Sequential assembly with geometric primitives has drawn attention in robotics
and 3D vision since it yields a practical blueprint to construct a target
shape. However, due to its combinatorial property, a greedy method falls short
of generating a sequence of volumetric primitives. To alleviate this
consequence induced by a huge number of feasible combinations, we propose a
combinatorial 3D shape generation framework. The proposed framework reflects an
important aspect of human generation processes in real life -- we often create
a 3D shape by sequentially assembling unit primitives with geometric
constraints. To find the desired combination regarding combination evaluations,
we adopt Bayesian optimization, which is able to exploit and explore
efficiently the feasible regions constrained by the current primitive
placements. An evaluation function conveys global structure guidance for an
assembly process and stability in terms of gravity and external forces
simultaneously. Experimental results demonstrate that our method successfully
generates combinatorial 3D shapes and simulates more realistic generation
processes. We also introduce a new dataset for combinatorial 3D shape
generation. All the codes are available at
https://github.com/POSTECH-CVLab/Combinatorial-3D-Shape-Generation.

通过采用基于进化算法的贝叶斯优化方法，提出了一种组合 3D 形状生成框架。该框架可以通过将体形学高斯过程与全局结构导向评估函数相结合来利用并探索当前基元状态下受约束的可行域。实验结果表明，我们的方法可以生成有效的组合 3D 形状。