Algorithm 1.

Nuclei segmentation algorithm (NUCLEI-SEGMENTATION).

Input:

- ${\mathcal{I}}_0$ is the original H&E image.

Output:

- $I_{\mathrm{nuclei}}$ is the binary nuclei mask. White regions are nuclei on a black background.

Function and variable description:

- BLUR($\mathcal{I},{\sigma }_s$) is the Gaussian blur function with kernel with $\sigma ={\sigma }_s$. Output is a grayscale image.

- Stain separation method is described by Ruifrok et al.49

- MOMENTS-THRESHOLD($\mathcal{I}$) thresholds $\mathcal{I}$ using the moments preserving image thresholding method.45 Output is a binary image.

- Median filter (blur) replaces each pixel intensity by the median of all the pixel intensities in its kernel neighborhood.

Parameters:

- Select Gaussian kernel with $\sigma =3$ for the blur operation. This value for sigma was optimized empirically.

1:  Procedure NUCLEI-SEGMENTATION(${\mathcal{I}}_0$)

2:   Separate the haemotoxylin and eosin channels of ${\mathcal{I}}_0$ into ${\mathcal{I}}_{\mathrm{Hematoxylin}}$ and ${\mathcal{I}}_{\mathrm{Eosin}}$.       ⊳ Both ${\mathcal{I}}_{\text{Hematoxylin}}$ and ${\mathcal{I}}_{\mathrm{Eosin}}$ are grayscale images.

3:   ${\mathcal{I}}_{\text{Hematoxylin}}^{\text{blur}}=\mathrm{BLUR}({\mathcal{I}}_{\text{Hematoxylin}},3)$.

4:   $I_{\text{Hematoxylin}}^{\text{threshold}}=\mathrm{MOMENTS}-\mathrm{THRESHOLD}({\mathcal{I}}_{\text{Hematoxylin}})$.

5:   Remove noise in $I_{\text{Hematoxylin}}^{\text{threshold}}$ to compute $I_{\mathrm{nuclei}}$ by median blur.

6:   return nuclei mask $I_{\mathrm{nuclei}}$.

7: end procedure