The BEM based on conformal Duffy-distance transformation for three-dimensional elasticity problems

Here,we describe the robust and efficient application of the conventional 3D BEM in solving elasticity problems. We have focused on the precise computation of weakly singular integrals. The conformal Duffy-distance transformation was employed to alleviate near singularities caused from two aspects:(1) the large aspect ratio of elements,i.e.,element shape distortions;and(2)the closeness of element boundaries to field points,i.e.,ill-shaped patches. Then,the rigid body motion method was employed to evaluate strongly singular integrals. Numerical solutions of 3D elastostatic problems demonstrated the high accuracy of the proposed method with coarse meshes and high convergence rates with mesh refinement. Compared with the Duffy transformation and original polar coordinate transformations,the proposed method is insensitive to element shapes.

A unified framework for isotropic meshing based on narrowband Euclidean distance transformation

In this paper, we propose a simpleyet-effective method for isotropic meshing relying on Euclidean distance transformation based centroidal Voronoi tessellation(CVT). Our approach improves the performance and robustness of computing CVT on curved domains while simultaneously providing highquality output meshes. While conventional extrinsic methods compute CVTs in the entire volume bounded by the input model, we restrict the computation to a 3D shell of user-controlled thickness. Taking voxels which contain surface samples as sites, we compute the exact Euclidean distance transform on the GPU. Our algorithm is parallel and memory-efficient,and can construct the shell space for resolutions up to 20483 at interactive speed. The 3D centroidal Voronoi tessellation and restricted Voronoi diagrams are also computed efficiently on the GPU. Since the shell space can bridge holes and gaps smaller than a certain tolerance, and tolerate non-manifold edges and degenerate triangles, our algorithm can handle models with such defects, which typically cause conventional remeshing methods to fail. Our method can process implicit surfaces, polyhedral surfaces, and point clouds in a unified framework. Computational results show that our GPU-based isotropic meshing algorithm produces results comparable to state-ofthe-art techniques, but is significantly faster than conventional CPU-based implementations.

Euclidean Distance Transform on the Sea Based on Cellular Automata Modeling

To explore the problem of distance transformations while obstacles existing,this paper presents an obstacle-avoiding Euclidean distance transform method based on cellular automata.This research took the South China Sea and its adjacent sea areas as an example,imported the data of land-sea distribution and target points,took the length of the shortest obstacle-avoiding path from current cell to the target cells as the state of a cellular,designed the state transform rule of each cellular that considering a distance operator,then simulated the propagation of obstacle-avoiding distance,and got the result raster of obstacle-avoiding distance transform.After analyzing the effect and precision of obstacle avoiding,we reached the following conclusions:first,the presented method can visually and dynamically show the process of obstacle-avoiding distance transform,and automatically calculate the shortest distance bypass the land;second,the method has auto-update mechanism and each cellular can rectify distance value according to its neighbor cellular during the simulation process;at last,it provides an approximate solution for exact obstacle-avoiding Euclidean distance transform and the proportional error is less than 1.96%.The proposed method can apply to the fields of shipping routes design,maritime search and rescue,etc.

Numerical Evaluation of CPV Boundary Integrals with Symmetrical Quadrature Schemes

Stemming from the definition of the Cauchy principal values (CPV) integrals, a newly developed symmetrical quadrature scheme was proposed in the paper for the accurate numerical evaluation of the singular boundary integrals in the sense of CPV encountered in the boundary element method. In the case of inner element singularities, the CPV integrals could be evaluated in a straightforward way by dividing the element into the symmetrical part and the remainder(s). And in the case of end singularities, the CPV integrals could be evaluated simply by taking a tangential distance transformation of the integrand after cutting out a symmetrical tiny zone around the singular point. In both cases, the operations are no longer necessary before the numerical implementation, which involves the dull routine work to separate out singularities from the integral kernels. Numerical examples were presented for both the two and the three dimensional boundary integrals in elasticity. Comparing the numerical results with those by other approaches demonstrates the feasibility and the effectiveness of the proposed scheme.

A Normalization Method of Moment Invariants for 3D Objects on Different Manifolds

3D objects can be stored in computer of different describing ways, such as point set, polyline, polygonal surface and Euclidean distance map. Moment invariants of different orders may have the different magnitude. A method for normalizing moments of 3D objects is proposed, which can set the values of moments of different orders roughly in the same range and be applied to different 3D data formats universally. Then accurate computation of moments for several objects is presented and experiments show that this kind of normalization is very useful for moment invariants in 3D objects analysis and recognition.

EDT Method for Multiple Labelled Objects Subject to Tied Distances

The success of new scientific areas can be assessed by their potential for contributing to new theoretical approaches aligned with real-world applications.The Euclidean distance transform(EDT)has fared well in both cases,providing a sound theoretical basis for a number of applications,such as median axis transform,fractal analysis,skeletonization,and Voronoi diagrams.Despite its wide applicability,the discrete form of the EDT includes interesting properties that have not yet been fully exploited in the literature.In this paper,we are particularly interested in the properties of 1)working with multiple objects/labels;and 2)identifying and counting equidistant pixels/voxels from certain points of interest.In some domains(such as dataset classification,texture,and complexity analysis),the result of applying the EDT transform with different objects,and their respective tied distances,may compromise the performance.In this sense,we propose an efficient modification in the method presented in[1],which leads to a novel approach for computing the distance transform in a space with multiple objects,and for counting equidistant pixels/voxels.

Robust and efficient edge-based visual odometry

Visual odometry,which aims to estimate relative camera motion between sequential video frames,has been widely used in the fields of augmented reality,virtual reality,and autonomous driving.However,it is still quite challenging for stateof-the-art approaches to handle low-texture scenes.In this paper,we propose a robust and efficient visual odometry algorithm that directly utilizes edge pixels to track camera pose.In contrast to direct methods,we choose reprojection error to construct the optimization energy,which can effectively cope with illumination changes.The distance transform map built upon edge detection for each frame is used to improve tracking efficiency.A novel weighted edge alignment method together with sliding window optimization is proposed to further improve the accuracy.Experiments on public datasets show that the method is comparable to stateof-the-art methods in terms of tracking accuracy,while being faster and more robust.