delaunay-watershed-3d 0.2.5

Geometrical reconstruction of cell assemblies from instance segmentations

Delaunay-Watershed 3D

Delaunay-Watershed-3D is an algorithm designed to reconstruct a sparse representation of the geometry of tissues and cell nuclei from instance segmentations, in 3D. It accomplishes this by building multimaterial meshes from segmentation masks. These multimaterial meshes are perfectly suited for storage, geometrical analysis, sharing and visualisation of data. We provide high level APIs to extract geometrical features from the meshes, as well as visualisation tools based on polyscope and napari.

Delaunay-Watershed was created by Sacha Ichbiah during his PhD in Turlier Lab, and is maintained by Sacha Ichbiah, Matthieu Perez and Hervé Turlier. For support, please open an issue. A preprint of the method will be published soon. If you use our library in your work please cite the paper.

Introductory notebooks with precise use case are provided. The algorithm takes as input segmentation masks and return multimaterial triangle meshes (3D).

This method is used as a backend for foambryo, our 3D tension inference library.

Example

Load an instance segmentation, reconstruct its multimaterial mesh, and extract its geometry:

pip install delaunay-watershed-3d

from dw3d import geometry_reconstruction_3d

## Load the labels
import skimage.io as io
labels = io.imread("data/Images/1.tif")

## Reconstruct a multimaterial mesh from the labels
DW = geometry_reconstruction_2d(labels,(image, min_dist = 5, expansion_labels =0,print_info=True)
DW.plot_cells_polyscope()
v = DW.plot_in_napari(add_mesh=True)

## Use the mesh to analyze the geometry:
Mesh=DW.return_dcel()
Mesh.compute_curvatures_interfaces()
Mesh.compute_areas_interfaces()
Mesh.compute_volumes_cells()
Mesh.compute_length_trijunctions()
Mesh.compute_angles_junctions()

Installation

pip install delaunay-watershed-3d

---

API and Documentation

1 - Creating a multimaterial mesh:

The first step is to convert your instance segmentation into a multimaterial mesh

• geometry_reconstruction_3d(labels,min_dist = 5, expansion_labels = 0,original_image = None,print_info = False, mode='torch'):
  • Mesh is a DCEL_Data object
  • min_dist defines the minimal distance, in pixels, between two points used for the delaunay-triangulation
  • expansion_labels can be used to expand the labels and make them touch each other.
  • original_image can be used for visualization purposes in napari
  • print_info measure time between several checkpoints and give usefull informations about the procedure
  • mode can be torch or skimage. It is highly recommeded to use torch
  • return DW, an object containing visualization and export utilities

2 - Visualize and export the mesh

Once a DW object is generated, we can use its methods the visualize and export the result:

• DW:
  • self.plot_cells_polyscope() plot the resulting mesh in polyscope
  • self.plot_in_napari(add_mesh=True) offers more information about the procedure.
  • self.return_mesh() return (Verts,Faces_multimaterial):
    • Verts is an V x 3 numpy array of vertex positions
    • Faces_multimaterial is an F x 5 numpy array of Edges and material indices, where at each row the 3 first indices refers to a vertex and the 2 last refer to a given material, 0 being the exterior media
  • self.return_dcel() return a DCEL_Data object, i.e a Half-edge implementation of the mesh

3 - Analyze the geometry

A DCEL_Data object can be used to analyze the geometry:

• DCEL_Data:
  • self.compute_angles_junctions() returns a dictionnary with the values of every angles formed by the cells (in rad)
  • self.compute_compute_curvatures(laplacian = "robust",weighted = True) returns a dictionnary with the values of the mean curvature averaged on all the vertices of all the interfaces. laplacian can be either "cotan" or "robust". If weighted, the sum is scaled with vertices areas.
  • `self.compute_length_halfedges(), self.compute_areas_faces(), self.compute_centroids_cells(), self.compute_areas_cells(), self.compute_areas_interfaces(), self.compute_volumes_cells(), compute_length_trijunctions()

---

Biological use-cases

Geometrical reconstruction of P.Mammilata Embryo

Data from Guignard et al.

Geometrical reconstruction of Cell Nuclei

Data from Stardist

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Credits, contact, citations

If you use this tool, please cite the associated preprint. Do not hesitate to contact Sacha Ichbiah and Hervé Turlier for practical questions and applications. We hope that Delaunay-Watershed could help biologists and physicists to shed light on the mechanical aspects of early development.

@article {Ichbiah2023.04.12.536641,
	author = {Sacha Ichbiah and Fabrice Delbary and Alex McDougall and R{\'e}mi Dumollard and Herv{\'e} Turlier},
	title = {Embryo mechanics cartography: inference of 3D force atlases from fluorescence microscopy},
	elocation-id = {2023.04.12.536641},
	year = {2023},
	doi = {10.1101/2023.04.12.536641},
	publisher = {Cold Spring Harbor Laboratory},
	abstract = {The morphogenesis of tissues and embryos results from a tight interplay between gene expression, biochemical signaling and mechanics. Although sequencing methods allow the generation of cell-resolved spatio-temporal maps of gene expression in developing tissues, creating similar maps of cell mechanics in 3D has remained a real challenge. Exploiting the foam-like geometry of cells in embryos, we propose a robust end-to-end computational method to infer spatiotemporal atlases of cellular forces from fluorescence microscopy images of cell membranes. Our method generates precise 3D meshes of cell geometry and successively predicts relative cell surface tensions and pressures in the tissue. We validate it with 3D active foam simulations, study its noise sensitivity, and prove its biological relevance in mouse, ascidian and C. elegans embryos. 3D inference allows us to recover mechanical features identified previously, but also predicts new ones, unveiling potential new insights on the spatiotemporal regulation of cell mechanics in early embryos. Our code is freely available and paves the way for unraveling the unknown mechanochemical feedbacks that control embryo and tissue morphogenesis.Competing Interest StatementThe authors have declared no competing interest.},
	URL = {https://www.biorxiv.org/content/early/2023/04/13/2023.04.12.536641},
	eprint = {https://www.biorxiv.org/content/early/2023/04/13/2023.04.12.536641.full.pdf},
	journal = {bioRxiv}
}