PDE-Based Graph Signal Processing for 3-D Color Point Clouds: Opportunities for cultural heritage

With the advance of three-dimensional (3-D) scanning technology, the cultural heritage community is increasingly interested in 3-D scans of cultural objects such as antiques, artifacts, and heritage sites. Digitization of these objects is commonly aimed at heritage preservation. Since 3-D color scanning has the potential to tackle a variety of traditional documentation challenges, the use of signal processing techniques on such data can be expected to yield new applications that are feasible for the first time with the aid of captured 3-D color point clouds. Our contributions are twofold. First, we propose a simple method to solve partial differential equations (PDEs) on point clouds using the framework of partial difference equations (PdEs) on graphs. Second, we survey several applications of 3-D color point cloud processing on real examples for which signal processing researchers can develop tools that can be valuable for museum specialists. The results of these methods have been reviewed by experts in the arts and found promising.