The method of common lines is a well-established reconstruction technique in cryogenic electron microscopy (cryo-EM), which can be used to extract the relative orientations of an object in tomographic projection images from different directions. In this paper, we deal with an analogous problem in optical diffraction tomography. Based on the Fourier diffraction theorem, we show that rigid motions, i.e., a map composed of rotations and translations, can be determined by detecting common circles in the Fourier-transformed data. We introduce two methods based on the idea of identifying common circles to reconstruct the object motion: While the first one is motivated by the common line approach for projection images and detects the relative orientation by the shape of the common circles in the two images, the second one assumes a smooth motion over time and calculates the angular velocity of the rotational motion from an infinitesimal version of the common circle method. Interestingly, using the stereographic projection, both methods can be reformulated as common line methods, but these lines are, in contrast to those used in cryo-EM, not confined to pass through the origin and allow for a full reconstruction of the relative orientation. Numerical proof-of-the-concept examples demonstrate the performance of our reconstruction methods.
翻译:通用线系的方法是一种成熟的低温电子显微镜(cryo-EM)重建技术,可以用来从不同方向提取成像投影图像中对象的相对方向。在本文中,我们处理光学分解成形成像学方面的类似问题。根据Fourier diffrap 定理,我们显示,硬动作,即由旋转和翻译组成的地图,可以通过探测Fourier- Transfer化数据中的共同圆圈来确定。我们引入了两种方法,其基础是确定用于重建物体运动的共同圆圈的想法:第一种是投影图像的共同直线方法的驱动力,用两个图像的普通圆圈的形状探测相对方向,第二种则假设时间的光滑动,并根据一般圆圈方法的极小的表面模型计算旋转运动的角速。有趣的是,利用地形预测,这两种方法都可以重新拟订为共同的线条方法。但是,与在Cry-EM中使用的方法相反,这些线条是用共同的直径方法,不局限于投影射图像的直线系方法,不局限于两个共同圆圈形图状图状图状图状图状图状的形状,通过两个图状图状图状图状图状图状图状图状的形状,通过我们的图状图状图状图状的图状图状图状,以我们的图状图状图状图状,以我们的图状图状图状图状图状图样,通过我们的图状,以我们的图状图样,通过我们的图样,以我们的图状图状图样,以我们的图状图状图状图案为我们的图状图案迹。