# 2005Jonic Splines

## Citation

Jonic, S.; Sorzano, C. O. S.; Thévenaz, P.; El-Bez, C.; De Carlo, S. & Unser, M. Spline-Based image-to-volume registration for three-dimensional electron microscopy Ultramicroscopy, 2005, 103/104, 303-317

## Abstract

This paper presents an algorithm based on a continuous framework for a posteriori angular and translational assignment in three-dimensional electron microscopy (3DEM) of single particles. Our algorithm can be used advantageously to refine the assignment of standard quantized-parameter methods by registering the images to a reference 3D particle model. We achieve the registration by employing a gradient-based iterative minimization of a least-squares measure of dissimilarity between an image and a projection of the volume in the Fourier transform (FT) domain. We compute the FT of the projection using the central-slice theorem (CST). To compute the gradient accurately, we take advantage of a cubic B-spline model of the data in the frequency domain. To improve the robustness of the algorithm, we weight the cost function in the FT domain and apply a "mixed" strategy for the assignment based on the minimum value of the cost function at registration for several different initializations. We validate our algorithm in a fully controlled simulation environment. We show that the mixed strategy improves the assignment accuracy; on our data, the quality of the angular and translational assignment was better than 2 voxel (i.e., 6.54 angstroms). We also test the performance of our algorithm on real EM data. We conclude that our algorithm outperforms a standard projection-matching refinement in terms of both consistency of 3D reconstructions and speed.

## Keywords

Fourier space, spline interpolation, continuous optimization

## Links

Article http://www.ncbi.nlm.nih.gov/pubmed/15885434

## Related software

Xmipp: http://xmipp.cnb.csic.es/twiki/bin/view/Xmipp/Angular_predict_continuous