Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new user3D Microstructure Segmentation by Topological Persistence
64
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Tomography is a widely used tool for analyzing microstructures in three dimensions (3D). The analysis, however, faces difficulty because the constituent materials produce similar grey-scale values. Sometimes, this prompts the image segmentation process to assign a pixel/voxel to the wrong phase (active material or pore). Consequently, errors are introduced in the microstructure characteristics calculation. In this work we develop a filtering algorithm based on topological persistence, a technique used in topological data analysis. One problem faced when evaluating filtering algorithms is that real image data in general are not equipped with the ground truth information about the microstructure characteristics. For this study, we construct synthetic images for which the ground truth values are known. Specifically, we compare interconnected pore tortuosity and phase fraction. Experimental results show that our filtering algorithm provides a significant improvement in reproducing tortuosity close to the ground truth, even when the grey-scale values of the phases are similar.
rate research
Read More
The notion of persistence partial matching, as a generalization of partial matchings between persistence modules, is introduced. We study how to obtain a persistence partial matching $mathcal{G}_f$, and a partial matching $mathcal{M}_f$, induced by a morphism $f$ between persistence modules, both being linear with respect to direct sums of morphisms. Some of their properties are also provided, including their stability after a perturbation of the morphism $f$, and their relationship with other induced partial matchings already defined in TDA.
Many physical systems can be modeled as large sets of domains glued together along boundaries - biological cells meet along cell membranes, soap bubbles meet along thin films, countries meet along geopolitical boundaries, and metallic crystals meet along grain interfaces. Each class of microstructures results from a complex interplay of initial conditions and particular evolutionary dynamics. The statistical steady-state microstructure resulting from isotropic grain growth of a polycrystalline material is canonical in that it is the simplest example of a cellular microstructure resulting from a gradient flow of a simple energy, directly proportional to the total length or area of all cell boundaries. As many properties of polycrystalline materials depend on their underlying microstructure, a more complete understanding of the grain growth steady-state can provide insight into the physics of a broad range of everyday materials. In this paper we report geometric and topological features of these canonical two- and three-dimensional steady-state microstructures obtained through large, accurate simulations of isotropic grain growth.
The classical persistence algorithm virtually computes the unique decomposition of a persistence module implicitly given by an input simplicial filtration. Based on matrix reduction, this algorithm is a cornerstone of the emergent area of topological data analysis. Its input is a simplicial filtration defined over the integers $mathbb{Z}$ giving rise to a $1$-parameter persistence module. It has been recognized that multi-parameter version of persistence modules given by simplicial filtrations over $d$-dimensional integer grids $mathbb{Z}^d$ is equally or perhaps more important in data science applications. However, in the multi-parameter setting, one of the main challenges is that topological summaries based on algebraic structure such as decompositions and bottleneck distances cannot be as efficiently computed as in the $1$-parameter case because there is no known extension of the persistence algorithm to multi-parameter persistence modules. We present an efficient algorithm to compute the unique decomposition of a finitely presented persistence module $M$ defined over the multiparameter $mathbb{Z}^d$.The algorithm first assumes that the module is presented with a set of $N$ generators and relations that are emph{distinctly graded}. Based on a generalized matrix reduction technique it runs in $O(N^{2omega+1})$ time where $omega<2.373$ is the exponent for matrix multiplication. This is much better than the well known algorithm called Meataxe which runs in $tilde{O}(N^{6(d+1)})$ time on such an input. In practice, persistence modules are usually induced by simplicial filtrations. With such an input consisting of $n$ simplices, our algorithm runs in $O(n^{2omega+1})$ time for $d=2$ and in $O(n^{d(2omega + 1)})$ time for $d>2$.
Zirconium based alloys have been irradiated with 11 and 15 MeV proton and 116 MeV oxygen ions at different doses. The changes in the microstructure have been studied for the ion irradiated alloys as a function of dose using X-Ray Diffraction Line Profile Analysis (XRDLPA) based on the whole powder pattern fitting technique. It was observed that the microstructural parameters like domain size, microstrain within the domain, dislocation density did not change significantly with the increase in dose for proton irradiated samples. A clear change was noticed in these microstructural parameters as a function of dose for oxygen irradiated samples. There was a drastic decrease in domain size at a dose of 1x10^17 O5+/m2 but these values reached a plateau with increasing dose. The values of microstrain and dislocation density increased significantly with the dose of irradiation.
In this paper we study the properties of the homology of different geometric filtered complexes (such as Vietoris-Rips, Cech and witness complexes) built on top of precompact spaces. Using recent developments in the theory of topological persistence we provide simple and natural proofs of the stability of the persistent homology of such complexes with respect to the Gromov--Hausdorff distance. We also exhibit a few noteworthy properties of the homology of the Rips and Cech complexes built on top of compact spaces.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
