Detecting structure in data is the first step to arrive at meaningful
representations for systems. This is particularly challenging for dislocation
networks evolving as a consequence of plastic deformation of crystalline
systems. Our study employs Isomap, a manifold learning technique, to unveil the
intrinsic structure of high-dimensional density field data of dislocation
structures from different compression axis. The resulting maps provide a
systematic framework for quantitatively comparing dislocation structures,
offering unique fingerprints based on density fields. Our novel, unbiased
approach contributes to the quantitative classification of dislocation
structures which can be systematically extended.

利用 Isomap 技术揭示不同压缩轴下位阶密度场数据的位错结构的内在结构，并提供了基于密度场的独特指纹，这种新颖的无偏方法有助于位错结构的定量分类。

位错制图：具有独特指纹的位错网络的表示和无监督分类

Dislocation cartography: Representations and unsupervised classification  of dislocation networks with unique fingerprints

While surface-based view synthesis algorithms are appealing due to their low
computational requirements, they often struggle to reproduce thin structures.
In contrast, more expensive methods that model the scene's geometry as a
volumetric density field (e.g. NeRF) excel at reconstructing fine geometric
detail. However, density fields often represent geometry in a "fuzzy" manner,
which hinders exact localization of the surface. In this work, we modify
density fields to encourage them to converge towards surfaces, without
compromising their ability to reconstruct thin structures. First, we employ a
discrete opacity grid representation instead of a continuous density field,
which allows opacity values to discontinuously transition from zero to one at
the surface. Second, we anti-alias by casting multiple rays per pixel, which
allows occlusion boundaries and subpixel structures to be modelled without
using semi-transparent voxels. Third, we minimize the binary entropy of the
opacity values, which facilitates the extraction of surface geometry by
encouraging opacity values to binarize towards the end of training. Lastly, we
develop a fusion-based meshing strategy followed by mesh simplification and
appearance model fitting. The compact meshes produced by our model can be
rendered in real-time on mobile devices and achieve significantly higher view
synthesis quality compared to existing mesh-based approaches.

在这项工作中，我们修改了密度场，以鼓励它们向表面聚集，同时保持它们重建薄结构的能力。我们采用了离散不透明度网格表示，通过像素投射多条光线来抗锯齿，最小化不透明度值的二元熵，并开发了基于融合的网格化策略，最后进行网格简化和外观模型拟合。与现有的基于网格的方法相比，我们的模型产生的紧凑网格可以在移动设备上实时渲染，并实现了更高的视角合成质量。