An object shape information plays a vital role in many computer applications. Among these applications, some tasks can allow object shape analysis directly solve the problem. Thus, how to extract shape features and model the shape is a crucial issue. This paper proposes a new shape modeling method utilizing the centered convolutional deep Boltzmann machine to model two-dimensional (2D) shape. The proposed method employs a probabilistic generative model based on deep Boltzmann machine and convolution computation to extract both local and global features of the shape within one framework. In addition, we also propose a bidirectional inference-based training algorithm coupled with the centering method to better learn the probability distribution of shapes without the need for a pre-training procedure. Our experimental results show that the proposed model can achieve best shape modeling performance in qualitative and quantitative evaluation compared with other probabilistic generative models, including the restricted Boltzmann machine, convolutional restricted Boltzmann machine, and deep Boltzmann machine.

对象形状信息在许多计算机应用程序中起着至关重要的作用。在这些应用程序中，某些任务可以使对象形状分析直接解决问题。因此，如何提取形状特征并为形状建模是至关重要的问题。本文提出了一种新的形状建模方法，该方法利用中心卷积深玻尔兹曼机对二维（2D）形状进行建模。该方法采用基于深度玻尔兹曼机和卷积计算的概率生成模型，以在一个框架内提取形状的局部和全局特征。此外，我们还提出了一种基于双向推理的训练算法，并结合了对中方法，可以更好地学习形状的概率分布，而无需进行预训练过程。