High-fidelity image analysis of archaeological artifacts using adaptive polynomial approximation

Abstract This paper presents a unified, adaptive framework for image approximation and edge detection based on bivariate polynomial approximation techniques, explicitly focusing on archaeological imaging applications. Motivated by the need to enhance the analysis of high-resolution visual data—particularly for fragile and deteriorated cultural artifacts—we explore a range of polynomial-based methods to improve interpolation, denoising, and feature extraction. We introduce advanced node selection schemes, including Chebyshev admissible meshes and pixel-based sampling approaches. These mathematical tools are then integrated into an adaptive image subdivision strategy that dynamically adjusts resolution based on local image complexity. The resulting approximation methodology enables high-fidelity image recovery, while a polynomial-driven edge detection process identifies symbolic patterns and contours with high precision. Finally, we present a series of numerical tests that assess the method’s performance in terms of approximation accuracy, edge detection quality, and computational efficiency. The proposed approach demonstrates strong potential for aiding the non-invasive digital preservation and analysis of archaeological imagery, particularly in contexts where manual inspection is limited by scale or visual degradation.