Convolution operations for relief-pattern retrieval, segmentation and classification on mesh manifolds

Relief patterns represent a surface characteristic that is well distinct from the 3D object shape. They can be seen as the 3D counterpart of the texture concept in the 2D images. A large part of texture analysis, in 2D image state-of-the-art, relies on some convolution-based filtering. Thus, the idea of extending such techniques to the mesh manifold domain is quite natural. Nevertheless, defining a convolution operator on a mesh manifold is not straightforward. In this paper, we propose two frameworks, namely, Mesh-Grid and Mesh-Convolution, to apply discrete and continuous filters directly on the mesh. We tested Mesh-Grid and Mesh-Convolution in the task of geometric texture retrieval, providing, to the best of our knowledge, the first results on the SHREC'18 dataset. Then, our convolution operator revealed to be effective also in the task of relief pattern classification on the SHREC'17 dataset, outperforming the state-of-the-art results. Finally, we propose a geometric texture segmentation approach to support manual annotation on large datasets, which revealed to be effective.