Displacement Mapping as a Metric Tool for Optimizing Mesh Models Originated by 3D Digitization

In the past 20 years, several methods have been proposed for re-coding 3D models with a low-spatial-frequency 3D representation plus a high-frequency 2D map for recovering the details. This approach has been explored with different kinds of mapping (bump, normal, relief, parallax, displacement), which have been shown to be effective in dramatically reducing model size while still maintaining a good visual appearance. For this reason, these approaches are widely applied in those situations where the rendering time constraints are critical (e.g., real-time rendering of complex models for gaming). However, the significant difference between the original detailed 3D model and the re-coded version has made it impossible to consider the latter as a metrically satisfying substitute for the former. The purpose of this article is to propose a re-coding method based on displaced subdivision surfaces that makes it possible to adapt the re-coded 3D representation to the metrological limitations of the 3D capturing technique used for generating the original mesh. In this way, it is possible to keep the geometric incoherency between the re-coded and the acquired mesh below the threshold determined by the natural capturing technology uncertainty. The resulting re-coded model can be therefore considered as close to the physical object/scenario, as the original acquired mesh, with a great advantage in terms of 3D representation size, UV parametrization, topological coherence, and scalability. The method has been tested on three cultural heritage objects with different complexity: a damaged wooden painting by Leonardo da Vinci (a nearly 2.5D shape), a Roman stone head sculpture (full 3D shape with simple topology), and a full body bronze sculpture by Donatello (full 3D shape with complex topology), demonstrating the coherency between the re-coded models and the originals, with a model size compression depending on the topological complexity that may reach a level of better than 1:25.