Algorithm 2.

Maxima-seeds generation algorithm (MAXIMA-SEEDS).

Input:

- $I_{\text{gland}}^{\text{threshold}}$ is the binary gland mask. White regions are glands on a black background.

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

Output:

- $I_{\text{seed}\_\text{maxima}}$ is the binary maxima-seed mask. White regions are centroid locations of the gland objects.

Function and variable description:

- DILATE($I,d$) conducts “$d$” dilation operations on binary image $I$ with a $3\times 3$ pixels dilation window. Output image is also binary.

- DISTANCE-TRANSFORM($I$) computes the Euclidean distance map of image $I$. Output image is grayscale.

- FIND-MAXIMA($\mathcal{I}$) computes the local intensity maxima pixels in the $\mathcal{I}$. Output is a binary image indicating the maxima pixels in white.

- Given a binary image $I$, $\overline{I}$ is a binary image with corresponding inverted pixel values.

- $I_a\wedge I_b$ is a Boolean operation defining pixel-wise AND operation between $I_a$ and $I_b$.

Parameters:

- Select number of dilation operations $d=8$. This value for $d$ was optimized empirically.

1:  Procedure MAXIMA-SEEDS ($I_{\text{gland}}^{\text{threshold}}$, $I_{\mathrm{nuclei}}$)

2:   $I_{\mathrm{nuclei}}^{\text{border}}=\text{DILATE}(I_{\mathrm{nuclei}},8)$.

3:   $I_{\text{mask}}=I_{\text{gland}}^{\text{threshold}}\wedge \overline{I_{\mathrm{nuclei}}^{\text{border}}}$.    ⊳ Remove nuclei borders from gland regions.

4:   $I_{\text{seed}\_\text{maxima}}=\mathrm{FIND}-\mathrm{MAXIMA}(\mathrm{DISTANCE}-\mathrm{TRANSFORM}[I_{\text{mask}})]$.    ⊳ Find the centers of the glandular objects.

5:   return maxima-seed mask $I_{\text{seed}\_\text{maxima}}$.

6: end procedure