Spatiotemporal Models

From Real-time cryo-electron microscopy data preprocessing with Warp

Many methods in Warp are based on a continuous parametrization of 1- to 3-dimensional spaces. This parameterization is achieved by spline interpolation between points on a coarse, uniform grid, which is computationally efficient. A grid extends over the entirety of each dimension that needs to be modeled. The grid resolution is defined by the number of control points in each dimension and is scaled according to physical constraints (for example, the number of frames or pixels) and available signal. The latter provides regularization to prevent overfitting of sparse data with too many parameters. When a parameter described by the grid is retrieved for a point in space (and time), for example for a particle (frame), B-spline interpolation is performed at that point on the grid. To fit a grid’s parameters, in general, a cost function associated with the interpolants at specifc positions on the grid is optimized. In the following, we distinguish between 2–3 spatial grid dimensions (X and Y axes in micrographs; X, Y and Z in tomographic volumes), and a temporal dimension as a function of the accumulated electron dose. We note that B-splines are only used to interpolate parameters, not image data. For the latter higher-order schemes are used.