We present a probabilistic 3D generative model, named Generative Cellular Automata, which is able to produce diverse and high quality shapes. We formulate the shape generation process as sampling from the transition kernel of a Markov chain, where the sampling chain eventually evolves to the full shape of the learned distribution. The transition kernel employs the local update rules of cellular automata, effectively reducing the search space in a high-resolution 3D grid space by exploiting the connectivity and sparsity of 3D shapes. Our progressive generation only focuses on the sparse set of occupied voxels and their neighborhood, thus enabling the utilization of an expressive sparse convolutional network. We propose an effective training scheme to obtain the local homogeneous rule of generative cellular automata with sequences that are slightly different from the sampling chain but converge to the full shapes in the training data. Extensive experiments on probabilistic shape completion and shape generation demonstrate that our method achieves competitive performance against recent methods.

提出一种名为生成元胞自动机的概率三维生成模型，其能够产生多样化和高质量的形状，利用细胞自动机的局部更新规则有效减少了搜索空间，在稀疏卷积网络的支持下进行渐进生成，通过抽样与训练轮廓数据的匹配学习得到了本地均匀规则，并在概率形状补全和形状生成的实验中取得了竞争性的性能。

使用生成元胞自动机学习生成3D形状