# Katrine Hommelhoff Jensen

Ph.D. StudentThe Image Group |

University of Copenhagen |

Universitetsparken 5 |

2100 København Ø |

Email: | katrine@diku.dk |

Office: | HCØ - Building E, Office 04.0.07 |

Phone (Reception): | (+45) 35321400 |

### Research Interests

Bio-/medical image analysis and computer graphics, in particular 3D imaging and reconstruction, shape analysis, mathematical modelling and statistical inversion.I have applied it to e.g. segmentation of objects from 3D CT scans, reconstruction of missing object parts in 3D scattered data and 3D vision based robot navigation. I currently work with Bayesian inversion for reconstructing the 3D structure of an object (protein) from randomly oriented, 2D electron microscopic projection images.

### References

The project is part of the Centre for Stochastic Geometry and Advanced Bioimaging (CSGB), an inter-institutional collaboration between the Universities of Aarhus, Aalborg and Copenhagen in Denmark. Main supervisor on the project is Sami S. Brandt.### Project description

Cryo-electron microscopy (cryo-EM) is a form of transmission electron microscopy, aimed at reconstructing the three-dimensional structure of a macromolecular complex (particle) from a large set of projection images, as they exhibit a very low SNR. In the single particle reconstruction problem, several randomly oriented copies of the particle are available, each representing a certain viewing direction of the structure. This implies two main computational problems: (1) to determine the angular relationship between the individual projection images, i.e. determine the particle pose in each view, and (2) to solve the ill-posed reconstruction problem.We use Bayesian statistical inversion in both problems to optimally cope with the high amount of noise, as well as to incorporate prior structural information into the reconstruction problem. In one approach, we investigate the statistical recovery of the common line geometry between a set of projection images. The common line geometry describes the uncalibrated, affine projection geometry of two views that can be estimated without establishing pointwise correspondences between the views. The basic 2-view algorithm was described in [1] and we are currently working on the N-view extended approach. This method will ultimately be combined with another approach, where we study the actual reconstruction problem. In this work, we find the maximum a posteriori (MAP) estimates for the particle structure from the marginal posterior, where the view orientations are integrated out. We aim at a statistically optimal result using a uniform prior in the space of particle rotations, and realize this with a novel approximation of the expected complete data log posterior, described in [2]. We are currently improving the projection model and studying advanced structural prior distributions. We also investigate efficient algorithms for reducing the computational complexity, allowing for further incorporation of model parameters, and a more complex subdivision of the reconstruction into different shape conformities. We are additionally investigating evaluation methods to objectively assess the validity of the reconstructions.

- Brandt, S.S., Jensen, K.H. & Lauze, F.B. (2012): Bayesian epipolar geometry estimation from tomographic projections. 11th Asian Conference on Computer Vision, Daejeon, South Korea.
- Brandt, S.S., Jensen, K.H. & Lauze, F.B. (2013): On the bayesian reconstruction method for randomly oriented particles in cryo-EM. International Symposium on Biomedical Imaging, San Fransisco, CA, USA