Deformable Radial Kernel Splatting

This repository contains the code for Deformable Radial Kernel Splatting (DRK).

Deformable Radial Kernel (DRK) extends Gaussian kernels with learnable radial bases, enabling the modeling of diverse shape primitives. It introduces parameters to control the sharpness and boundary curvature of these primitives. The following video showcases the effectiveness of each parameter:

DRK can flexibly fit various basic primitives with diverse shapes and sharp boundaries:

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Updated densification strategy

DRK with an updated densification strategy, compared to 3DGS on Tanks & Temples (Family, COLMAP poses, 896×512, test split):

Family	PSNR	SSIM	L1	prims
3DGS	22.25	0.782	0.047	1.70M
DRK	22.46	0.765	0.045	0.90M

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Real-time rendering via the traditional pipeline (web / mobile)

A trained soft-DRK model can be rendered as a triangle soup by a standard hardware rasterization pipeline — each primitive becomes a billboard whose fragment shader evaluates the DRK radial kernel, composited with per-primitive depth sort + single-pass alpha blend. This runs in WebGL2 / OpenGL ES (web, mobile, headsets) with no CUDA dependency, while preserving the soft DRK appearance. scripts/drk_soup_gl.py is the reference renderer; scripts/web/viewer.html is a self-contained WebGL2 viewer.

Web / mobile deployment

# export a trained DRK model to a portable WebGL viewer folder (geometry + attributes + GLSL)
python scripts/export_soup_web.py -m <run_dir> --load-iteration <N> --out viewer_out
# view it — WebGL2 == the mobile GLES path, so in-browser FPS gauges on-device feasibility
cd viewer_out && python3 -m http.server 8000   # open http://localhost:8000

Add --embed for a single double-click HTML, or --skybox <asset_dir> to composite a learned multi-shell background panorama behind the foreground. A ready-to-open example (50k-primitive Family soup + skybox, no server needed) is in demo/family_50k_viewer.html — open it in any browser (drag = orbit, scroll = zoom, slider = visible-primitive radius / FPS).

Comparison with 3DGS (same WebGL pipeline)

Both methods rendered as billboard soups in the same pipeline (Tanks & Temples Family, test split, 896×512; FPS excludes offline read-back):

method	primitives	PSNR	FPS
3DGS	1.70 M	21.5	116
DRK (ours)	50 k	20.8	186
DRK (ours)	150 k	21.0	81

DRK reaches comparable quality with ~11–34× fewer primitives (3DGS collapses if subsampled), yielding a ~19× smaller asset (≈21 MB vs ≈395 MB) and higher FPS at the low primitive counts mobile devices need. Reproduce with scripts/gs_soup_gl.py + scripts/export_compare_web.py (scripts/web/compare.html toggles DRK ⇄ 3DGS live).

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Environment Setup

Create and Activate Python Environment

Using Conda:

conda create -n drkenv python=3.9  # (Python >= 3.8)
conda activate drkenv

Using Virtualenv:

virtualenv drkenv -p python3.9  # (Python >= 3.8)
source drkenv/bin/activate

Install Dependencies

python -m pip install -U pip setuptools wheel importlib-metadata
python -m pip install -r requirements.txt

# Use the CUDA toolkit that matches the PyTorch wheels above.
source ./switch-cuda.sh 11.8

cd submodules/depth-diff-gaussian-rasterization
python -m pip install --no-build-isolation --no-deps .
cd ../drk_splatting
python -m pip install --no-build-isolation --no-deps .
cd ../simple-knn
python -m pip install --no-build-isolation --no-deps .
cd ../..

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UI Demo

We provide a UI demo to better understand the effects of DRK attributes and cache-sorting. To run the demo, execute the following script:

python drk_demo.py

The demo allows you to adjust attribute bars, switch rendering modes (normal, alpha, depth, RGB), toggle cache-sorting, and explore DRK's flexible representation capabilities.

