def split_areas(u, tck, z, xs, ps, a):
"""
Find the areas of the parent and nascent daughter cells.
args:
u (ndarray): 1D array giving paramaterization of the spline
z (ndarray): coordinates of division plane on midline
tck (list): spline representation of border
xs (ndarray): coordinates along the border
ps (ndarray): coordinates of cell poles
a (float): area of the entire cell
returns:
ao (float): area of the parent cell
an (float): area of the daughter cell
"""
# Split the border into two contours, one for each new cell
uo, un = splitborder(u, xs, z)
# Identify the contours with the old and new cells
xso = np.asarray(zip(*splev(uo, tck)))
xsn = np.asarray(zip(*splev(un, tck)))
# Verify the identifications
po, pn = ps
do = np.min([norm(po - v) for v in xso])
dn = np.min([norm(pn - v) for v in xso])
if dn < do:
xso, xsn = xsn, xso
# Make new periodic splines for each cell
tcko = makebspline(xso, 0., True)[0]
tckn = makebspline(xsn, 0., True)[0]
# Return the area of each cell
ao = splineprops(u, tcko, ('Area', ))['Area']
an = splineprops(u, tckn, ('Area', ))['Area']
# Scale the results to be commensurate with the full area
f = a / (ao + an)
return f * ao, f * an
def split_areas(u, tck, z, xs, ps, a):
"""
Find the areas of the parent and nascent daughter cells.
args:
u (ndarray): 1D array giving paramaterization of the spline
z (ndarray): coordinates of division plane on midline
tck (list): spline representation of border
xs (ndarray): coordinates along the border
ps (ndarray): coordinates of cell poles
a (float): area of the entire cell
returns:
ao (float): area of the parent cell
an (float): area of the daughter cell
"""
# Split the border into two contours, one for each new cell
uo, un = splitborder(u, xs, z)
# Identify the contours with the old and new cells
xso = np.asarray(zip(*splev(uo, tck)))
xsn = np.asarray(zip(*splev(un, tck)))
# Verify the identifications
po, pn = ps
do = np.min([norm(po - v) for v in xso])
dn = np.min([norm(pn - v) for v in xso])
if dn < do:
xso, xsn = xsn, xso
# Make new periodic splines for each cell
tcko = makebspline(xso, 0.0, True)[0]
tckn = makebspline(xsn, 0.0, True)[0]
# Return the area of each cell
ao = splineprops(u, tcko, ("Area",))["Area"]
an = splineprops(u, tckn, ("Area",))["Area"]
# Scale the results to be commensurate with the full area
f = a / (ao + an)
return f * ao, f * an
def get_width_profile_new(s, num_points=500):
"""
Get the width profile and associated variables with a recalculated midline.
args:
s (Series): data read in from file for a single frame
returns:
d (dict): calculated values
"""
# Evaluate the midline at discrete points starting at the old pole
u = np.linspace(0., 1., num_points)
d = {
'Radius': np.nan,
'RadiusStalked': np.nan,
'RadiusSwarmer': np.nan,
'Widths': np.empty(0),
'WidthMin': np.nan,
'WidthStalkedMax': np.nan,
'WidthSwarmerMax': np.nan,
'WidthStalkedMin': np.nan,
'WidthSwarmerMin': np.nan,
'Area': np.nan,
'AreaStalked': np.nan,
'AreaSwarmer': np.nan,
'Length': np.nan,
'LengthStalked': np.nan,
'LengthSwarmer': np.nan,
'LengthStalkedMin': np.nan,
'LengthSwarmerMin': np.nan,
'MidSpline': []
}
try:
# Get coordinates and first derivative of contour
tck = s['EdgeSpline']
es = np.asarray(zip(*splev(u, tck)))
des = np.asarray(zip(*splev(u, tck, der=1)))
# Find a crude approximation of the cell poles
ps = (s['StalkedPole'], s['SwarmerPole'])
# Approximate the midline by taking the Voronoi diagram
vs = find_midline(es)
