Pattern analysis is a wide domain that has wide applicability in many fields. In fact, texture analysis is one of those fields, since the texture is defined as a set of repetitive or quasi-repetitive patterns. Despite its importance in analyzing 3D meshes, geometric texture analysis is less studied by geometry processing community. This paper presents a new efficient approach for geometric texture analysis on 3D triangular meshes. The proposed method is a scale-aware approach that takes as input a 3D mesh and a user-scale. It provides, as a result, a similarity-based clustering of texels in meaningful classes. Experimental results of the proposed algorithm are presented for both real-world and synthetic meshes within various textures. Furthermore, the efficiency of the proposed approach was experimentally demonstrated under mesh simplification and noise addition on the mesh surface. In this paper, we present a practical application for semantic annotation of 3D geometric salient texels.
We present a new method to convert the geometry of a mesh into frequency space. The eigenfunctions of the Laplace-Beltrami operator are used to define Fourier-like function basis and transform. Since this generalizes the classical Spherical Harmonics to arbitrary manifolds, the basis functions will be called Manifold Harmonics. It is well known that the eigenvectors of the discrete Laplacian define such a function basis. However, important theoretical and practical problems hinder us from using this idea directly. From the theoretical point of view, the combinatorial graph Laplacian does not take the geometry into account. The discrete Laplacian (cotan weights) does not have this limitation, but its eigenvectors are not orthogonal. From the practical point of view, computing even just a few eigenvectors is currently impossible for meshes with more than a few thousand vertices. In this paper, we address both issues. On the theoretical side, we show how the FEM (Finite Element Modeling) formulation defines a function basis which is both geometry-aware and orthogonal. On the practical side, we propose a band-by-band spectrum computation algorithm and an out-of-core implementation that can compute thousands of eigenvectors for meshes with up to a million vertices. Finally, we demonstrate some applications of our method to interactive convolution geometry filtering and interactive shading design. We propose a novel method for detecting mesh saliency, a perceptually-based measure of the importance of a local region on a 3D surface mesh. Our method incorporates global considerations by making use of spectral attributes of the mesh, unlike most existing methods which are typically based on local geometric cues. We first consider the properties of the log-Laplacian spectrum of the mesh. Those frequencies which show differences from expected behaviour capture saliency in the frequency domain. Information about these frequencies is considered in the spatial domain at multiple spatial scales to localise the salient features and give the final salient areas. The effectiveness and robustness of our approach are demonstrated by comparisons to previous approaches on a range of test models. The benefits of the proposed method are further evaluated in applications such as mesh simplification, mesh segmentation, and scan integration, where we show how incorporating mesh saliency can provide improved results. Very large polygonal models, which are used in more and more graphics applications today, are routinely generated by a variety of methods such as surface reconstruction algorithms from 3D scanned data, isosurface construction algorithms from volumetric data, and photogrametric methods from aerial photography. In this report we provide an overview of several closely related methods developed during the last few yers, to smooth, denoise, edit, compress, transmit, and animate very large polygonal models. In this paper, we present an automatic method which can transfer geometric textures from one object to another, and can apply a manually designed geometric texture to a model. Our method is based on geometry images as introduced by The key ideas in this method involve geometric texture extraction, boundary consistent texture synthesis, discretized orientation and scaling, and reconstruction of synthesized geometry. Compared to other methods, our approach is efficient and easy-to-implement, and produces results of high quality.