Formation of a Three-dimensional Relief Model Based on a 2D Image

Abstract

This paper introduces an automated pipeline for generating high-quality 3D bas-relief models directly from single 2D images. Our method replaces laborious manual height‐map editing with ZoeDepth, a state-of-the-art neural network that outputs dense depth maps without camera calibration or manual annotations. Input photographs, whether of architectural facades, artwork reproductions, or industrial scenes, are first contrast-normalized and preprocessed prior to depth estimation. The raw depth output then undergoes metric‐attractor correction, which refines depth-bin centers using multiple predicted attractor points per pixel to improve continuity and reduce quantization artifacts. A custom depth-aware triangulation algorithm subsequently converts the refined depth field into a surface mesh, with user-controlled parameters for real-world scale, spatial resolution, and triangulation density. The final mesh is exported as an STL file, enabling immediate compatibility with CAD software and 3D printers. The performance, robustness and fidelity of the elaborated pipeline were evaluated on a quad-core Intel i5 CPU and a variety of image domains. It turned out that depth inference for an 800 × 800 pixel image took around 120 seconds, while mesh generation and STL export took approximately 110 seconds. These times scale linearly with image resolution. Quantitative assessment yields a mean relative error below 7.7 % and threshold accuracy above 95.3 %, indicating that over 95 % of pixel depth estimates fall within 25 % of true values. A qualitative inspection has confirmed that the obtained reliefs preserve critical geometric details and maintain surface smoothness, even on previously unnoticeable inputs. Comparative analysis highlights significant reductions in manual effort and total modeling time versus traditional Blender-based sculpting workflows, without sacrificing mesh quality.