Research map / Architectures and efficiency / RNNs and normalization
Shape Abstraction via Marching Differentiable Support Functions
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes shape abstraction of SDF data into differentiable support function (DSF) primitives using a differentiable shape parameterization and hyperplane-based marching, enabling differentiable contact features.
Problem
Abstracting shapes into a small set of primitives with high accuracy and versatility, while keeping contact features differentiable for contact-related downstream tasks.
Approach
Represents convex primitives as differentiable support functions with a smooth center parameterization and abstracts SDFs by marching hyperplanes (region reduction and region expansion, plus a hybrid) to fit DSFs within convex regions.
Key results
- MDSF achieves mean IoU 0.9333 and Chamfer-L1 0.0810 with 13.85 primitives on average, versus MP's 0.9171 IoU and 37.7 primitives.
- CvxNet baseline reaches mean IoU 0.8107 and Chamfer-L1 0.1900 with 50 primitives.
- Small overlap parameter variant reaches IoU 0.9399 but increases primitives to 19.4.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use MDSF instead of CoDSF | DSF shape abstraction · Franka-fr3, Lite6, Xarm7, A1, G1, YCB (mean) | IoU: 0.9309 -> 0.9333 | Helped |
| Use MDSF instead of CoDSF | DSF shape abstraction · Franka-fr3, Lite6, Xarm7, A1, G1, YCB (mean) | Chamfer-L1 (×10): 0.0835 -> 0.0810 | Helped |
| Use MDSF instead of CoDSF | DSF shape abstraction · Franka-fr3, Lite6, Xarm7, A1, G1, YCB (mean) | number of primitives (Nc): 20.8308 -> 13.8462 | Helped |
| Use region reduction instead of the hybrid method (ablation) | MDSF · Franka-fr3, Lite6, Xarm7, A1, G1, YCB | IoU: 0.9333 -> 0.9399 | Helped |
| Use region reduction instead of the hybrid method (ablation) | MDSF · Franka-fr3, Lite6, Xarm7, A1, G1, YCB | Chamfer-L1 (×10): 0.0810 -> 0.0780 | Helped |
| Use region reduction instead of the hybrid method (ablation) | MDSF · Franka-fr3, Lite6, Xarm7, A1, G1, YCB | number of primitives (Nc): 13.8462 -> 17.3846 | Hurt |
| Use region expansion instead of the hybrid method (ablation) | MDSF · Franka-fr3, Lite6, Xarm7, A1, G1, YCB | IoU: 0.9333 -> 0.9170 | Hurt |
| Use region expansion instead of the hybrid method (ablation) | MDSF · Franka-fr3, Lite6, Xarm7, A1, G1, YCB | Chamfer-L1 (×10): 0.0810 -> 0.0938 | Hurt |
| Use region expansion instead of the hybrid method (ablation) | MDSF · Franka-fr3, Lite6, Xarm7, A1, G1, YCB | number of primitives (Nc): 13.8462 -> 12.1077 | Helped |
| Use a small overlap parameter od instead of a large od (ablation) | MDSF hybrid method · Franka-fr3, Lite6, Xarm7, A1, G1, YCB | IoU: 0.9333 -> 0.9399 | Helped |
| Use a small overlap parameter od instead of a large od (ablation) | MDSF hybrid method · Franka-fr3, Lite6, Xarm7, A1, G1, YCB | Chamfer-L1 (×10): 0.0810 -> 0.0783 | Helped |
| Use a small overlap parameter od instead of a large od (ablation) | MDSF hybrid method · Franka-fr3, Lite6, Xarm7, A1, G1, YCB | number of primitives (Nc): 13.8462 -> 19.4308 | Hurt |
Surprising findings
- Region reduction alone gives higher IoU but needs more primitives (17.4) than the hybrid, so the hybrid trades accuracy for fewer components.
Limitations
- Relies on SDF input; does not directly use visual information such as texture or rendering.
- Overlap parameter trades off IoU against primitive count.
Experimental setup
Datasets: YCB dataset MuJoCo Menagerie robot link CAD data
Benchmarks: YCB dataset MuJoCo Menagerie robot links
Metrics: IoU Chamfer-L1 number of primitives (Nc)
Baselines: CvxNet Marching-Primitives (MP) CoDSF (CoACD + DSF fitting)
Builds on: differentiable support function (DSF) Marching-Primitives CoACD CvxNet
Closest papers by meaning
- Marching-Primitives: Shape Abstraction From Signed Distance Function (CVPR 2023 · similarity 0.88)
- EchoMatch: Partial-to-Partial Shape Matching via Correspondence Reflection (CVPR 2025 · similarity 0.85)
- Partial-to-Partial Shape Matching with Geometric Consistency (CVPR 2024 · similarity 0.85)
- Diffusion 3D Features (Diff3F): Decorating Untextured Shapes with Distilled Semantic Features (CVPR 2024 · similarity 0.85)
- PyTorchGeoNodes: Enabling Differentiable Shape Programs for 3D Shape Reconstruction (CVPR 2025 · similarity 0.84)
- DMesh: A Differentiable Mesh Representation (NeurIPS 2024 · similarity 0.84)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.