Finding correspondences between drosophila embryo

1. Finding correspondences between drosophila embryo Charless Fowlkes, Jitendra Malik UCB Computer Sciences

2. ?

4. % egg length coordinate system 10% strip Warp x-axis to align peak features Myasnikova et al (2001)

5. Advantages: Treats cells as discrete units Discontinuities in expression levels between cells are preserved Given a correspondence, it is easy to find a global coordinate system Cell-to-Cell Correspondence • Cell lineage gives “ground-truth” correspondence

6. Sources of Variation • Not so interesting: • Staining • Shrinking • Spinning • Squashing • Staging • Interesting: • Biological Variation

7. Correspondence as Optimzation • Of all possible correspondences between two embryos, find the one which pairs cells with similar expression levels.

8. Correspondence as Optimzation • Of all possible correspondences between two embryos, find the one which pairs cells with similar expression levels.

9. Correspondence as Optimzation • Of all possible correspondences between two embryos, find the one which pairs cells with similar expression levels and results in a smooth transformation

10. Correspondence Overview Nuclear Segmentation Coarse Registration X Y Z Sna Ftz 220.3 40.2 31.0 0.28 0.99 182.4 30.1 44.9 0.22 0.77 . . Detailed Correspondence and Model Building Mesh Generation Feature Extraction

11. Coarse Registration • Align the center of masses of two embryos • Scale along AP axis in order to match length • Sphere perpendicular to AP axis in order to remove squashing • Rotate along AP axis to align SNA expression pattern

12. Coarse Registration Scale and Rotate

13. Coarse Consensus Model

14. Correspondence Overview Nuclear Segmentation Coarse Registration X Y Z Sna Ftz 220.3 40.2 31.0 0.28 0.99 182.4 30.1 44.9 0.22 0.77 . . Detailed Correspondence and Model Building Mesh Generation Feature Extraction

15. Mesh generation • Point cloud doesn’t capture the blastoderm topology. Locally, it is a 2D sheet of cells

16. Mesh generation • Utilize standard tools from computer graphics and computational geometry

17. Feedback Mesh Information to Segmentation ? Nuclear Segmentation X Y Z Sna Ftz 220.3 40.2 31.0 0.28 0.99 182.4 30.1 44.9 0.22 0.77 . . Mesh Generation

18. Feedback Mesh Information to Segmentation ?

19. Correspondence Overview Nuclear Segmentation Coarse Registration X Y Z Sna Ftz 220.3 40.2 31.0 0.28 0.99 182.4 30.1 44.9 0.22 0.77 . . Detailed Correspondence and Model Building Mesh Generation Feature Extraction

20. Feature Extraction • Extract expression levels in the neighborhood of a given cell by flattening the sheet.

21. Correspondence Overview Nuclear Segmentation Coarse Registration X Y Z Sna Ftz 220.3 40.2 31.0 0.28 0.99 182.4 30.1 44.9 0.22 0.77 . . Detailed Correspondence and Model Building Mesh Generation Feature Extraction

22. Detailed Correspondence • Set up quadratic optimzation problem which includes matching and smoothness terms • only considers correspondences between points which are nearby after the coarse registration • 100 fold reduction in potential matches • utilize features extracted from the mesh • much better match accuracy • further pruning • Results…soon

23. Conclusion • Techniques aimed at cellular correspondence between multiple embroys • Utilize knowledge of embryo topology along with rough alignment to make detailed correspondence tractable