# Prune the Voronoi diagram to remove branch points
cs0 = prune_midline(es, des, vs)
# Reorient the midline from stalked to swarmer pole
cs1 = orient_midline(es, cs0, ps)
# Find approximate width along the medial axis
ws1 = get_width(es, cs1[:-1], np.diff(cs1, axis=0))
# Find the radius of curvature of the entire cell
cre0 = fit_circle(cs1)
# Get the minimum cell width
j1_min, w1_min = find_min_width(ws1)
if np.any(j1_min):
# Split contours according to minimum cell width
wso1, wsn1 = ws1[:j1_min], ws1[j1_min:]
# Find the maximum widths of either side
jo1_max, wo1_max = find_max_width(wso1)
jn1_max, wn1_max = find_max_width(wsn1)
# Only keep exterior points within 98% of maximum width
ko1_max = np.flatnonzero(wso1[jo1_max:] > wo1_max * 0.75)
ko1 = np.hstack((range(jo1_max), jo1_max + ko1_max))
kn1_max = np.flatnonzero(wsn1[:jn1_max] > wn1_max * 0.75)
kn1 = np.hstack((kn1_max, range(jn1_max, len(wsn1))))
# Fit circles to either cell
cre1 = fit_circle(cs1[ko1])
cre2 = fit_circle(cs1[j1_min + kn1])
else:
cre1, cre2, = cre0, cre0
# Extend the midline in a way that maintains curvature
cs2 = extend_midline(es, cs1, (cre1[:2], cre2[:2]), ps)
# Spline the new midline
tck4 = makebspline(cs2, smoothing=0.1)[0]
d['MidSpline'] = tck4
cs4 = np.asarray(zip(*splev(u, tck4)))
dcs4 = np.asarray(zip(*splev(u, tck4, der=1)))
# Get the correct cell poles
po, pn = cs4[0], cs4[-1]
# Get the index of the stalked pole
jo = np.argmin(np.sum((es - po)**2, axis=1))
# Overall cell area and length
a = splineprops(u, tck, 'Area')['Area']
d['Area'] = a
l = splineprops(u, tck4, 'Length')['Length']
d['Length'] = l
# Fit best-fit circle to entire cell
cre0 = fit_circle(cs4)
d['Radius'] = cre0[1]
# Get the cell width and minimum and maximum cell widths
ws4 = get_width(es, cs4, dcs4)
d['Widths'] = ws4
j4_min, w_min = find_min_width(ws4)
d['WidthMin'] = w_min
if np.any(j4_min):
# Split contours according to minimum cell width
wso4, wsn4 = ws4[:j4_min], ws4[j4_min:]
# Find the maximum widths of either side
jo4_max, wo_max = find_max_width(wso4)
jn4_max, wn_max = find_max_width(wsn4)
# Find the minimum widths of either side
jo4_min, wo_min = find_min_width(wso4)
jn4_min, wn_min = find_min_width(wsn4)
if not np.any(jo4_min): jo4_min = np.nan
if not np.any(jn4_min): jn4_min = np.nan
# Get points on contour at division plane
es_min = get_divn_plane(es, cs4[j4_min], dcs4[j4_min])
# Split the cell areas and lengths
ao, an = split_areas(u, tck, es_min, es, (po, pn), a)
lo, ln = split_lengths(u, tck4, j4_min, es, (po, pn), l)
# Find the lengths to either secondary minimum
ro_min = float(jo4_min) / float(len(wso4))
rn_min = 1. - float(jn4_min) / float(len(wsn4))
lo_min = lo * ro_min
ln_min = ln * rn_min
# Find best-fit circle to each cell half
cre1 = fit_circle(cs4[:j4_min])
cre2 = fit_circle(cs4[j4_min:])
else:
wo_max, wn_max = np.nan, np.nan
wo_min, wn_min = np.nan, np.nan
ao, an = np.nan, np.nan
lo, ln = np.nan, np.nan
cre1 = (np.nan, np.nan)
cre2 = (np.nan, np.nan)
lo_min, ln_min = np.nan, np.nan
d['RadiusStalked'] = cre1[1]
d['RadiusSwarmer'] = cre2[1]
d['WidthStalkedMax'] = wo_max
d['WidthSwarmerMax'] = wn_max
d['WidthStalkedMin'] = wo_min
d['WidthSwarmerMin'] = wn_min
d['AreaStalked'] = ao
d['AreaSwarmer'] = an
d['LengthStalked'] = lo
d['LengthSwarmer'] = ln
d['LengthStalkedMin'] = lo_min
d['LengthSwarmerMin'] = ln_min
except Exception:
pass
return d
def get_width_profile_new(s, num_points=500):
"""
Get the width profile and associated variables with a recalculated midline.
