论文标题
客观，概率和广义噪声水平依赖于或多或少的2D周期性图像集成平面对称组的分类
Objective, Probabilistic, and Generalized Noise Level Dependent Classifications of sets of more or less 2D Periodic Images into Plane Symmetry Groups
论文作者
论文摘要
来自具有二维的周期性（2D）的现实世界图像的晶体学对称分类对计算机视觉研究的晶体学家和实践者都很感兴趣。目前，这些分类通常由两个社区以一种主观的方式进行，该方式依赖于任意判断的阈值，并以确定性的假装报道，这是不可能的。此外，计算机视觉社区倾向于使用直接空间方法来进行此类分类，而不是更强大，更有效的傅立叶空间方法。这是因为这些方法的正确功能需要比计算机视觉社区分析的图像中通常存在的单位单元图案的定期重复。我们展示了一种新颖的方法来实现平面对称组分类，该方法由Kenichi Kanatani的几何Akaike信息标准和相关的几何akaike重量启用。我们的方法利用了在傅立叶空间中工作的优势，非常适合处理晶体学对称的层次结构，并产生依赖噪声水平的概率结果。后一个功能意味着当较少的嘈杂图像数据和更准确的处理算法可用时，可以更新晶体学对称分类。我们证明了我们的方法能够客观地估计合成2D-周期图像集的平面对称性和伪对称性，并具有不同量的红绿色蓝色和扩散噪声。此外，我们建议一个简单的解决方案来解决输入图像中太少重复的问题，以实际应用傅立叶空间方法。这样一来，我们从噪声存在下的对称性检测和分类的计算机视觉中有效地解决了数十年和迄今为止的棘手问题。
Crystallographic symmetry classifications from real-world images with periodicities in two dimensions (2D) are of interest to crystallographers and practitioners of computer vision studies alike. Currently, these classifications are typically made by both communities in a subjective manner that relies on arbitrary thresholds for judgments, and are reported under the pretense of being definitive, which is impossible. Moreover, the computer vision community tends to use direct space methods to make such classifications instead of more powerful and computationally efficient Fourier space methods. This is because the proper functioning of those methods requires more periodic repeats of a unit cell motif than are commonly present in images analyzed by the computer vision community. We demonstrate a novel approach to plane symmetry group classifications that is enabled by Kenichi Kanatani's Geometric Akaike Information Criterion and associated Geometric Akaike weights. Our approach leverages the advantages of working in Fourier space, is well suited for handling the hierarchic nature of crystallographic symmetries, and yields probabilistic results that are generalized noise level dependent. The latter feature means crystallographic symmetry classifications can be updated when less noisy image data and more accurate processing algorithms become available. We demonstrate the ability of our approach to objectively estimate the plane symmetry and pseudosymmetries of sets of synthetic 2D-periodic images with varying amounts of red-green-blue and spread noise. Additionally, we suggest a simple solution to the problem of too few periodic repeats in an input image for practical application of Fourier space methods. In doing so, we effectively solve the decades-old and heretofore intractable problem from computer vision of symmetry detection and classification from images in the presence of noise.
