Algorithm 4.

Field computation algorithm (COMPUTE-FIELD).

Inputs:

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

- ${\text{pixels}}^{+}$ is a set of pixels with an assigned positive charge.

- ${\text{pixels}}^{-}$ is a set of pixels with an assigned negative charge.

Output:

- ${\mathcal{I}}_{\text{field}}$ is the grayscale field image. Pixel intensity is directly proportional to field magnitude at its location. Pixel intensities are within [0, 255].

Parameters:

- Define +ve and −ve charges as $+1$ and $-1$, respectively. Set decay rate for +ve and −ve charges as 1.0 and 1.6, respectively. These charge values and decay rates were optimized empirically.

1:  Procedure COMPUTE-FIELD($I_{\text{gland}}^{\text{threshold}}$, ${\text{pixels}}^{+}$, ${\text{pixels}}^{-}$)

2:   Initialize all pixels in ${\mathcal{I}}_{\text{field}}$ to zero.

3:   for All pixels $(x,y)\in I_{\text{gland}}^{\text{threshold}}$do

4:   ${\mathcal{I}}_{\text{field}}(x,y)=\sum _{(x_j,y_j)\in {\text{pixels}}^{+}}\frac{(1.0)}{{[{(x-x_j)}^2+{(y-y_j)}^2]}^{\frac{1}{2}}}+\sum _{(x_k,y_k)\in {\text{pixels}}^{-}}\frac{(-1.0)}{{[{(x-x_k)}^2+{(y-y_k)}^2]}^{\frac{1.6}{2}}}$.

5:   end for

6:   Linearly rescale ${\mathcal{I}}_{\text{field}}$ to values within [0, 255] for further numerical operations.

7:   return field image ${\mathcal{I}}_{\mathrm{field}}$.

8: end procedure