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Commit 4d83b318 authored by NADAL Morgane's avatar NADAL Morgane
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handle singular matrices

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brick/processing/best_fit_ellipsoid.py
+ 94
− 80
View file @ 4d83b318
......@@ -42,17 +42,22 @@ def ls_ellipsoid(xx: array_t, yy: array_t, zz: array_t) -> array_t: # finds the
JT = J.transpose()
JTJ = np_.dot(JT, J)
InvJTJ = np_.linalg.inv(JTJ);
ABC = np_.dot(InvJTJ, np_.dot(JT, K))
try:
InvJTJ = np_.linalg.inv(JTJ);
ABC = np_.dot(InvJTJ, np_.dot(JT, K))
# Rearrange, move the 1 to the other side
# Ax^2 + By^2 + Cz^2 + Dxy + Exz + Fyz + Gx + Hy + Iz - 1 = 0
# or
# Ax^2 + By^2 + Cz^2 + Dxy + Exz + Fyz + Gx + Hy + Iz + J = 0
# where J = -1
ellipsoid_coef = np_.append(ABC, -1)
# Rearrange, move the 1 to the other side
# Ax^2 + By^2 + Cz^2 + Dxy + Exz + Fyz + Gx + Hy + Iz - 1 = 0
# or
# Ax^2 + By^2 + Cz^2 + Dxy + Exz + Fyz + Gx + Hy + Iz + J = 0
# where J = -1
ellipsoid_coef = np_.append(ABC, -1)
return (ellipsoid_coef)
return (ellipsoid_coef)
except:
print("Singular matrix, cannot find the best fitting ellipsoid.")
return (np_.zeros(9))
def polyToParams3D(ellipsoid_coef: array_t, printMe: bool = False) -> tuple:
......@@ -70,74 +75,78 @@ def polyToParams3D(ellipsoid_coef: array_t, printMe: bool = False) -> tuple:
if printMe:
print('\npolynomial\n', ellipsoid_coef)
Amat = np_.array(
[
[ellipsoid_coef[0], ellipsoid_coef[3] / 2.0, ellipsoid_coef[4] / 2.0, ellipsoid_coef[6] / 2.0],
[ellipsoid_coef[3] / 2.0, ellipsoid_coef[1], ellipsoid_coef[5] / 2.0, ellipsoid_coef[7] / 2.0],
[ellipsoid_coef[4] / 2.0, ellipsoid_coef[5] / 2.0, ellipsoid_coef[2], ellipsoid_coef[8] / 2.0],
[ellipsoid_coef[6] / 2.0, ellipsoid_coef[7] / 2.0, ellipsoid_coef[8] / 2.0, ellipsoid_coef[9]]
])
if printMe:
print('\nAlgebraic form of polynomial\n', Amat)
# See B.Bartoni, Preprint SMU-HEP-10-14 Multi-dimensional Ellipsoidal Fitting
# equation 20 for the following method for finding the center
A3 = Amat[0:3, 0:3]
A3inv = inv(A3)
ofs = ellipsoid_coef[6:9] / 2.0
center = -np_.dot(A3inv, ofs)
if printMe:
print('\nCenter at:', center)
# Center the ellipsoid at the origin
Tofs = np_.eye(4)
Tofs[3, 0:3] = center
R = np_.dot(Tofs, np_.dot(Amat, Tofs.T))
if printMe:
print('\nAlgebraic form translated to center\n', R, '\n')
R3 = R[0:3, 0:3]
s1 = -R[3, 3]
R3S = R3 / s1
(el, ec) = eig(R3S)
el = np_.abs(el)
# Sorting in descending order of the eigenvalues and eigenvectors
sorting_vec = np_.argsort(-el)
el = el[sorting_vec]
ec = ec[:, sorting_vec]
# Calculating cartesian axes
recip = 1.0 / el
axes = np_.sqrt(recip) # axes are in ascending order
if printMe:
print('\nAxes are\n', axes, '\n')
# Calculating the orientation
inverse = inv(ec) # inverse is actually the transpose here
if printMe:
print('\nRotation matrix\n', inverse)
# Calculating spherical axes
# # eigenvector 1
r1 = np_.sqrt(sum(axe**2 for axe in ec[:, 0]))
phi1 = np_.arctan2(ec[1, 0], ec[0, 0])
theta1 = np_.arccos(ec[2, 0] / r1)
spherical_axes1 = (r1, theta1, phi1)
# # eigenvector 2
r2 = np_.sqrt(sum(axe**2 for axe in ec[:, 1]))
phi2 = np_.arctan2(ec[1, 1], ec[0, 1])
