQU with 1024x1024 output resolution and saved as .pt file. |
AFHQ StyleGAN3 | StyleGAN3 model trained on AFHQv2 with 512x512 output resolution and saved as .pt file. Model is taken from the official StyleGAN3 repository. |
Landscapes HQ StyleGAN3 | StyleGAN3 model trained on Landscapes HQ with 256x256 output resolution and saved as .pt file. Model taken from Justin Pinkney. |
Path | Description |
---|---|
IR-SE50 Model | Pretrained IR-SE50 model taken from TreB1eN for use in our ID loss and encoder backbone on human facial domain. |
CurricularFace Backbone | Pretrained CurricularFace model taken from HuangYG123 for use in ID similarity metric computation. |
MTCNN | Weights for MTCNN model taken from TreB1eN for use in ID similarity metric computation. (Unpack the tar.gz to extract the 3 model weights.) |
Note: while you may use the official StyleGAN3 pkl
files, we highly recommend using our provided .pt
generators. The generators themselves are identical, but using the pt
files provide more flexibility.
By default, we assume that all auxiliary models are downloaded and saved to the directory pretrained_models. However, you may use your own paths by changing the necessary values in configs/path_configs.py
.
Training
Recall, that our encoders are trained solely on aligned data. After training is complete, we can perform inference on both aligned and unaligned data by using the user-specified transformations supported by StyleGAN3.
To prepare your data configs, we refer the reader to the ReStyle repository which we follow.
To train our ReStyle-pSp encoder, you can run the following command:
python inversion/scripts/train_restyle_psp.py \
--dataset_type ffhq_encode \
--encoder_type BackboneEncoder \
--exp_dir experiments/restyle_psp_ffhq_encode \
--batch_size 2 \
--test_batch_size 2 \
--workers 8 \
--test_workers 8 \
--val_interval 5000 \
--save_interval 10000 \
--start_from_latent_avg True \
--lpips_lambda 0.8 \
--l2_lambda 1 \
--id_lambda 0.1 \
--input_nc 6 \
--n_iters_per_batch 3 \
--output_size 1024 \
--stylegan_weights pretrained_models/sg3-r-ffhq-1024.pt
Similarly training a ReStyle-e4e encoder can be run with the following command:
python inversion/scripts/train_restyle_e4e.py \
--dataset_type ffhq_encode \
--encoder_type ProgressiveBackboneEncoder \
--exp_dir experiments/restyle_e4e_ffhq_encode \
--batch_size 2 \
--test_batch_size 2 \
--workers 8 \
--test_workers 8 \
--start_from_latent_avg True \
--lpips_lambda 0.8 \
--l2_lambda 1 \
--id_lambda 0.1 \
--w_discriminator_lambda 0.1 \
--use_w_pool True \
--input_nc 6 \
--n_iters_per_batch 3 \
--truncation_psi 0.7 \
--output_size 1024 \
--stylegan_weights pretrained_models/sg3-r-ffhq-1024.pt
Additional Notes:
- All hyper-parameters are set as the defaults as used in ReStyle except that when training ReStyle-e4e we do not use the progressive training scheme.
- You should also adjust the
--output_size
and--stylegan_weights
flags according to your StyleGAN3 generator. - See
inversion/options/train_options.py
andinversion/options/e4e_train_options.py
for all training-specific flags.
Inference and Evaluation
Sample reconstructions for unaligned images obtained with our ReStyle encoders.
Inversion
You can use inversion/scripts/inference_iterative.py
to apply a trained model on a set of images. For example:
python inversion/scripts/inference_iterative.py \
--output_path experiments/restyle_e4e_ffhq_encode/inference \
--checkpoint_path experiments/restyle_e4e_ffhq_encode/checkpoints/best_model.pt \
--data_path /path/to/aligned_test_data \
--test_batch_size 4 \
--test_workers 4 \
--n_iters_per_batch 3 \
--landmarks_transforms_path /path/to/landmarks_transforms.npy
This script will save each step's outputs in a separate sub-directory and the iterative results side-by-side.
Notes:
- Note that the
--data_path
flag should point to your aligned data since this is the data that is passed to the encoder. - If you are inverting unaligned images, you should specify the landmarks-based transforms using the flag
--landmarks_transforms_path
.- When generating the final reconstruction, these transforms will be used to reconstruct the placement and rotation of the unaligned image.
