Precise 3D image alignment in micro-axial tomography

Micro (µ‐) axial tomography is a challenging technique in microscopy which improves quantitative imaging especially in cytogenetic applications by means of defined sample rotation under the microscope objective. The advantage of µ‐axial tomography is an effective improvement of the precision of distance measurements between point‐like objects. Under certain circumstances, the effective (3D) resolution can be improved by optimized acquisition depending on subsequent, multi‐perspective image recording of the same objects followed by reconstruction methods. This requires, however, a very precise alignment of the tilted views. We present a novel feature‐based image alignment method with a precision better than the full width at half maximum of the point spread function. The features are the positions (centres of gravity) of all fluorescent objects observed in the images (e.g. cell nuclei, fluorescent signals inside cell nuclei, fluorescent beads, etc.). Thus, real alignment precision depends on the localization precision of these objects. The method automatically determines the corresponding objects in subsequently tilted perspectives using a weighted bipartite graph. The optimum transformation function is computed in a least squares manner based on the coordinates of the centres of gravity of the matched objects. The theoretically feasible precision of the method was calculated using computer‐generated data and confirmed by tests on real image series obtained from data sets of 200 nm fluorescent nano‐particles. The advantages of the proposed algorithm are its speed and accuracy, which means that if enough objects are included, the real alignment precision is better than the axial localization precision of a single object. The alignment precision can be assessed directly from the algorithm's output. Thus, the method can be applied not only for image alignment and object matching in tilted view series in order to reconstruct (3D) images, but also to validate the experimental performance (e.g. mechanical precision of the tilting). In practice, the key application of the method is an improvement of the effective spatial (3D) resolution, because the well‐known spatial anisotropy in light microscopy can be overcome. This allows more precise distance measurements between point‐like objects.