Derivatives sum algorithm for 3D nuclear segmentation.

(a) 2D 8-bit gray scale image slice of a 3D stack of dimension 167 × 172 × 39 voxels from the posterior PSM of an 18-somite stage zebrafish embryo. (b) De-noised image after Gaussian blur (σ = 0.5, window size = 5×5 squared pixels). (c) Image smoothened by a non-linear isotropic diffusion filter (κ = 10, n = 4). (d) Magnitude of Gauss gradient (σ_g = 1.5), (e) Laplacian where positive and (f) Determinant of Hessian where negative, we show the absolute value. (g) De-noised image shown in (c). (h) A tangent hyperbolic masking function (α = β = ε = γ = δ = 1). (i) Masked image obtained by the pair-wise product between the de-noised image in (g) and the masking function in (h). (j) Slices of binary images obtained by Otsu’s thresholding method. (k) Surface rendered 3D binary objects colored with respect to their position along the z-direction. All tunable parameters are highlighted by Greek glyphs in red. See S1 Text for more details.

Assessment of 3D segmentation using experimental image data.

(a) Schematic illustration of transplantation experiment. Cells in a donor embryo at blastula stage expressing two histone variants fused to GFP and mCherry (h2Aflv-gfp/ h2Aflv-mCherry) are colored orange. (b) Bright-field image of a 13 somite-stage chimeric embryo. The white box indicates the tailbud. (c) 15 somite-stage chimeric embryo in gfp (left) and mcherry (middle) channels, and merged (right). White box in each image indicates the cropped region (50×50 squared pixels) used for the sensitivity analysis. Inset image is magnification of boxed region. (d) Sensitivity plot over density for five cropped images from four chimeric embryos. Each symbol and error bar indicates the temporal average and standard deviation, respectively, of the sensitivity over 10 time frames for a cropped image. Parameters in DS are α = β = γ = δ = 1, ε = 2, and σ_g = 1.2. De-noising filters; Gaussian filter (σ = 0.5, window size = 5×5 squared pixels) and median filter (window size = 3×3), Lucy-Richardson deconvolution filter with σ = 0.5, non-linear isotropic diffusion filter (κ = 50, n = 5). Both channels for all five cropped images were processed with same parameter values.