- Follow the instructions above for preparing the
landmarks_transforms
file. - Please note, if this file is not specified, then all outputs will be aligned.
- By default, the images will be saved at their original output resolutions (e.g., 1024x1024 for faces).
- If you wish to save outputs resized to resolutions of
256x256
, you can do so by adding the flag--resize_outputs=True
.
- If you wish to save outputs resized to resolutions of
This script will also save all the latents as an .npy
file in a dictionary format as follows:
{
"0.jpg": [latent_step_1, latent_step_2, ..., latent_step_N],
"1.jpg": [latent_step_1, latent_step_2, ..., latent_step_N],
...
}
That is, the keys of the dictionary are the image file names and the values are lists of length N
containing the output latent of each step where N
is the number of inference steps. Each element in the list is of shape (Kx512)
where K
is the number of style inputs of the generator.
You can use the saved latents to perform latent space manipulations, for example.
Inversion Animation
If you would like to create animations showing interpolations between the inversions of unaligned images (like those on the project page), you can run the script inversion/scripts/create_inversion_animation.py
. For example,
python inversion/scripts/create_inversion_animation.py \
--generator_path pretrained_models/sg3-r-ffhq-1024.pt \
--output_path experiments/restyle_e4e_ffhq_encode/inference/animations \
--latents_path experiments/restyle_e4e_ffhq_encode/inference/latents.npy \
--data_path /path/to/animation/data \
--landmarks_transforms_path /path/to/animation/data/landmarks_transforms.npy \
--n_images 10
Note that we assume that you have already run the inference script from above and have saved the saved latents to the path --latents_path
(similarly for the landmarks transforms). By default, the script will randomly sample n_images
from the data_path
or use all images if n_images
is None
.
Computing Metrics
Given a trained model and generated outputs, we can compute the loss metrics on a given dataset.
These scripts receive the inference output directory and ground truth directory.
- Calculating L2/LPIPS/MS-SSIM losses and similarities:
python inversion/scripts/calc_losses_on_images.py \
--metrics "[lpips, l2, msssim]" \
--output_path /path/to/experiment/inference/inference_results \
--gt_path /path/to/test_images
- Calculating the identity loss for the facial domain:
python inversion/scripts/calc_id_loss_parallel.py \
--output_path /path/to/experiment/inference/inference_results \
--gt_path /path/to/test_images
These scripts will traverse through each sub-directory of output_path
to compute the metrics on each step's output images.
Editing Real Images
For editing real images, we provide two techniques: InterFaceGAN and StyleCLIP's global directions.
InterFaceGAN
Sample editing results for unaligned images obtained with our ReStyle-e4e encoder and InterFaceGAN. Additional results are provided in the project page.
For editing with InterFaceGAN, you can run the following command:
python inversion/scripts/inference_editing.py \
--output_path /path/to/experiment/inference \
--checkpoint_path experiments/restyle_e4e_ffhq_encode/checkpoints/best_model.pt \
--data_path /path/to/test_data \
--test_batch_size 4 \
--test_workers 4 \
--n_iters_per_batch 3 \
--edit_directions "[age,pose,smile]" \
--factor_ranges "[(-5_5),(-5_5),(-5_5)]" \
--landmarks_transforms_path /path/to/landmarks_transforms.npy
This will run inversion and edit each image in the specified data_path
using the trained encoder.
Notes:
- The edits supported by this script are defined in the
FaceEditor
class inediting/interfacegan/face_editor.py
.- You may add your own directions to expand support for additional edits.
- To specify the
lambda
(range) of each edit, you can change the flag--factor_ranges
.- Here,
-5_5
means that the range is(-5,5)
for each edit. - For example, specifying
--edit_directions="[age,pose]"
andfactor_ranges="[(-5_5),(-2_2)]"
will perform edits of age and pose with ranges of(-5,5)
and(-2,2)
, respectively.
- Here,
StyleCLIP Global Directions
Sample editing results for unaligned images obtained with our ReStyle-e4e encoder and StyleCLIP. Additional results are provided in the project page.
