The reconstruction of 3D microstructures from 2D slices is considered to hold
significant value in predicting the spatial structure and physical properties
of materials.The dimensional extension from 2D to 3D is viewed as a highly
challenging inverse problem from the current technological
perspective.Recently,methods based on generative adversarial networks have
garnered widespread attention.However,they are still hampered by numerous
limitations,including oversimplified models,a requirement for a substantial
number of training samples,and difficulties in achieving model convergence
during training.In light of this,a novel generative model that integrates the
multiscale properties of U-net with and the generative capabilities of GAN has
been proposed.Based on this,the innovative construction of a multi-scale
channel aggregation module,a multi-scale hierarchical feature aggregation
module and a convolutional block attention mechanism can better capture the
properties of the material microstructure and extract the image information.The
model's accuracy is further improved by combining the image regularization loss
with the Wasserstein distance loss.In addition,this study utilizes the
anisotropy index to accurately distinguish the nature of the image,which can
clearly determine the isotropy and anisotropy of the image.It is also the first
time that the generation quality of material samples from different domains is
evaluated and the performance of the model itself is compared.The experimental
results demonstrate that the present model not only shows a very high
similarity between the generated 3D structures and real samples but is also
highly consistent with real data in terms of statistical data analysis.

该研究提出了一种集成多尺度特性和生成对抗网络的创新生成模型，用于重建三维微结构，提高模型的准确性，并通过结合图像正则化损失和 Wasserstein 距离损失进一步改进模型，实现了生成的三维结构与真实样本的高相似性和统计数据一致性。

材料微结构三维重建与性能评估的生成式机器学习模型

A Generative Machine Learning Model for Material Microstructure 3D  Reconstruction and Performance Evaluation

Regression loss design is an essential topic for oriented object detection.
Due to the periodicity of the angle and the ambiguity of width and height
definition, traditional L1-distance loss and its variants have been suffered
from the metric discontinuity and the square-like problem. As a solution, the
distribution based methods show significant advantages by representing oriented
boxes as distributions. Differing from exploited the Gaussian distribution to
get analytical form of distance measure, we propose a novel oriented regression
loss, Wasserstein Distance(EWD) loss, to alleviate the square-like problem.
Specifically, for the oriented box(OBox) representation, we choose a
specially-designed distribution whose probability density function is only
nonzero over the edges. On this basis, we develop Wasserstein distance as the
measure. Besides, based on the edge representation of OBox, the EWD loss can be
generalized to quadrilateral and polynomial regression scenarios. Experiments
on multiple popular datasets and different detectors show the effectiveness of
the proposed method.

回归损失设计是面向对象检测的一个重要课题，由于角度的周期性和宽度和高度定义的不确定性，传统的 L1 距离损失及其变种一直以来都面临着度量不连续和类似于方形的问题，分布基方法则通过将有方向的框表示为分布而显示出显著优势，我们提出了一种新颖的有方向回归损失，Wasserstein 距离（EWD）损失，以缓解类似于方形的问题。同时，基于有方向框的边缘表示，EWD 损失可以推广到四边形和多项式回归场景，对多个常用数据集和不同的检测器的实验表明了该方法的有效性。