theta2 = np_.arccos(ec[2, 1] / r2)
spherical_axes2 = (r2, theta2, phi2)
spherical_axes = (spherical_axes1, spherical_axes2)
if printMe:
print('\nAxes in spherical coord are\n', spherical_axes, '\n')
return center, axes, inverse, spherical_axes
if ellipsoid_coef == (np_.zeros(9)):
return "NaN", "NaN", "NaN", "NaN"
else:
Amat = np_.array(
[
[ellipsoid_coef[0], ellipsoid_coef[3] / 2.0, ellipsoid_coef[4] / 2.0, ellipsoid_coef[6] / 2.0],
[ellipsoid_coef[3] / 2.0, ellipsoid_coef[1], ellipsoid_coef[5] / 2.0, ellipsoid_coef[7] / 2.0],
[ellipsoid_coef[4] / 2.0, ellipsoid_coef[5] / 2.0, ellipsoid_coef[2], ellipsoid_coef[8] / 2.0],
[ellipsoid_coef[6] / 2.0, ellipsoid_coef[7] / 2.0, ellipsoid_coef[8] / 2.0, ellipsoid_coef[9]]
])
if printMe:
print('\nAlgebraic form of polynomial\n', Amat)
# See B.Bartoni, Preprint SMU-HEP-10-14 Multi-dimensional Ellipsoidal Fitting
# equation 20 for the following method for finding the center
A3 = Amat[0:3, 0:3]
A3inv = inv(A3)
ofs = ellipsoid_coef[6:9] / 2.0
center = -np_.dot(A3inv, ofs)
if printMe:
print('\nCenter at:', center)
# Center the ellipsoid at the origin
Tofs = np_.eye(4)
Tofs[3, 0:3] = center
R = np_.dot(Tofs, np_.dot(Amat, Tofs.T))
if printMe:
print('\nAlgebraic form translated to center\n', R, '\n')
R3 = R[0:3, 0:3]
s1 = -R[3, 3]
R3S = R3 / s1
(el, ec) = eig(R3S)
el = np_.abs(el)
# Sorting in descending order of the eigenvalues and eigenvectors
sorting_vec = np_.argsort(-el)
el = el[sorting_vec]
ec = ec[:, sorting_vec]
# Calculating cartesian axes
recip = 1.0 / el
axes = np_.sqrt(recip) # axes are in ascending order
if printMe:
print('\nAxes are\n', axes, '\n')
# Calculating the orientation
inverse = inv(ec) # inverse is actually the transpose here
if printMe:
print('\nRotation matrix\n', inverse)
# Calculating spherical axes
# # eigenvector 1
r1 = np_.sqrt(sum(axe**2 for axe in ec[:, 0]))
phi1 = np_.arctan2(ec[1, 0], ec[0, 0])
theta1 = np_.arccos(ec[2, 0] / r1)
spherical_axes1 = (r1, theta1, phi1)
# # eigenvector 2
r2 = np_.sqrt(sum(axe**2 for axe in ec[:, 1]))
phi2 = np_.arctan2(ec[1, 1], ec[0, 1])
theta2 = np_.arccos(ec[2, 1] / r2)
spherical_axes2 = (r2, theta2, phi2)
spherical_axes = (spherical_axes1, spherical_axes2)
if printMe:
print('\nAxes in spherical coord are\n', spherical_axes, '\n')
return center, axes, inverse, spherical_axes
def GetConvexHull3D(soma_sites: site_h) -> tuple:
......@@ -169,7 +178,12 @@ def FindBestFittingEllipsoid3D(soma: soma_t) -> tuple:
# fit ellipsoid on the convex hull
# # get ellipsoid polynomial coefficients
ellipsoid_coef = ls_ellipsoid(convex_hull[0], convex_hull[1], convex_hull[2])
# # get ellipsoid 3D parameters
center, axes, orientation, spherical_coor = polyToParams3D(ellipsoid_coef, False)
return ellipsoid_coef, center, axes, orientation, spherical_coor, convex_hull, volume_hull
if ellipsoid_coef == (np_.zeros(9)):
return ellipsoid_coef, "NaN", "NaN", "NaN", "NaN", "NaN", "NaN"
else:
# # get ellipsoid 3D parameters
center, axes, orientation, spherical_coor = polyToParams3D(ellipsoid_coef, False)
return ellipsoid_coef, center, axes, orientation, spherical_coor, convex_hull, volume_hull
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