Delaunay algorithm and principal component analysis for 3D visualization of mitochondrial DNA nucleoids by Biplane FPALM/dSTORM

Super-resolution localization microscopy determines the spatial location of fluorophores below the diffraction limit of light by isolating single point sources in time and determining their position through statistical fitting of their recorded point-spread functions to either optical theory or to a calibration curve. A localization microscopy data set then consists of a set of localized points in 3D space containing the location of the fluorophores within the biological sample, which are then computationally rendered to create an image containing spatial information below the classical diffraction limit. Due to the nature of the method, the final image is a computer-generated image of localized data points, and not a conventional captured image.

Various methods of image reconstruction can be employed within localization microscopy, such as direct rendering of the localization data of spheroids of size associated with their localization precision, convolving every localization with a Gaussian distribution, and adaptive histogram binning. Another popular method is based upon Delaunay triangulation, where the two-dimensional case the data set of localized points is connected in such a way that no data points lie within the circumcircle of the triangle formed by three connected points. The data set can then be segmented into “pixels” whose size is based upon the local density of localization points. In three dimensions, this is extended to the circumsphere created by a unique polyhedron composed of four localization points, with no localization points in the interior. This can lead to direct assessment of the local density of points in three-dimensional space, and estimations for the volume that the proteins in question occupy.