Resampling approaches for the quantitative analysis of spatially distributed cells

Image segmentation is a crucial step in various image analysis pipelines and constitutes one of the cutting-edge areas of digital pathology. The advent of quantitative analysis has enabled the evaluation of millions of individual cells in tissues, allowing for the combined assessment of morphological features, biomarker expression, and spatial context. The recorded cells can be described as a point pattern process. However, the classical statistical approaches to point pattern processes prove unreliable in this context due to the presence of multiple irregularly-shaped interstitial cell-devoid spaces in the domain, which correspond to anatomical features (e.g. vessels, lipid vacuoles, glandular lumina) or tissue artefacts (e.g. tissue fractures), and whose coordinates are unknown. These interstitial spaces impede the accurate calculation of the domain area, resulting in biased clustering measurements. Moreover, the mistaken inclusion of empty regions of the domain can directly impact the results of hypothesis testing. The literature currently lacks any introduced bias correction method to address interstitial cell-devoid spaces. To address this gap, we propose novel resampling methods for testing spatial randomness and evaluating relationships among different cell populations. Our methods obviate the need for domain area estimation and provide non-biased clustering measurements. We created the SpaceR software (https://github.com/GBertolazzi/SpaceR) to enhance the accessibility of our methodologies.