Non-linear Bundle Adjustment for Electron Tomography

High quality tomographic reconstruction from electron microscope images requires precise alignment of the images. This cannot be accomplished by simple 2D image transformations because the electron trajectories through the object are curvilinear. Accordingly, the alignment process requires an inferred object position and, in addition, nonlinear projection maps for each image. This may be accomplished by means of a generalized bundle adjustment when a consistent set of point-like objects is visible in each EM image. Alternatively, alignment may be accomplished by an extension of the method of occluded contours when a consistent set of linear features, such as projected outlines of surfaces can be identified. In the first case, we report on new results derived from multiple tilt series data, and in the second we report on high quality alignment and reconstruction when the number of point features is insufficient for proper alignment.