Fine-grained, nonlinear registration of live cell movies reveals spatiotemporal organization of diffuse molecular processes
Fig 2
Computational elements for the remapping process.
a) Extraction of the mask gradient ∇fmask. Based on a cell mask, we calculate for each pixel the distance to the nearest cell boundary element for both the cell-interior and cell-exterior spaces. The gradient on this distance field defines ∇fmask. b) Diffeomorphism constraint. From left to right, illustrations of interpolation fields, where edges indicate the sampling position of an input image to remap onto a target. The mesh diagram shows displacements as deviation from a square mesh (1st diagram from left). A diffeomorphic transform (2nd diagram) is represented by a deformed mesh. A break in diffeomorphism (3rd diagram) is represented by crossings of mesh edges. By sorting the mesh coordinates in sequential order, breaks in diffeomorphism can be reverted (4th diagram). c) Effect of algorithm components on cell edge registration. Accuracy of registration over n iterations is indicated by the area of mismatch (green and purple) between the moving cell and the target cell image, normalized by the target cell perimeter. Removing the mask regularization and topological constraint enforcing diffeomorphism reduces both the rate of convergence and the final accuracy. The dashed line indicates the iteration stop for a visualization of the registration results (bottom row). The proposed algorithm gives a near pixel perfect registration of the two images. Removing the mask regularization largely reduces the rate of convergence. Removing both mask regularization and topological constraint causes failure in the capture of small protrusions.