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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 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 • 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
Related Work – 1D Registration 10% strip Warp x-axis to align peak features Myasnikova et al (2001)
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.
Clyindrical Projection Dorsal Ventral Dorsal Anterior Posterior
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
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
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
FTZ average after coarse alignment FTZ average after detailed matching
ftz eve snail kni hb Composite Map: View #1
Composite Map: View #2 ftz eve snail kni hb
Discussion • What constitutes a good correspondence? • should respect compartment boundaries • should be smooth within a compartment