Optimizing Image Retrieval with an Extended b-Metric Space

This article provides a new approach on how to enhance data storage and retrieval in the Query By Image Content Systems (QBIC) by introducing the ${\mathrm{N}\mathrm{E}\mathrm{M}}_{\sigma }$ distance measure, satisfying the relaxed triangle inequality. By leveraging the concept of extended $b$-metric spaces, we address complex distance relationships, thereby improving the accuracy and efficiency of image database management. The use of ${\mathrm{N}\mathrm{E}\mathrm{M}}_{\sigma }$ facilitates better scalability and accuracy in large-scale image retrieval systems, optimizing both the storage and retrieval processes. The proposed method represents a significant advancement over traditional distance measures, offering enhanced flexibility and precision in the context of image content-based querying. Additionally, we take inspiration from ice flow models using ${\mathrm{N}\mathrm{E}\mathrm{M}}_{\sigma }$ and ${\mathrm{N}\mathrm{E}\mathrm{M}}_r$, adding dynamic and location-based factors to better capture details in images.