[论文解读] UCSG-Net -- Unsupervised Discovering of Constructive Solid Geometry Tree

Kacper Kania, Maciej Zięba+1 more|arXiv (Cornell University)|Jun 16, 2020

3D Shape Modeling and Analysis参考文献 39被引用 41

一句话总结

UCSG-Net 学习在无监督条件下为三维形状预测一个构造性实体几何（CSG）解析树，使用 CSG 层和基于占用的操作从原语参数重建形状。该方法能够产生可解释的 CSG 树和具有竞争力的重建质量，同时无需真实解析树。

ABSTRACT

Signed distance field (SDF) is a prominent implicit representation of 3D meshes. Methods that are based on such representation achieved state-of-the-art 3D shape reconstruction quality. However, these methods struggle to reconstruct non-convex shapes. One remedy is to incorporate a constructive solid geometry framework (CSG) that represents a shape as a decomposition into primitives. It allows to embody a 3D shape of high complexity and non-convexity with a simple tree representation of Boolean operations. Nevertheless, existing approaches are supervised and require the entire CSG parse tree that is given upfront during the training process. On the contrary, we propose a model that extracts a CSG parse tree without any supervision - UCSG-Net. Our model predicts parameters of primitives and binarizes their SDF representation through differentiable indicator function. It is achieved jointly with discovering the structure of a Boolean operators tree. The model selects dynamically which operator combination over primitives leads to the reconstruction of high fidelity. We evaluate our method on 2D and 3D autoencoding tasks. We show that the predicted parse tree representation is interpretable and can be used in CAD software.

研究动机与目标

• Motivate interpretable 3D shape reconstruction using a CSG framework.
• Develop an end-to-end neural model that predicts primitive parameters and an unsupervised CSG parse tree.
• Introduce differentiable CSG layers operating on occupancy values to enable stable training.
• Demonstrate unsupervised CSG parsing on 2D CAD-like data and 3D ShapeNet-like data.

提出的方法

• Encode input into a latent vector using a 2D/3D CNN encoder.
• Predict multiple primitive parameters (shape type, size, translation, rotation) in SDF form.
• Convert signed distance values to occupancy values using a learnable clipping parameter alpha.
• Compose shapes with a stack of CSG layers performing union, intersection, and difference using learnable operand selection (K_left, K_right) and Gumbel-Softmax reparameterization.
• Propagate layer-wise information with a GRU-based refinement of the latent code to stabilize multi-layer synthesis.
• Train in two stages: (i) end-to-end optimization of reconstruction and parameter penalties, (ii) fine-tuning towards interpretable, one-hot CSG selections by reducing layer temperatures tau.

实验结果

研究问题

• RQ1 Can a neural network discover a usable CSG parse tree for reconstructing objects without supervision?
• RQ2 How well can occupancy-valued CSG operations approximate standard Boolean operations across 2D and 3D data?
• RQ3 Does unsupervised CSG parsing yield interpretable representations executable in CAD pipelines?
• RQ4 What is the trade-off between interpretability and reconstruction fidelity in an unsupervised CSG framework?

主要发现

表1. 2D CAD 重建 — Chamfer 距离 (CD)（越小越好）跨模式的跨方法比较	k	i=0	i=∞
Method	Mode	CSG-NetStack	Our	-
CSG-NetStack	Supervised	1	3.98	-	-	-
CSG-NetStack	Supervised	10	1.38	-	-	-
CSG-NetStack	RL	1	1.27	-	-	-
CSG-NetStack	RL	10	1.02	-	-	-
Our	Unsupervised	1	0.32	-	-	-

• In 2D CAD data, UCSG-Net achieves an unsupervised reconstruction performance (CD metric) superior to supervised CSG-Net variants, e.g., 0.32 vs 1.02–3.98 in comparable setups.
• The method discovers meaningful CSG parse trees and primitive selections, providing interpretable reconstructions that can be rendered in CAD software.
• In 3D ShapeNet-like data, UCSG-Net attains a Chamfer Distance of 2.085 on the high-interpretability setup, while several baselines (VP, SQ, BAE, BSP-Net) range from 0.446 to 2.259, indicating a trade-off where UCSG-Net prioritizes interpretability and explicit parse trees.
• The approach demonstrates the ability to reuse primitives across layers to form complex shapes and to reveal semantic parts (e.g., wings, hull) within reconstructed objects.
• The model supports recovering a full CSG tree that can be pruned to binary form, enabling direct mesh generation without extra post-processing.