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

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Motivation for combining measurements Average noisy flouresence data over multiple embryos High throughput –N versus N 2 hybridizations to capture colocation of N gene products Visualization of composite expression map Study shape of expression patterns

Sources of Variation Not so interesting: –Staining –Shrinking –Spinning –Squashing –Staging Interesting: –Biological Variation

Overview Finding Correspondences –Nuclear segmentation –Deformable matching Exploiting Correspondences –Preliminary results –Discussion

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

Segmentation output

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]

Clyindrical Projection

Ventral Dorsal Anterior Posterior

Overview Finding Correspondences –Nuclear segmentation –Deformable matching Exploiting Correspondences –Preliminary results –Discussion

FTZ expression

FTZ Edge Points

Two Coarsely Registered Embryos

“Shape Context Descriptor”

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

1.Find correspondence by optimizing Xij 2.Smoothly warp source embryo to bring into alignment with corresponding points 3.Repeat… Problem: correspondence may not be smooth Solution: iteratively correspond and warp

Deformable Matching

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

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

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

FTZ average after coarse alignment FTZ average after detailed matching

ftz eve snail kni hb Composite Map: View #1

ftz eve snail kni hb Composite Map: View #2

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

Nuclear Density

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

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

Eve Slp Kni Sna Hb Ftz Hybridization Design

Eve Slp Kni Sna Hb Ftz Hybridization Design Eve Slp Kni Sna Hb Ftz Eve Sna Hb Ftz 1.Can build composite map from any connected graph 2.Error accumulates so diameter should be small 3.Some genes provide more powerful constraints than others

Future Work