The pipeline

Segmentation

.svs files and .nd2 files need to be processed differently.

• svs files can be all processed in qupath
• small nd2 files (< 2GB) can be processed in qupath directly
• large nd2 files (> 2GB) are converted into tif, split into vertical chuncks and then processed in qupath

Morphology table

The morphology table is the one generated by qupath

Graph

Is the 1-simplex originated by UMAP in the uniform manifold approximation step. It allows to quantify the weighted degree and the clustering coefficients.

Graph Laplacian of the morphology

By constructing the graph Laplacian we can measure the differential structure of morphological and topological features

Selection of relevant morphological and topological features

Decide which features to include in the downstream analysis

Normalization of the feature set

Normalize features in order to have a meaningful inter-feature comparison. Some have values in the range [0,1] (like circularity and eccentricity), others have values in a different range (like area, perimeter, intensinsity, etc).

PCA of the feature matrix

Find the major direction of variations in the data

Projection on real space of the principal components

Picture the spatial distribution of the principal components

Partitioning of reals space based on projected components

Find spatio-morphological communities

Covariance descriptor of the partitions

Construct the covariance descriptor for each community/partition