With the advance of 3D scanning technology, the cultural heritage community is increasingly interested in 3D scans of cultural objects such as antiques, artifacts and heritage sites. Digitization of these objects is commonly aimed at heritage preservation. Since 3D 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 3D color point clouds. Our contributions are twofold. First, we propose a simple method to solve PDEs (Partial Differential Equations) on point clouds using the framework of PdEs (Partial difference Equations) on graphs. Second, we survey several applications of 3D 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.