Hyperspectral image spectral-spatial classification via weighted Laplacian smoothing constraint-based sparse representation

As a powerful tool in hyperspectral image (HSI) classification, sparse representation has gained much attention in recent years owing to its detailed representation of features. In particular, the results of the joint use of spatial and spectral information has been widely applied to HSI classification. However, dealing with the spatial relationship between pixels is a nontrivial task. This paper proposes a new spatial-spectral combined classification method that considers the boundaries of adjacent features in the HSI. Based on the proposed method, a smoothing-constraint Laplacian vector is constructed, which consists of the interest pixel and its four nearest neighbors through their weighting factor. Then, a novel large-block sparse dictionary is developed for simultaneous orthogonal matching pursuit. Our proposed method can obtain a better accuracy of HSI classification on three real HSI datasets than the existing spectral-spatial HSI classifiers. Finally, the experimental results are presented to verify the effectiveness and superiority of the proposed method.

Designing Parallel Adaptive Laplacian Smoothing for Improving Tetrahedral Mesh Quality on the GPU

Mesh quality is a critical issue in numerical computing because it directly impacts both computational efficiency and accuracy. Tetrahedral meshes are widely used in various engineering and science applications. However, in large-scale and complicated application scenarios, there are a large number of tetrahedrons, and in this case, the improvement of mesh quality is computationally expensive. Laplacian mesh smoothing is a simple mesh optimization method that improves mesh quality by changing the locations of nodes. In this paper, by exploiting the parallelism features of the modern graphics processing unit (GPU), we specifically designed a parallel adaptive Laplacian smoothing algorithm for improving the quality of large-scale tetrahedral meshes. In the proposed adaptive algorithm, we defined the aspect ratio as a metric to judge the mesh quality after each iteration to ensure that every smoothing improves the mesh quality. The adaptive algorithm avoids the shortcoming of the ordinary Laplacian algorithm to create potential invalid elements in the concave area. We conducted 5 groups of comparative experimental tests to evaluate the performance of the proposed parallel algorithm. The results demonstrated that the proposed adaptive algorithm is up to 23 times faster than the serial algorithms; and the accuracy of the tetrahedral mesh is satisfactorily improved after adaptive Laplacian mesh smoothing. Compared with the ordinary Laplacian algorithm, the proposed adaptive Laplacian algorithm is more applicable, and can effectively deal with those tetrahedrons with extremely poor quality. This indicates that the proposed parallel algorithm can be applied to improve the mesh quality in large-scale and complicated application scenarios.

Bridging between topology optimization and additive manufacturing via Laplacian smoothing

The potential of Additive Layer Manufacturing (ALM) is high, with a whole new set of manufacturable parts with unseen complexity being offered. Moreover, the combination of Topology Optimization (TO) with ALM has brought mutual advantages. However, the transition between TO and ALM is a non-trivial step that requires a robust methodology. Thus, the purpose of this work is to evaluate the capabilities of adopting the commonly used Laplacian smoothing methodology as the bridging tool between TO and ALM. Several algorithms are presented and compared in terms of efficiency and performance. Most importantly, a different concept of Laplacian smoothing is presented as well as a set of metrics to evaluate the performance of the algorithms, with the advantages and disadvantages of each algorithm being discussed. In the end, the proposed mutable diffusion Laplacian algorithm is presented and exhibits less volume shrinkage and shows better preservation of some geometrical features such as thin members and edges. Moreover, a new volume constraint is presented, decreasing the resulting structural changes in the presented geometry and improving the final mesh quality.

Smooth adversarial examples

This paper investigates the visual quality of the adversarial examples. Recent papers propose to smooth the perturbations to get rid of high frequency artifacts. In this work, smoothing has a different meaning as it perceptually shapes the perturbation according to the visual content of the image to be attacked. The perturbation becomes locally smooth on the flat areas of the input image, but it may be noisy on its textured areas and sharp across its edges.This operation relies on Laplacian smoothing, well-known in graph signal processing, which we integrate in the attack pipeline. We benchmark several attacks with and without smoothing under a white box scenario and evaluate their transferability. Despite the additional constraint of smoothness, our attack has the same probability of success at lower distortion.

Parametric Blending of Hole Patches Based on Shape Difference

A triangular mesh obtained by scanning 3D models typically contains holes. We present an effective technique for filling a hole in a triangular mesh in geometric modeling. Simple triangulation of a hole is refined and remeshed iteratively to generate an initial patch. The generated patch is then enhanced to become a target patch by minimizing the variation of principal curvatures. In discrete approximation, this produces a third-order Laplacian system of sparse symmetric positive definite matrix, and the symmetry can efficiently be used to find the robust solutions to the given Laplacian system. Laplacian smoothing of the target patch is defined as a source patch. The shape difference between two corresponding vertices of the source and the target patches is measured in terms of Euclidean distance and curvature variation. On the basis of the shape difference and a user-specified control parameter, different blending weights are determined for each vertex, and the final patch is generated by blending two patches. We demonstrate the effectiveness of our technique by discussing several examples. The experimental results show that our technique can effectively restore salient geometric features of the original shape.

Going Deep: Graph Convolutional Ladder-Shape Networks

Neighborhood aggregation algorithms like spectral graph convolutional networks (GCNs) formulate graph convolutions as a symmetric Laplacian smoothing operation to aggregate the feature information of one node with that of its neighbors. While they have achieved great success in semi-supervised node classification on graphs, current approaches suffer from the over-smoothing problem when the depth of the neural networks increases, which always leads to a noticeable degradation of performance. To solve this problem, we present graph convolutional ladder-shape networks (GCLN), a novel graph neural network architecture that transmits messages from shallow layers to deeper layers to overcome the over-smoothing problem and dramatically extend the scale of the neural networks with improved performance. We have validated the effectiveness of proposed GCLN at a node-wise level with a semi-supervised task (node classification) and an unsupervised task (node clustering), and at a graph-wise level with graph classification by applying a differentiable pooling operation. The proposed GCLN outperforms original GCNs, deep GCNs and other state-of-the-art GCN-based models for all three tasks, which were designed from various perspectives on six real-world benchmark data sets.

Graph Dilated Network with Rejection Mechanism

Recently, graph neural networks (GNNs) have achieved great success in dealing with graph-based data. The basic idea of GNNs is iteratively aggregating the information from neighbors, which is a special form of Laplacian smoothing. However, most of GNNs fall into the over-smoothing problem, i.e., when the model goes deeper, the learned representations become indistinguishable. This reflects the inability of the current GNNs to explore the global graph structure. In this paper, we propose a novel graph neural network to address this problem. A rejection mechanism is designed to address the over-smoothing problem, and a dilated graph convolution kernel is presented to capture the high-level graph structure. A number of experimental results demonstrate that the proposed model outperforms the state-of-the-art GNNs, and can effectively overcome the over-smoothing problem.