Algorithm 1.

Blood vasculature under the skin layer

Input: breast mask without skin, $N_x$, $N_y$, $N_z$, ${\sigma }_1$, ${\sigma }_2$, ${\sigma }_3$

Output: artery mask, vein mask

1: Obtain a $N_y\times N_z$ random sample matrix from a uniform distribution

2: Obtain two blurred matrices via Gaussian filtering with ${\sigma }_1$ and ${\sigma }_2$ to the result of step (1)

3: Calculate the difference between the results of step (2)

4: Binarize the result of step (3) by Otsu’s thresholding

5: Skeletonize the result of step (4)

6: Obtain a $N_x\times N_y\times N_z$ matrix that contains $N_x$ copies of the result of step (5) in the first dimension of 3D

7: Perform bit-wise exclusive or operation (XOR) between breast mask without skin and that after erosion for 0.375 mm

8: Perform XOR of the results of steps (6) and (7)

9: Skeletonize the result of step (8)

10: Blur the result of step (9) by Gaussian filtering with ${\sigma }_3$

11: Binarize the result of step (10) by Otsu’s thresholding

12: Obtain artery mask and vein mask by labeling the segments in the result of step (11) with either arteries or veins, respectively

13: return artery mask, vein mask