For editing with StyleCLIP global directions, you can run the following command:
python editing/styleclip_global_directions/edit.py \
--output_path /path/to/experiment/inference \
--latents_path /path/to/experiment/inference/latents.npy \
--neutral_text "a face" \
--target_tex "a happy face" \
--landmarks_transforms_path /path/to/landmarks_transforms.npy
Notes:
- Before running the above script, you may need to install the official CLIP package:
pip install git+https://github.com/openai/CLIP.git
- For each input image we save a grid of results with different values of
alpha
andbeta
as defined in StyleCLIP.
Pivotal Tuning Inversion (PTI)
We also provide support for running PTI for inverting real images. This can be run using the run_pti_images.py
script. For example:
python inversion/scripts/run_pti_images.py \
--output_path /path/to/experiment/inference/pti \
--generator_path pretrained_models/sg3-r-ffhq-1024.pt \
--images_path /path/to/data \
--latents_path /path/to/experiment/inference/latents.npy \
--landmarks_transforms_path /path/to/landmarks_transforms.npy \
--steps 350 \
--save_interval 100
Currently, instead of starting the PTI inversion process with the mean latent code, we begin with the inversions predicted from our encoder. This speeds up the inversion process by starting from a better initialization point.
Note, as usual, if working with unaligned data, you should pass the landmarks-based transforms in order to reconstruct the original unaligned input pose.
Inverting and Editing Videos
Inference
To invert a given video sequence, you can run the script inversion/video/inference_on_video.py
. For example,
python inversion/video/inference_on_video.py \
--video_path /path/to/input/video.mp4 \
--checkpoint_path experiments/restyle_e4e_ffhq_encode/checkpoints/best_model.pt \
--output_path /path/to/experiment/inference/video_inference
Notes:
- If the
landmarks_transforms_path
is specified, we will compute and save the landmarks transforms to the specified path. If it is not specified, we will save it to the output path, by default.- Then, in future runs, we will load the pre-saved transforms.
- Users can also specify the following paths:
raw_frames_path
,aligned_frames_path
,cropped_frames_path
If these paths are not specified, then they will be saved tooutput_path/raw_frames
,output_path/aligned_frames
, andoutput_path/cropped_frames
, by default.
Once the images are extracted and saved once, they will be loaded in future runs from the specified paths.
The result of the script will be several output videos, including:
input_video
: the video containing the cropped framesresult_video
: the reconstruction video without the smoothing technique from the paperresult_video_smoothed
: the reconstruction video with the smoothing techniqueresult_video_coupled
: a video with the cropped images and smoothed reconstruction side-by-side
PTI Training on Videos
After running the inference script above, you may notice that the results can be improved. We therefore provide the script inversion/video/run_pti_video.py
which runs PTI on the input video to improve the reconstruction obtained by using only the encoder. Running the script can be done using the following command template:
python inversion/video/run_pti_video.py \
--output_path /path/to/experiment/inference/video_inference/pti \
--generator_path pretrained_models/stylegan3/sg3-r-ffhq-1024.pt \
--images_path /path/to/experiment/inference/video_inference/cropped_frames \
--latents_path /path/to/experiment/inference/video_inference/latents.npy \
--landmarks_transforms_path /path/to/experiment/inference/video_inference/landmarks_transforms.npy \
--steps 8000 \
--save_interval 500 \
--model_save_interval 1000 \
--save_final_model
Notes:
- We train PTI using the unaligned images as inputs. This allows us to improve on image regions which were "cut off" by the aligned pre-processing.
- The
images_path
,latents_path
, andlandmarks_transforms_path
should have all be saved when running theinference_on_video.py
script beforehand. - In our experiments, we trained PTI for
8000
steps per input video.
After running PTI, to get the final video reconstructions, you can run the inference_on_video.py
script again and add the --generator_path
flag pointing to the final PTI model. This will replace the original SG3 generator with the PTI-tuned generator. For example,
python inversion/video/inference_on_video.py \
--video_path /path/to/input/video.mp4 \
--checkpoint_path experiments/restyle_e4e_ffhq_encode/checkpoints/best_model.pt \
--output_path /path/to/experiment/inference/video_inference/with_pti \
--raw_frames_path /path/to/experiment/inference/video_inference/raw_frames \
--aligned_frames_path /path/to/experiment/inference/video_inference/aligned_frames \
--cropped_frames_path /path/to/experiment/inference/video_inference/cropped_frames \
--landmarks_transforms_path /path/to/experiment/inference/video_inference/landmarks_transforms.npy \
--generator_path /path/to/experiment/inference/video_inference/pti/final_pti_model.pt
Notice, this time, we will use the aligned images, cropped images, and landmarks transforms from last time.