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Mesh2DRK

We also provide a script to convert mesh assets into DRK representation without training. To achieve mixed rendering of meshes and reconstructed scenes, specify the scene_path in mesh2drk.py. If scene_path is left empty, the script will render the mesh only. You can modify the mesh_path_list to include any assets you wish to render. Currently, .obj + .mtl and .ply formats are supported. For reference, we provide example assets in the meshes folder.

python mesh2drk.py

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Data Download

Download the datasets using the following links:

• MipNeRF-360
• DiverseScenes

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Running the Code

Commands

Run the following commands in your terminal:

Training:

CUDA_VISIBLE_DEVICES=${GPU} python train.py -s ${PATH_TO_DATA} -m ${LOG_PATH} --eval --gs_type DRK --kernel_density dense --cache_sort  # Optional: --gui --is_unbounded

Evaluation:

CUDA_VISIBLE_DEVICES=${GPU} python train.py -s ${PATH_TO_DATA} -m ${LOG_PATH} --eval --gs_type DRK --kernel_density dense --cache_sort --metric

Command Options:

• --kernel_density: Specifies the primitive density (number) for reconstruction. Choose from dense, middle, or sparse.
• --cache_sort: (Optional) Use cache sorting to avoid popping artifacts and slightly increase PSNR (approx. +0.1dB). Ensure consistency between training and evaluation. Note: In specular scenes, disabling cache-sort may yield better results as highlights are better modeled without strict sorting.
• --is_unbounded: Use different hyperparameters for unbounded scenes (e.g., Mip360).
• --gui: Enables an interactive visualization UI. Toggle cache-sorting, tile-culling, and view different rendering modes (normal, depth, alpha) via the control panel.

Batch Scripts

Scripts for evaluating all scenes in the dataset are provided in the scripts folder. Modify the paths in the scripts before running them.

python ./scripts/diverse_script.py  # For DiverseScenes
python ./scripts/mip360_script.py   # For MipNeRF-360

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Recent Optimizations

CUDA Optimization

• Precomputed kernel vectors: scale * [cos(θ), sin(θ)] computed once in preprocess, reused in rendering and tile culling
• atan2f replaces acos+sqrt: faster angle computation in inner loop
• Removed roundf truncation: eliminated expensive per-hit rounding
• Shared memory optimization: geometry buffer strategy to stay within 48KB limit
• Densification stats via CUDA: collect absolute gradients (fabsf) directly in backward kernel, avoiding Python overhead
• Branchless segment search: replaced branch-heavy linear scan with predicated additions for better warp coherence
• Fast math intrinsics: __expf, __cosf, __sincosf, __frcp_rn to replace standard exp/cos/sin/division
• Cached reciprocals: pre-compute 1/delta, 1/(scale²), 1/(theta_r−theta_l), 1/dir_dot_n etc. to eliminate redundant divisions
• Compiler flags: --use_fast_math -O3 --ftz=true in setup.py

Rendering Quality

• Opacity-gradient driven densification: combine position and opacity gradients for more accurate densification decisions
• Visibility-aware pruning: prune low-visibility + low-opacity floaters during densification
• Multi-scale anti-aliasing loss (--lambda_multiscale): optional multi-resolution L1+SSIM supervision
• Opacity regularization (--lambda_opacity_reg): entropy-based regularization to suppress semi-transparent floaters

Misc

• Fixed install instructions and added .gitignore for build outputs
• simple_knn.cu: use <float.h> instead of hardcoded FLT_MAX
• gui_utils: graceful fallback when dearpygui is not installed

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Citing

If you find our work useful, please consider citing:

@article{huang2024deformable,
  title={Deformable Radial Kernel Splatting},
  author={Huang, Yi-Hua and Lin, Ming-Xian and Sun, Yang-Tian and Yang, Ziyi and Lyu, Xiaoyang and Cao, Yan-Pei and Qi, Xiaojuan},
  journal={arXiv preprint arXiv:2412.11752},
  year={2024}
}