  The surge in 3D modeling has led to a pronounced research emphasis on the
field of 3D shape retrieval. Numerous contemporary approaches have been put
forth to tackle this intricate challenge. Nevertheless, effectively addressing
the intricacies of cross-modal 3D shape retrieval remains a formidable
undertaking, owing to inherent modality-based disparities. This study presents
an innovative notion, termed "geometric words", which functions as elemental
constituents for representing entities through combinations. To establish the
knowledge graph, we employ geometric words as nodes, connecting them via shape
categories and geometry attributes. Subsequently, we devise a unique graph
embedding method for knowledge acquisition. Finally, an effective similarity
measure is introduced for retrieval purposes. Importantly, each 3D or 2D entity
can anchor its geometric terms within the knowledge graph, thereby serving as a
link between cross-domain data. As a result, our approach facilitates multiple
cross-domain 3D shape retrieval tasks. We evaluate the proposed method's
performance on the ModelNet40 and ShapeNetCore55 datasets, encompassing
scenarios related to 3D shape retrieval and cross-domain retrieval.
Furthermore, we employ the established cross-modal dataset (MI3DOR) to assess
cross-modal 3D shape retrieval. The resulting experimental outcomes, in
conjunction with comparisons against state-of-the-art techniques, clearly
highlight the superiority of our approach.
