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Finding correspondences between Drosophila embryos

Finding correspondences between Drosophila embryos. Charless Fowlkes and Jitendra Malik, UCB Computer Science. ?. Sources of Variation. Not so interesting: Staining Shrinking Spinning Squashing Staging Interesting: Biological Variation. Motivation for combining measurements.

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Finding correspondences between Drosophila embryos

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  1. Finding correspondences between Drosophila embryos Charless Fowlkes and Jitendra Malik, UCB Computer Science

  2. ?

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

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

  5. Related Work – 1D Registration 10% strip Warp x-axis to align peak features Myasnikova et al (2001)

  6. Overview of Algorithm • Segment out cellular volumes and quantify expression levels (C. Luengo, D. Knowles) • Align set of pointclouds using expression patterns as a “registration marker” to find corresponding cells • Use correpsondences to transfer expression levels onto composite model.

  7. Clyindrical Projection

  8. Clyindrical Projection Dorsal Ventral Dorsal Anterior Posterior

  9. FTZ Edge Points

  10. Two Coarsely Registered Embryos

  11. Shape Context Descriptor

  12. Cij = similarity of shape context for points i and j Dij = distance between points i and j maximize : 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

  13. 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

  14. Deformable Matching

  15. Initial Results • 34 embryos stained for FTZ and one other gene product • Choose a target embryo • Find correspondences with remaining embryos and transfer expression levels

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

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

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

  19. Discussion • What constitutes a good correspondence? • should respect compartment boundaries • should be smooth within a compartment

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