def run_lap(img0, img1, labels0, labels1, DISPLACEMENT=30, MASSTHRES=0.2):
'''Linear assignment problem for mammalian cells.
Cost matrix is simply the distance.
costDie and costBorn are variables changing over frame. Update it through holder.
Args:
DISPLACEMENT (int): The maximum distance (in pixel)
MASSTHRES (float): The maximum difference of total intensity changes.
0.2 means it allows for 20% total intensity changes.
'''
labels = -labels1.copy()
rps0 = regionprops(labels0, img0)
rps1 = regionprops(labels1, img1)
if not rps0 or not rps1:
return labels0, labels
dist = cdist([i.centroid for i in rps0], [i.centroid for i in rps1])
massdiff = calc_massdiff(rps0, rps1)
'''search radius is now simply set by maximum displacement possible.
In the future, I might add data-driven approach mentioned in LAP paper (supple pg.7)'''
dist[dist >
DISPLACEMENT] = np.Inf # assign a large cost for unlikely a pair
# dist[abs(massdiff) > MASSTHRES] = np.Inf
cost = dist
if cost.shape[0] == 0 or cost.shape[1] == 0:
return labels0, labels
# Define initial costBorn and costDie in the first frame
if not hasattr(holder, 'cost_born') or not hasattr(holder, 'cost_die'):
holder.cost_born = np.percentile(cost[~np.isinf(cost)], 80)
holder.cost_die = np.percentile(cost[~np.isinf(cost)], 80)
# try:
binary_cost = call_lap(cost, holder.cost_die, holder.cost_born)
# The first assignment of np.Inf is to reduce calculation of linear assignment.
# This part will make sure that cells outside of these range do not get connected.
binary_cost[(np.abs(massdiff) > MASSTHRES)] = False
binary_cost[(dist > DISPLACEMENT)] = False
gp, gc = np.where(binary_cost)
idx0, idx1 = list(gp), list(gc)
for i0, i1 in zip(idx0, idx1):
labels[labels1 == rps1[i1].label] = rps0[i0].label
labels0[labels0 == rps0[i0].label] = -rps0[i0].label
# update cost
linked_dist = [dist[i0, i1] for i0, i1 in zip(idx0, idx1)]
if linked_dist:
cost = np.max(linked_dist) * 1.05
if cost != 0: # solver freezes if cost is 0
holder.cost_born, holder.cost_die = cost, cost
return labels0, labels
def nn_closer(img0, img1, labels0, labels1, DISPLACEMENT=30, MASSTHRES=0.25):
labels = -labels1.copy()
rps0 = regionprops(labels0, img0)
rps1 = regionprops(labels1, img1)
if not rps0 or not rps1:
return labels0, labels
dist = cdist([i.centroid for i in rps0], [i.centroid for i in rps1])
massdiff = calc_massdiff(rps0, rps1)
binary_cost = (dist < DISPLACEMENT) * (abs(massdiff) < MASSTHRES)
binary_cost = pick_closer_cost(binary_cost, dist)
binary_cost = pick_closer_cost(binary_cost.T, dist.T).T
idx1, idx0 = find_one_to_one_assign(binary_cost)
for i0, i1 in zip(idx0, idx1):
labels[labels1 == rps1[i1].label] = rps0[i0].label
labels0[labels0 == rps0[i0].label] = -rps0[i0].label
return labels0, labels
def nearest_neighbor(img0,
img1,
labels0,
labels1,
DISPLACEMENT=20,
MASSTHRES=0.2):
"""
labels0 and labels1: the positive values for non-tracked objects and the negative values for tracked objects.
"""
labels = -labels1.copy()
rps0 = regionprops(labels0, img0)
rps1 = regionprops(labels1, img1)
if not rps0 or not rps1:
return labels0, labels
dist = cdist([i.centroid for i in rps0], [i.centroid for i in rps1])
massdiff = calc_massdiff(rps0, rps1)
binary_cost = (dist < DISPLACEMENT) * (abs(massdiff) < MASSTHRES)
idx1, idx0 = find_one_to_one_assign(binary_cost)
for i0, i1 in zip(idx0, idx1):
labels[labels1 == rps1[i1].label] = rps0[i0].label
labels0[labels0 == rps0[i0].label] = -rps0[i0].label
return labels0, labels