Achieving sub-picometer precision measurements of atomic column positions in high-resolution scanning transmission electron microscope images using nonrigid registration (NRR) and averaging of image series requires careful optimization of experimental conditions and the parameters of the registration algorithm. On experimental data from SrTiO3 [100], sub-pm precision requires alignment of the sample to the zone axis to within 1 mrad tilt and sample drift of less than 1 nm/min. At fixed total electron dose for the series, precision in the fast scan direction improves with shorter pixel dwell time to the limit of our microscope hardware, but the best precision along the slow scan direction occurs at 6 μs/px dwell time. Within the NRR algorithm, the “smoothness factor” that penalizes large estimated shifts is the most important parameter for sub-pm precision, but in general, the precision of NRR images is robust over a wide range of parameters.

We propose a new nonrigid registration algorithm which is based on the optimal control approach. In our previously proposed methods, the Jacobian determinant and the curl vector were used as control functions. In this algorithm, we use a new set of control functions. A main advantage of using the new controls is that the positivity and normalization of the Jacobian determinant are satisfied automatically. Numerical results on large deformation brain images are provided to show the accuracy and efficiency of the algorithm.

With the advent of in vivo laser scanning fluorescence microscopy techniques, time-series and three-dimensional volumes of living tissue and vessels at micron scales can be acquired to firmly analyze vessel architecture and blood flow. Analysis of a large number of image stacks to extract architecture and track blood flow manually is cumbersome and prone to observer bias. Thus, an automated framework to accomplish these analytical tasks is imperative. The first initiative toward such a framework is to compensate for motion artifacts manifest in these microscopy images. Motion artifacts in in vivo microscopy images are caused by respiratory motion, heart beats, and other motions from the specimen. Consequently, the amount of motion present in these images can be large and hinders further analysis of these images. In this article, an algorithmic framework for the correction of time-series images is presented. The automated algorithm is comprised of a rigid and a nonrigid registration step based on shape contexts. The framework performs considerably well on time-series image sequences of the islets of Langerhans and provides for the pivotal step of motion correction in the further automatic analysis of microscopy images.