As the number of processor cores on supercomputers becomes larger and larger, algorithms with high degree of parallelism attract more attention. In this work, we propose a novel space-time coupled algorithm for solving an inverse problem associated with the time-dependent convection-diffusion equation in three dimensions. We introduce a mixed finite element/finite difference method and a one-le...

Efficient and reliable path planning is crucial for smart ships when avoiding collisions with static dynamic obstacles in complex marine environments. This research proposes a novel method based on the fast marching to specifically assist safe navigation autonomous ships. At very beginning, unified representation specially produced describe space parametric speed function. In addition, spatial–...

This paper addresses the generation of aircraft emergency trajectories with obstacle avoidance. After presenting in detail fast marching tree algorithm, this we propose an improvement its performance. First, free space checking function is sped up. Then, algorithm used twice, firstly sampling a few points to generate approximate trajectory, and secondly close first computed trajectory refine it...

Bacteria exist in a variety of groups of shapes, sizes, and single or multiple cell formations. In this paper, the level set shape reconstruction technique, the method of moments, and the marching cubes methods are integrated in the high frequency band for imaging three dimensional bacteria. The time step and the resolution of the marching cubes method are investigated to smooth the error funct...

This paper presents a new method for polygonization of implicit surfaces. Our method put emphasis on the shape of triangles of the resulting polygonal mesh. The main advantages of the triangulation presented are simplicity and the stable features that can be used for next expanding. The implementation is not complicated and only the standard data structures are used. This algorithm is based on ...

Shape-from-Shading (SfS) is a fundamental problem in Computer Vision. Its goal is to solve the image irradiance equation. One prominent solution is the Fast Marching Method of Kimmel & Sethian. When the light source is oblique, Kimmel & Sethian proposed to rotate the image to the light source coordinate system and then solve an ‘almost’ Eikonal equation. This paper presents a new iterative vari...

We present a method for calculating the boundary of objects from Discrete Indicator Functions that store 2material volume fractions with a high degree of accuracy. Although Marching Cubes and its derivatives are effective methods for calculating contours of functions sampled over discrete grids, these methods perform poorly when contouring non-smooth functions such as Discrete Indicator Functio...

Crystalline porous materials are an important class of materials that can be used for oil refinement, hydrogen or methane storage, as well as carbon dioxide capture. Selecting optimal materials for these important applications requires analysis and screening of millions of potential candidates. Recently, we proposed an automatic approach based on the fast marching method for analyzing void spac...

In real world scenarios for mobile robots, socially acceptable navigation is a key component to interact naturally with other persons. On the one hand this enables a robot to behave more human-like, and on the other hand it increases the acceptance of the user towards the robot as an interaction partner. As part of this research field, we present in this paper a strategy of approaching a person...

A computational study of the Fast Marching and the Fast Sweeping methods for the Eikonal equation is given. It is shown that even though Fast Sweeping requires asymptotically less operations than Fast Marching, the latter method is faster than the former for the problems under consideration and for realistic grid sizes. Fully second order generalizations of methods of this type for problems wit...