Sample coordinates from a Gaussian distribution instead of the SC centerline

[naga-karthik]

Current approach randomly samples the coordinates from the centerline of the healthy SC mask to decide where to paste the lesion. The problem is that the distribution of the pasted lesions lies only along the center of the spinal cord, which is not how MS lesions manifest.

Consider sampling coordinates from a Gaussian distribution instead.

[naga-karthik]

Examples of coordinates sampled from a Gaussian distrubtion

code snippet for gaussian sampling

healthy_sc_coords = np.argwhere(mask_healthy_sc > 0)
# sample a coordinate from the healthy SC mask Gaussian distribution
mean_coords, cov_coords = np.mean(healthy_sc_coords, axis=0), np.cov(healthy_sc_coords.T)
new_position_target = rng.multivariate_normal(mean_coords, cov=cov_coords).astype(int)
# ensure that new position coordinates are within the image dimensions
new_position_target = np.clip(
    new_position_target, 
    a_min=healthy_sc_coords.min(axis=0)+5, 
    a_max=healthy_sc_coords.max(axis=0)-5
)

Examples of coordinates sampled from the SC centerline

It does seem that sampling from a Gaussian gives a good (and unbiased) coverage of the SC coordinates. Hence, proceeding with Gaussian sampling (instead of the biased centerline sampling).