args:
s (Series): data read in from file for a single frame
returns:
d (dict): calculated values
"""
# Evaluate the midline at discrete points starting at the old pole
u = np.linspace(0.0, 1.0, num_points)
d = {
"Radius": np.nan,
"RadiusStalked": np.nan,
"RadiusSwarmer": np.nan,
"Widths": np.empty(0),
"WidthMin": np.nan,
"WidthStalkedMax": np.nan,
"WidthSwarmerMax": np.nan,
"WidthStalkedMin": np.nan,
"WidthSwarmerMin": np.nan,
"Area": np.nan,
"AreaStalked": np.nan,
"AreaSwarmer": np.nan,
"Length": np.nan,
"LengthStalked": np.nan,
"LengthSwarmer": np.nan,
"LengthStalkedMin": np.nan,
"LengthSwarmerMin": np.nan,
"MidSpline": [],
}
try:
# Get coordinates and first derivative of contour
tck = s["EdgeSpline"]
es = np.asarray(zip(*splev(u, tck)))
des = np.asarray(zip(*splev(u, tck, der=1)))
# Find a crude approximation of the cell poles
ps = (s["StalkedPole"], s["SwarmerPole"])
# Approximate the midline by taking the Voronoi diagram
vs = find_midline(es)
# Prune the Voronoi diagram to remove branch points
cs0 = prune_midline(es, des, vs)
# Reorient the midline from stalked to swarmer pole
cs1 = orient_midline(es, cs0, ps)
# Find approximate width along the medial axis
ws1 = get_width(es, cs1[:-1], np.diff(cs1, axis=0))
# Find the radius of curvature of the entire cell
cre0 = fit_circle(cs1)
# Get the minimum cell width
j1_min, w1_min = find_min_width(ws1)
if np.any(j1_min):
# Split contours according to minimum cell width
wso1, wsn1 = ws1[:j1_min], ws1[j1_min:]
# Find the maximum widths of either side
jo1_max, wo1_max = find_max_width(wso1)
jn1_max, wn1_max = find_max_width(wsn1)
# Only keep exterior points within 98% of maximum width
ko1_max = np.flatnonzero(wso1[jo1_max:] > wo1_max * 0.75)
ko1 = np.hstack((range(jo1_max), jo1_max + ko1_max))
kn1_max = np.flatnonzero(wsn1[:jn1_max] > wn1_max * 0.75)
kn1 = np.hstack((kn1_max, range(jn1_max, len(wsn1))))
# Fit circles to either cell
cre1 = fit_circle(cs1[ko1])
cre2 = fit_circle(cs1[j1_min + kn1])
else:
cre1, cre2, = cre0, cre0
# Extend the midline in a way that maintains curvature
cs2 = extend_midline(es, cs1, (cre1[:2], cre2[:2]), ps)
# Spline the new midline
tck4 = makebspline(cs2, smoothing=0.1)[0]
d["MidSpline"] = tck4
cs4 = np.asarray(zip(*splev(u, tck4)))
dcs4 = np.asarray(zip(*splev(u, tck4, der=1)))
# Get the correct cell poles
po, pn = cs4[0], cs4[-1]
# Get the index of the stalked pole
jo = np.argmin(np.sum((es - po) ** 2, axis=1))
# Overall cell area and length
a = splineprops(u, tck, "Area")["Area"]
d["Area"] = a
l = splineprops(u, tck4, "Length")["Length"]
d["Length"] = l
# Fit best-fit circle to entire cell
cre0 = fit_circle(cs4)
d["Radius"] = cre0[1]
# Get the cell width and minimum and maximum cell widths
ws4 = get_width(es, cs4, dcs4)
d["Widths"] = ws4
j4_min, w_min = find_min_width(ws4)
d["WidthMin"] = w_min
if np.any(j4_min):
# Split contours according to minimum cell width
wso4, wsn4 = ws4[:j4_min], ws4[j4_min:]
# Find the maximum widths of either side
jo4_max, wo_max = find_max_width(wso4)
jn4_max, wn_max = find_max_width(wsn4)
# Find the minimum widths of either side
jo4_min, wo_min = find_min_width(wso4)
jn4_min, wn_min = find_min_width(wsn4)
if not np.any(jo4_min):
jo4_min = np.nan
if not np.any(jn4_min):
jn4_min = np.nan
# Get points on contour at division plane
es_min = get_divn_plane(es, cs4[j4_min], dcs4[j4_min])
# Split the cell areas and lengths
ao, an = split_areas(u, tck, es_min, es, (po, pn), a)
lo, ln = split_lengths(u, tck4, j4_min, es, (po, pn), l)
# Find the lengths to either secondary minimum
ro_min = float(jo4_min) / float(len(wso4))
rn_min = 1.0 - float(jn4_min) / float(len(wsn4))
lo_min = lo * ro_min
ln_min = ln * rn_min
# Find best-fit circle to each cell half
cre1 = fit_circle(cs4[:j4_min])
cre2 = fit_circle(cs4[j4_min:])
else:
wo_max, wn_max = np.nan, np.nan
wo_min, wn_min = np.nan, np.nan
ao, an = np.nan, np.nan
lo, ln = np.nan, np.nan
cre1 = (np.nan, np.nan)
cre2 = (np.nan, np.nan)
lo_min, ln_min = np.nan, np.nan
d["RadiusStalked"] = cre1[1]
d["RadiusSwarmer"] = cre2[1]
d["WidthStalkedMax"] = wo_max
d["WidthSwarmerMax"] = wn_max
d["WidthStalkedMin"] = wo_min
d["WidthSwarmerMin"] = wn_min
d["AreaStalked"] = ao
d["AreaSwarmer"] = an
d["LengthStalked"] = lo
d["LengthSwarmer"] = ln
d["LengthStalkedMin"] = lo_min
d["LengthSwarmerMin"] = ln_min
except Exception:
pass
return d