Field of View Expansion
We provide an Expander object in utils/fov_expansion.py
that allows to generate images with an extended field-of-view by employing Fourier Features transformations. The Expander should be intiallized with a StyleGAN3 Generator object. Then, images can be generated with the function generate_expanded_image
which recieves latent codes if form of w or s and a landmark transform. To expand in 100 pixels to the left, set pixels_left = 100
. Note that it is possible to expand in more than one direction.
An example to the Expander usage can be seen in inversion/video/video_editor.py
in which we generate an edited video with expanded FOV.
Editing
InterFaceGAN
Editing synthetic images with the aligned StyleGAN3 generator using directions learned with InterFaceGAN.
Pre-trained InterFaceGAN Boundaries
Pre-trained boundaries for age, pose, and the 40 CelebA dataset attributes can be found in the following links:
Path | Description |
---|---|
Aligned FFHQ | InterFaceGAN boundaries for the Aligned FFHQ StyleGAN3 generator. |
Unaligned FFHQ | InterFaceGAN boundaries for hte Unaligned FFHQ StyleGAN3 generator. |
We include boundaries for both the aligned StyleGAN3 generator and the unaligned StyleGAN3 generator for human faces.
Training Your Own InterFaceGAN Boundaries
We provide code for training boundaries for InterFaceGAN in editing/interfacegan
. In our implementation we provide classifiers for age, pose, and the 40 attributes from the CelebA dataset (predicted using the classifier from AnyCostGAN.
The age and pose pre-trained classifiers can be downloaded from the following links (the classifier from AnyCostGAN is downloaded automatically via the code):
Path | Description |
---|---|
Age Classifier | An VGG-based age classifier taken from SAM. |
Pose Classifier | A HopeNet pose classifier taken from deep-head-pose. |
First, you need to generate a set of latent codes and predict their attribute scores. This can be done by running:
python editing/interfacegan/generate_latents_and_attribute_scores.py \
--generator_path pretrained_models/stylegan3-r-ffhq-1024x1024.pkl \
--n_images 500000 \
--truncation_psi 0.7 \
--output_path /path/to/predicted/latents/and/scores \
--save_interval 10000
An npy
file will be saved every save_interval
samples. By default, we train boundaries for the aligned StyleGAN3 generator. If training boundaries for an unaligned generator, the psuedo-alignment trick will be performed before passing the images to the classifier.
Once the latents and scores are saved, the boundaries can be trained using the script train_boundaries.py
. For example,
python editing/interfacegan/train_boundaries.py \
--input_path /path/to/predicted/latents/and/scores \
--output_path /path/to/trained/boundaries
This script will save a set of boundaries (in npy
format) for each attribute predicted in the first step.
Editing Synthetic Images with InterFaceGAN
We also provide a script for editing synthetic images with InterFaceGAN. Given a generator (either aligned or unaligned), the script generates the edited images using the directions specified in configs.paths_config.interfacegan_aligned_edit_paths
and configs.paths_config.interfacegan_unaligned_edit_paths
.
For example, users can run the following command to edit images:
python editing/interfacegan/edit_synthetic.py \
--generator_path pretrained_models/stylegan3-r-ffhq-1024x1024.pkl \
--generator_type ALIGNED \
--output_path /path/to/edit/outputs \
--attributes_to_edit "[age,smile,pose]" \
--n_images_per_edit 100 \
--truncation_psi 0.7
Notes:
generator_type
can either bealigned
orunaligned
. This controls which set of editing directions to use.- We currently support edits of
age
,smile
,pose
, andMale
, but this is easily configurable by adding a new range toINTERFACEGAN_RANGES
inedit_synthetic.py
. - If working with aligned generator, users can also generate randomly unaligned images by adding the flag
--apply_random_transforms=True
. This will apply a random translation and rotation before generating the edited image. - Users can also specify the flag
--generate_animation=True
which will create an interpolation video depicting the edits. Note, generating these animations does take about 30 seconds per image.
