Finding and exploiting correspondences in Drosophila embryos

1. Finding and exploiting correspondences in Drosophila embryos Charless Fowlkes and Jitendra Malik UC Berkeley Computer Science

2. ?

3. Motivation for combining measurements • Average noisy flouresence data over multiple embryos • High throughput • N versus N2 hybridizations to capture colocation of N gene products • Visualization of composite expression map • Study shape of expression patterns

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

6. Overview • Finding Correspondences • Nuclear segmentation • Deformable matching • Exploiting Correspondences • Preliminary results • Discussion

7. x-y x-y x-z Segmenting Nuclei [C. Luengo, D. Knowles] ~200µm ~500µm Embryo is approximately 500µm by 200µm and contains about 5000 to 6000 nuclei

8. Segmentation output

9. Mesh generation • Point cloud doesn’t capture the blastoderm topology. Locally, it is a 2D sheet of cells • Utilize off the shelf tools from computational geometry [Kolluri et al, 2004]

10. Clyindrical Projection

11. Clyindrical Projection Dorsal Ventral Dorsal Anterior Posterior

12. Overview • Finding Correspondences • Nuclear segmentation • Deformable matching • Exploiting Correspondences • Preliminary results • Discussion

13. FTZ expression

14. FTZ Edge Points

15. Two Coarsely Registered Embryos

16. “Shape Context Descriptor”

17. “Shape Context Descriptor”

18. Cij = disimilarity of local descriptor for points i and j Dij = distance between points i and j minimize : Σij (Cij + λDij) • Xij subject to : ΣiXij = 1 Σj Xij = 1 λ sets the relative importance of distance versus shape context match Correspondence as optimization Xij = 1 if point i is matched to point j 0 otherwise i j

19. Problem: correspondence may not be smooth • Find correspondence by optimizing Xij • Smoothly warp source embryo to bring into alignment with corresponding points • Repeat… Solution: iteratively correspond and warp

20. Deformable Matching

21. Overview • Finding Correspondences • Nuclear segmentation • Deformable matching • Exploiting Correspondences • Preliminary results • Composite Expression Map • Nuclear Density Map • Shape • Discussion

22. Preliminary Results • 34 embryos stained for ftz and one other gene product • Choose a target embryo • Find correspondences with remaining embryos and “transfer” measurements

23. Building a composite expression map Source Embryos Target Embryo X Y Push expression levels forward thru correspondence function X

24. FTZ average after coarse alignment FTZ average after detailed matching

26. ftz eve snail kni hb Composite Map: View #1

27. ftz eve snail kni hb Composite Map: View #2

28. Building a nuclear density map X Y Push average nuclear density forward thru correspondence function X

29. Nuclear Density

30. Shape Analysis X-1 Y-1 Pull back selected region thru inverse correspondence function.

31. Current/Future Work • Verifying the correspondences are biologically “correct” • Analysis of variation in shapes of expression patterns • Hybridization experiment design

32. Hybridization Design Sna Kni Hb Ftz Slp Eve

33. Hybridization Design Eve Hb Ftz Sna Sna Sna Kni Slp Kni Hb Hb Ftz Ftz Slp Eve Eve • Can build composite map from any connected graph • Error accumulates so diameter should be small • Some genes provide more powerful constraints than others

34. Future Work