A graph theoretic approach is proposed for object shape representation in a
hierarchical compositional architecture called Compositional Hierarchy of Parts
(CHOP). In the proposed approach, vocabulary learning is performed using a
hybrid generative-descriptive model. First, statistical relationships between
parts are learned using a Minimum Conditional Entropy Clustering algorithm.
Then, selection of descriptive parts is defined as a frequent subgraph
discovery problem, and solved using a Minimum Description Length (MDL)
principle. Finally, part compositions are constructed by compressing the
internal data representation with discovered substructures. Shape
representation and computational complexity properties of the proposed approach
and algorithms are examined using six benchmark two-dimensional shape image
datasets. Experiments show that CHOP can employ part shareability and indexing
mechanisms for fast inference of part compositions using learned shape
vocabularies. Additionally, CHOP provides better shape retrieval performance
than the state-of-the-art shape retrieval methods.

提出了一种基于图论的方法，用于在由部分组成的分层组合架构中表示对象形状，通过统计模型和最小描述长度原则，在受限制的形状单词表达中学习形状的描述，并将内部数据表示与发现的子结构压缩来构建部分组成。在六个基准二维形状图像数据集上验证了该方法。实验证明，Compositional Hierarchy of Parts（CHOP）可以使用部分共享和索引机制快速推断出形状组成，并提供比现有技术更好的形状检索性能。