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.
The prerequisite to analysing geometric textures consists on separating geometric details from the base mesh that represents the basic geometric shape @cite_12 . To achieve this separation, frequency-based approaches are converting the geometry of a mesh into frequency space using low-pass filters @cite_22 , eigenfunctions of the Laplace-Beltrami operator @cite_9 or log-Laplacian spectrum @cite_18 .
@cite_9 @cite_18 @cite_22 @cite_12
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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. This study introduces a new approach based on Bidimensional Empirical Mode Decomposition (BEMD) to extract texture features at multiple scales or spatial frequencies. Moreover, it can resolve the intrawave frequency modulation provided the frequency modulation. This decomposition, obtained by the bidimensional sifting process, plays an important role in the characterization of regions in textured images. The sifting process is realized using morphological operators to analyze the spatial frequencies and thanks to radial basis functions (RBF) for surface interpolation. We modified the original sifting algorithm to permit a pseudo bandpass decomposition of images by inserting scale criterion. Its effectiveness is demonstrated on synthetic and natural textures. In particular, we show that many different elements in textures can be extracted through the bidimensional empirical mode decomposition, which is fully unsupervised. We adapt the CNN architecture to texture analysis.We introduce an energy layer to discard the overall shape information and focus on texture features.We evaluate the domain transferability and the depth of networks that are from scratch or pretrained.Our network is simpler than a classic CNN and obtains better classification results on texture datasets.We combine our texture CNN to a classic CNN (overall shape analysis) and further improve the results. Deep learning has established many new state of the art solutions in the last decade in areas such as object, scene and speech recognition. In particular Convolutional Neural Network (CNN) is a category of deep learning which obtains excellent results in object detection and recognition tasks. Its architecture is indeed well suited to object analysis by learning and classifying complex (deep) features that represent parts of an object or the object itself. However, some of its features are very similar to texture analysis methods. CNN layers can be thought of as filter banks of complexity increasing with the depth. Filter banks are powerful tools to extract texture features and have been widely used in texture analysis. In this paper we develop a simple network architecture named Texture CNN (T-CNN) which explores this observation. It is built on the idea that the overall shape information extracted by the fully connected layers of a classic CNN is of minor importance in texture analysis. Therefore, we pool an energy measure from the last convolution layer which we connect to a fully connected layer. We show that our approach can improve the performance of a network while greatly reducing the memory usage and computation.