# Interchanging Geometry Conventions in 3DEM: Mathematical Context for the Development of Standards

## Abstract

The specification of the information on the three-dimensional orientation of an image with respect to a given coordinate system is at the heart of our ability to reconstruct a three-dimensional object from sets of its two-dimensional projection images. Transferring this information from one package to another is important to structural biologists wanting to get the best from each software suite. In this chapter, we review in depth the main considerations and implications associated with the unambiguous specification of geometrical specifications, in this way paving the way to the future specifications of standards in the field of three-dimensional electron microscopy. This is the case of EMX in which affine transformations have been adopted as the means to communicate geometrical information.

## Keywords

Spatial Frequency Euler Angle Affine Transformation Geometrical Information Fourier Space## Notes

### Acknowledgements

The authors would like to acknowledge economical support from the Spanish Ministry of Economy and Competitiveness through Grants AIC-A-2011-0638, BFU2009-09331, BIO2010-16566, ACI2009-1022, ACI2010-1088, CAM(S2010/BMD-2305), and NSF Grant 1114901, as well as postdoctoral Juan de la Cierva Grants with references JCI-2011-10185 and JCI-2010-07594. C.O.S. Sorzano is recipient of a Ramón y Cajal fellowship. This work was funded by Instruct, part of the European Strategy Forum on Research Infrastructures (ESFRI), and supported by national member subscriptions. The research leading to these results has received funding from the European Community’s Seventh Framework Programme (FP7/2007-2013) under BioStruct-X (grant agreement No. 283570).

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