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u-Unwrap3D Analysis Notebooks

u-Unwrap3D Analysis Notebooks

Basics

Introduction
Installation

Standard Workflow

Standard workflow for unwrapping 3D surfaces
Step 0: Segmenting a single cell from a volume image
Step 1: Find and create a genus-0 reference surface, \(S_{ref}(x,y,z)\)
Step 2: Quasi-conformal spherical parameterization of the genus-0 reference surface, \(S_{ref}(x,y,z)\)
Step 3: Quasi-equiareal spherical parameterization of a genus-0 surface, \(S_{\text{ref}}(x,y,z)\)
Step 4: UV mapping \(S_{ref}(x,y,z)\) into 2D using its spherical parameterization, \(S_{\text{ref}}^{\Omega}(x,y,z)\)
Step 5: Building the topographic \((d,u,v)\) space of \(S_{ref}(x,y,z)\)
Step 6: Compute topographic surface \(S(d,u,v)\) from topographic binary segmentation
Step 7: Flattening the topographic surface \(S(d,u,v)\) onto the 2D plane
Full examples of standard workflow

Customizing the standard workflow to input data

Customizing the standard workflow for downstream analysis

In-depth Breakdown of Mapping Steps

Extracting surfaces from microscopy imaging
Finding the best reference shape for the analysis
UV unwrapping of spherical parameterizations
Building topography space
Spherical parameterizations
Flattening topography surfaces

Transporting measurements between representations

Transferring measurements across meshes

Applying u-Unwrap3D to live-cell imaging

Shape registration
Computing distortion-corrected measurements for analysis in uv and topopraphy space
Motion and information flow of measurements
Tracking protrusions in 2D uv space
Analyzing temporally tracked protrusions

Applications of different surface representations

Segmenting surface protrusions
- Binary protrusion segmentation
- Instance protrusion segmentation
Decomposing surface into reference and protrusion meshes
Harmonics analysis of surfaces

Mapping open 3D surfaces into 2D

Unwrapping individual protrusions
- Example: Unwrapping a lamellipodia

Appendix

Glossary

Repository
Open issue

.md

Building topography space

Building topography space#

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Spherical parameterizations

By Felix Y. Zhou

Copyright: Licensed GPL3 unless mentioned otherwise.