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.

浮雕图案表示与3D对象形状完全不同的表面特征。可以将它们视为2D图像中纹理概念的3D对应物。在2D图像的最新技术中，很大一部分纹理分析依赖于一些基于卷积的滤波。因此，将此类技术扩展到网格流形域的想法是很自然的。然而，在网格流形上定义卷积算符并不是一件容易的事。在本文中，我们提出了两个框架，即Mesh-Grid和Mesh-Convolution，以将离散和连续过滤器直接应用于网格。我们测试了网格网格和网格卷积在几何纹理检索任务中，据我们所知，在SHREC'18数据集上提供了第一个结果。然后，我们的卷积算子表明在SHREC'17数据集的浮雕模式分类任务中也有效，胜过了最新的结果。最后，我们提出了一种几何纹理分割方法来支持对大型数据集进行手动注释，这被证明是有效的。