This is the computational experiment which appeared in the paper "Stable topological summaries for analysing the organization of cells in a packed tissue". We use TDA to prove the existence of significant differences in the topological-geometrical organization of 2D epithelial tissues. Functions must be executed in the following order:
- Follow the numerical order of the folders
- Inside each folder, execute only functions begining with a capital letter following the alphabetic order.
The following software is required:
- Matlab/Octabe
- python
- R
- Jupyter with R kernel
The working folder must be the same where the executed function is stored. If you have any doubt or comment about the code, you can email to msoriano4 at us dot es
The folder original_data/ contains: images from epithelial tissues saved in original_data/epithelial_images/ and info about the CVT-path images saved as .mat files in CVT/ We will obtain the .mat file from the epithelial images and the png images from the CVT
A_calculate_epithelial_images.m takes the epithelial images and transform them to black&white png files.
B_calculate_epithelial_data.m obtain the labeled image from the png images and use regionprops to obtain the data from images and save them in cell_data/
auxiliar functions: calculate_neighboors.m
C_calculate_CVT.m extract the original black&white png images from each .mat file, save them in cell_images/ and rename the mat data, saving it in cell_data/
D_extract_cells.m extract a list with the desired number of cells and its centroids following the spiral algorithm. A list with the tags of the selected cells can be found in sample_of_cells/ and the point cloud formed by their centroids in point_clouds/
auxiliar function: spiral.m
number_valid_cells.ods is a table with the number of maximum cells in each epithelial image
A_compute_clique.py reads files in 0_data/cell_data/ and in 0_data/sample_of_cells/ to calculate the barcodes from the sub/sup clique filtration. A txt with the barcode is saved in barcode_txt/ and its image in barcode_png/
B_compute_rips.R reads the point clouds in 0_data/point_clouds/ and calculte the rips complex persistent homology. A txt with the barcode is saved in barcode_txt/ and its image in barcode_png/
auxiliar functions: load_pc.R, barcode_generator.R
A_tda_frame calculates the TDA variable from each of the barcodes and save them as a frame in the folder frames/
auxiliar funtions: normaL1.R, normalization.R, send_infinity_to.R, shannon.R
B_network.py calculates some of the network variables and save them as a txt in network_variables/
C_network.R read the network variables and save them as an R frame in frames/
sta_N.ipynb contains the statistical analysis of the tda variables when the fixed number of cells is N
RF_N.ipynb contains the random forest experiment with tda and network variables when the fixed number of cells is N
boxplot_generator.R save the boxplot for each of the variables in boxplots/
A_plot_clique_filtration calculate the simplicial complex for the sub/sup clique filtration and saves them in filtration_images/