A 3D-CNN Approach for the Spatio-Temporal Modeling of Surface Deterioration Phenomena

The modeling of spatio-temporal changes on the surface of materials is an open problem with important applications in domain such as computer graphics and cultural heritage. Significant progress has been achieved over the years and the results of several methods look realistic up to a certain degree. Nonetheless, the proposed approaches are not directly connected to physical measurements in most cases. In this paper, we propose a method that uses 3D surface measurements on bronze panels that are artificially aged and models the variations that occur over time due to the different physiochemical processes that take place. The input of our algorithm is the 3D point cloud of a material's surface while the output is a prediction of this point cloud in other time instances. At the core of the method lies a module that maps the point cloud of a material's surface into 3D occupancy grids and a 3D Convolutional Neural Network (CNN) that captures geometric changes over time. The training of the 3D-CNN is performed using registered point clouds from bronze panels that are artificially aged and scanned in three time instants. In order to measure the convergence of the training process, aside the minimization of the the 3D-CNN cost function, a complementary approach is proposed using the Normal Distribution Function of the generated surface. The experimental evaluation of the method demonstrates its potential.