Mesh saliency via spectral processing

We propose a novel method for detecting mesh saliency, a perceptuallybased 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

SAGA: Spectral Adversarial Geometric Attack on 3D Meshes

A triangular mesh is one of the most popular 3D data representations. As such, the deployment of deep neural networks for mesh processing is widely spread and is increasingly attracting more attention. However, neural networks are prone to adversarial attacks, where carefully crafted inputs impair the model's functionality. The need to explore these vulnerabilities is a fundamental factor in the future development of 3D-based applications. Recently, mesh attacks were studied on the semantic level, where classifiers are misled to produce wrong predictions. Nevertheless, mesh surfaces possess complex geometric attributes beyond their semantic meaning, and their analysis often includes the need to encode and reconstruct the geometry of the shape. We propose a novel framework for a geometric adversarial attack on a 3D mesh autoencoder. In this setting, an adversarial input mesh deceives the autoencoder by forcing it to reconstruct a different geometric shape at its output. The malicious input is produced by perturbing a clean shape in the spectral domain. Our method leverages the spectral decomposition of the mesh along with additional mesh-related properties to obtain visually credible results that consider the delicacy of surface distortions. Our code is publicly available at https://github.com/StolikTomer/SAGA

A spectral multi-domain technique with application to generalized curvilinear coordinates

Spectral collocation methods have proven to be efficient discretization schemes for many aerodynamic and fluid mechanic problems. The high order accuracy and resolution shown by these methods allows one to obtain engineering accuracy solutions on coarse meshes, or alternatively, to obtain solutions with very small error. One drawback to these techniques was the requirement that a complicated physical domain must map into a simple computational domain for discretization. This mapping must be smooth if the high order accuracy and expontential convergence rates associated with spectral methods are to be preserved. Additionally even smooth stretching transformations can decrease the accuracy of a spectral method, if the stretching is severe. A further difficulty with spectral methods was in their implementation on parallel processing computers, where efficient spectral algorithms were lacking. The above restrictions are overcome by splitting the domain into regions, each of which preserve the advantages of spectral collocation, and allow the ratio of the mesh spacing between regions to be several orders of magnitude higher than allowable in a single domain. Such stretchings would be required to resolve the thin viscous region in an external aerodynamic problem. Adjoining regions are interfaced by enforcing a global flux balance which preserves high-order continuity of the solution, regardless of the type of the equations being solved

Novel spectral kurtosis technology for adaptive vibration condition monitoring of multi-stage gearboxes

In this paper, the novel wavelet spectral kurtosis (WSK) technique is applied for the early diagnosis of gear tooth faults. Two variants of the wavelet spectral kurtosis technique, called variable resolution WSK and constant resolution WSK, are considered for the diagnosis of pitting gear faults. The gear residual signal, obtained by filtering the gear mesh frequencies, is used as the input to the SK algorithm. The advantages of using the wavelet-based SK techniques when compared to classical Fourier transform (FT)-based SK is confirmed by estimating the toothwise Fisher's criterion of diagnostic features. The final diagnosis decision is made by a three-stage decision-making technique based on the weighted majority rule. The probability of the correct diagnosis is estimated for each SK technique for comparison. An experimental study is presented in detail to test the performance of the wavelet spectral kurtosis techniques and the decision-making technique

Neural 3D Morphable Models: Spiral Convolutional Networks for 3D Shape Representation Learning and Generation

Generative models for 3D geometric data arise in many important applications in 3D computer vision and graphics. In this paper, we focus on 3D deformable shapes that share a common topological structure, such as human faces and bodies. Morphable Models and their variants, despite their linear formulation, have been widely used for shape representation, while most of the recently proposed nonlinear approaches resort to intermediate representations, such as 3D voxel grids or 2D views. In this work, we introduce a novel graph convolutional operator, acting directly on the 3D mesh, that explicitly models the inductive bias of the fixed underlying graph. This is achieved by enforcing consistent local orderings of the vertices of the graph, through the spiral operator, thus breaking the permutation invariance property that is adopted by all the prior work on Graph Neural Networks. Our operator comes by construction with desirable properties (anisotropic, topology-aware, lightweight, easy-to-optimise), and by using it as a building block for traditional deep generative architectures, we demonstrate state-of-the-art results on a variety of 3D shape datasets compared to the linear Morphable Model and other graph convolutional operators.Comment: to appear at ICCV 201

Steklov Spectral Geometry for Extrinsic Shape Analysis

We propose using the Dirichlet-to-Neumann operator as an extrinsic alternative to the Laplacian for spectral geometry processing and shape analysis. Intrinsic approaches, usually based on the Laplace-Beltrami operator, cannot capture the spatial embedding of a shape up to rigid motion, and many previous extrinsic methods lack theoretical justification. Instead, we consider the Steklov eigenvalue problem, computing the spectrum of the Dirichlet-to-Neumann operator of a surface bounding a volume. A remarkable property of this operator is that it completely encodes volumetric geometry. We use the boundary element method (BEM) to discretize the operator, accelerated by hierarchical numerical schemes and preconditioning; this pipeline allows us to solve eigenvalue and linear problems on large-scale meshes despite the density of the Dirichlet-to-Neumann discretization. We further demonstrate that our operators naturally fit into existing frameworks for geometry processing, making a shift from intrinsic to extrinsic geometry as simple as substituting the Laplace-Beltrami operator with the Dirichlet-to-Neumann operator.Comment: Additional experiments adde