The Linearized Compressed Polar Coordinates (LCPC) Transform
The LCPC Transform has been made into an easy-to-use open source software called Shape Genie OpS (OpS stands for Open Source). The original Python code for doing the the LCPC Transform are be available on GitHub:
The code for Shape Genie OpS (the no-coding necessary version) will be posted on GitHub soon.
See the many uses of the Shape Genie OpS in our page called "Use Cases of LCPC".
How The LCPC Transform Works
Tutorial on Calculations Behind the LCPC Transform
Read the First Peer-Reviewed Paper About the LCPC Transform
Nguyen, D.H., Bruck, M., Rosenbluth, J.M. A Shape Analysis Algorithm Quantifies Spatial Morphology and Context of 2D to 3D Cell Culture for Novel Quantitation of Phenotypes. J. Vis. Exp. (233), e71066, doi:10.3791/71066. (2026). [Download the free pre-print that is the same version as the published paper]
Part 1. How to Run The Python Scripts from GitHub
How to Run RADIAL Grid LCPC & Do Quality Control Checks
How to Run PARALLEL Grid LCPC & Do Quality Control Checks
Part 2. How to Prepare Shape Outlines
(Otherwise Known as “Masks”)
The Scale Parameter - How to Prepare Shape Outlines
The Line Thickness Parameter - How to Prepare Shape Outlines
The Margin Thickness Parameter - How to Prepare Shape Outlines
Why Should You Strategically Name Your Images BEFORE Working With Them?
Part 3. What Grid System to Use? Radial vs. Parallel
What Grid System to Use?
How to Prepare Shapes for The Parallel Grid System
Part 4. Ways to Analyze the Fast Fourier Transform (FFT) Results Produced by the LCPC Transform
Calculating Shape Indices in the CSV Output File [20 min]
See This Example Use Case of How We Analyzed the FFT Output Multidimensionally with Principal Component Analysis
Part 5. How to Use the Pre-Processing Tools
The link to the GitHub repository that contains the pre-processing scripts are at the top of this page.
Part 6. How to Use the POST-Processing Tools
How to Run the PCA Script for LCPC Results
How to Run the the Loading Plot Script
How to Run the Interactive 3D Dot Plot Script
How to Run the DBSCAN Script