Figure 3.

Exemplary pattern distributions and the corresponding K-function and pcf. All images in this figure were taken from the Shiny apps by C.A.N.B. and J.K. Lines corresponding to the computed functions are shown in red, while the lines corresponding to a Poisson distribution are shown in blue. (A) A randomly distributed pattern (Poisson distribution). While the pcf in the second column varies around the line of a theoretical Poisson distribution, the K-function of the pattern in the third column is very close to the line of a theoretical Poisson distribution, implying that the pattern might be close to complete spatial randomness (CSR). (B) A pattern with a clustering behavior. The corresponding pcf in the second column stays mostly above the pcf of a theoretical Poisson distribution, as does the K-function in the third column. This implies a clustering behavior. (C) A pattern with inhibitive behavior. The corresponding pcf in the second column stays mostly below the pcf of CSR. The K-function in the third column is below the line of CSR as well, which implies an inhibitive or regular behavior. (D) An exemplary dataset of the second app where tumor (blue points) and stroma (red points) cells were differentiated. Instead of the K-function and pcf used before, their Cross-functions are being used. Here one can clearly see an inhibitive or avoiding pattern where cells of one type are mostly close to each other while avoiding close contact with cells of the other type. This effect is enhanced by the inhomogeneity in the general distribution, with tumor cells being mainly on the left side of the ROI and stromal cells being almost exclusively on the right half.