Frequency-domain oversampling for multi-resolution surface reconstruction: towards digital modeling of cultural heritage

Surface reconstruction enables the generation of continuous three-dimensional surfaces from discrete point cloud data and is fundamental to digital modeling and scientific visualization. However, existing methods often suffer from surface irregularities and the loss of complex geometric features, particularly in cultural heritage digitization. Here, we propose a multi-resolution surface reconstruction framework based on frequency domain oversampling. The method introduces a novel implicit global fitting formulation with strict gradient constraints to jointly enforce surface smoothness and geometric consistency across scales. By incorporating frequency domain oversampling, we further develop a curvature adaptive octree subdivision strategy that improves spatial sampling accuracy and supports faithful recovery of fine-scale geometric details. Extensive experiments on diverse point cloud datasets and applications to cultural heritage data acquired from computed tomography and laser scanning demonstrate higher reconstruction accuracy while preserving computational efficiency, enabling high-resolution digital models and reliable support for heritage documentation and restoration.