A order-based content-based information retrieval system proposal applied in 3D meshes

In computer graphics, Content-Based Informaion Retrieval (CBIR) is a database system designed to take an object as input and return a list of similar objects. Originally intended for images, CBIR systems now extend to various types of data, including sounds and three-dimensional models represented as geometrical meshes, broadening their applicability beyond images. In the field of information retrieval, it’s customary to interpret the “I” in CBIR as “Information.” Throughout this text, we adopt this interpretation. To evaluate the similarity between 3D meshes, several techniques involve transforming meshes into feature vectors and measuring the distance between these vectors. In our research, we propose leveraging an algorithm rooted in compressive sensing theory to extract features from 3D meshes. Additionally, we introduce a prototype of a 3D meshes CBIR system that utilizes an order relation, rather than a distance function, to assess the similarity between objects. We introduce an order in \({\mathbb {R}}^n\) ${\mathbb{R}}^n$ called the Extended Lexicographical Order (ELO), designed to incorporate all information present in the vectors being compared. Our comparative analysis includes traditional distance functions as well as classical \({\mathbb {R}}^n\) ${\mathbb{R}}^n$ order relations such as lexicographical and revlex. Furthermore, we employ two types of descriptors: a spectral descriptor based on compressive sensing theory, which builds upon previous work from our research group, and a harmonic spherical-based descriptor, which has already been established in the literature as a successful extractor in the context of medical models. Across all experiments, our prototype consistently outperforms traditional techniques, showcasing its efficacy in CBIR applications.