StyleCLIP
Editing synthetic images with using StyleCLIP's global directions technique.
StyleCLIP Latent Mapper
We provide in editing/styleclip_mapper
an adaptation of the StyleCLIP latent mapper approach to StyleGAN3. Please refer to the original StyeCLIP latent mapper implementation for more details.
Training:
- The main training script can be found at
editing/styleclip_mapper/scripts/train.py
. - Training arguments can be found at
editing/styleclip_mapper/options/train_options.py
. - Note:
--description
is where you provide the driving text. - Note that the latent codes dataset is automatically generated in the case where
opts.latents_train_path
does not exist (and similarly for the test set). - Note that the losses coefficients from StyleGAN2 may not optimal!
As an example, training a mapper for the bob-cut hairstyle can be done by running the following commands:
cd editing/styleclip_mapper/scripts
python train.py --exp_dir ../results/bobcut_hairstyle --description "bobcut hairstyle"
Inference:
- The main inference script can be found at
editing/styleclip_mapper/scripts/inference.py
. - All necessary inference parameters can be found at
editing/styleclip_mapper/options/test_options.py
.
StyleCLIP Global Directions
Preprocessing
The StyleCLIP global directions technique requires two preprocessing steps (that are general to any type of edit):
- First, we must generate the
s_stats
file, which can be done by running:
python editing/styleclip_global_directions/preprocess/s_statistics.py
- Second, we must generate the
delta_i_c.npy
file, which can be fone by running:python editing/styleclip_global_directions/preprocess/create_delta_i_c.py
Please note that this script may take a long time to run.
We provide our precomputed files for FFHQ, FFHQ-U, AFHQ, Landscapes-HQ in the following links:
Path | Description |
---|---|
FFHQ | Folder containing s_stats and delta_i_c.npy computed on StyleGAN3 FFHQ. |
FFHQ-U | Folder containing s_stats and delta_i_c.npy computed on StyleGAN3 FFHQ-U. |
AFHQ | Folder containing s_stats and delta_i_c.npy computed on StyleGAN3 AFHQv2. |
Landscapes HQ | Folder containing s_stats and delta_i_c.npy computed on Landscapes-HQ. |
If you would like to download all files, you can also run the following script:
python editing/styleclip_global_directions/preprocess/download_all_files.py
Editing
For editing randomly sampled images with StyleCLIP global directions, you can run the following command:
python editing/styleclip_global_directions/edit.py \
--output_path /path/to/experiment/inference \
--neutral_text "a sad face" \
--target_text "a happy face" \
--n_images=10
Here, we will randomly sample 10
latents and edit them using the specified edit.
Notes:
- To apply random transformations to the images, you can set the flag
--apply_random_transforms=True
. - For each input image we save a grid of results with different values of
alpha
andbeta
as defined in StyleCLIP.
StyleGAN-NADA
In our paper, we perform various experiments with StyleGAN-NADA trained over StyleGAN3.
We invite the reader to head over to the StyleGAN3-NADA branch in the official paper repository for running StyleGAN-NADA over StyleGAN3.
We provide a set of trained models for FFHQ, FFHQ-U, and AFHQ-v2:
Path | Description |
---|---|
FFHQ | Folder a set of trained StyleGAN3-NADA models fine-tuned from the original FFHQ model. |
FFHQ-U | Folder a set of trained StyleGAN3-NADA models fine-tuned from the original FFHQ-U model. |
AFHQ | Folder a set of trained StyleGAN3-NADA models fine-tuned from the original AFHQ-v2 model. |
Acknowledgments
This code borrows from various repositories, including:
- StyleGAN3
- StyleGAN2
- pixel2style2pixel (pSp)
- encoder4editing (e4e)
- ReStyle
- StyleCLIP
- InterFaceGAN
- IR-SE50
- LPIPS
- MS-SSIM
- Ranger
Citation
If you use this code for your research, please cite the following work:
@misc{alaluf2022times,
title={Third Time's the Charm? Image and Video Editing with StyleGAN3},
author={Yuval Alaluf and Or Patashnik and Zongze Wu and Asif Zamir and Eli Shechtman and Dani Lischinski and Daniel Cohen-Or},
year={2022},
eprint={2201.13433},
archivePrefix={arXiv},
primaryClass={cs.CV}
}