# Applying optimal re-parameterization to the second curve
beta2n = fs.group_action_by_gamma_coord(beta2, gamI)
q2n = fs.curve_to_q(beta2n)
if rotation:
beta2n, O2, tau = fs.find_rotation_and_seed_coord(beta1, beta2n)
centroid2 = fs.calculatecentroid(beta2n)
beta2n = beta2n - np.tile(centroid2, [T, 1]).T
q2n = fs.curve_to_q(beta2n)
O = O1.dot(O2)
else:
q2n = q2
O = O1
# Forming geodesic between the registered curves
dist = np.arccos(fs.innerprod_q(q1, q2n))
if returnpath:
PsiQ = np.zeros((n, T, k))
PsiX = PsiQ
for tau in range(0, k):
s = dist * tau / (k - 1)
PsiQ[:, :,
tau] = (np.sin(dist - s) * q1 + np.sin(s) * q2n) / np.sin(dist)
PsiX[:, :, tau] = fs.q_to_curve(PsiQ[:, :, tau])
path = PsiQ
else:
path = 0
if Disp_registration_between_curves:
centroid1 = fs.calculatecentroid(beta1)
eps = np.finfo(np.double).eps
gam = np.linspace(0, 1, TT)
psi = np.sqrt(np.abs(np.gradient(gam, binsize)) + eps)
gam_old = gam
psi_old = psi
itr = 0
max_val = np.zeros(max_itr+1)
while itr <= max_itr:
A = np.zeros(m)
Adiff = np.zeros((TT, m))
qtmp = np.interp((time[-1] - time[0]) * gam_old + time[0], time, q)
qtmp_diff = np.interp((time[-1] - time[0]) * gam_old + time[0],
time, np.gradient(q, binsize))
for i in range(0, m):
A[i] = fs.innerprod_q(time, qtmp * psi_old, beta[:, i])
tmp1 = trapz(qtmp_diff * psi_old * beta[:, i], time)
tmp2 = cumtrapz(qtmp_diff * psi_old * beta[:, i], time, initial=0)
tmp = tmp1 - tmp2
Adiff[:, i] = 2 * psi_old * tmp + qtmp * beta[:, i]
tmp1 = np.sum(np.exp(alpha + A))
tmp2 = np.sum(np.exp(alpha + A) * Adiff, axis=1)
h = np.sum(y * Adiff, axis=1) - (tmp2 / tmp1)
tmp = fs.innerprod_q(time, h, psi_old)
vec = h - tmp*psi_old
vecnorm = norm(vec) * binsize
costmp = np.cos(delta * vecnorm) * psi_old
sintmp = np.sin(delta * vecnorm) * (vec / vecnorm)
psi_new = costmp + sintmp
# Applying optimal re-parameterization to the second curve
beta2n = fs.group_action_by_gamma_coord(beta2, gamI)
q2n = fs.curve_to_q(beta2n)
if rotation:
beta2n, O2, tau = fs.find_rotation_and_seed_coord(beta1, beta2n)
centroid2 = fs.calculatecentroid(beta2n)
beta2n = beta2n - np.tile(centroid2, [T, 1]).T
q2n = fs.curve_to_q(beta2n)
O = O1.dot(O2)
else:
q2n = q2
O = O1
# Forming geodesic between the registered curves
dist = np.arccos(fs.innerprod_q(q1, q2n))
if returnpath:
PsiQ = np.zeros((n, T, k))
PsiX = PsiQ
for tau in range(0, k):
s = dist * tau / (k - 1)
PsiQ[:, :, tau] = (np.sin(dist-s)*q1+np.sin(s)*q2n)/np.sin(dist)
PsiX[:, :, tau] = fs.q_to_curve(PsiQ[:, :, tau])
path = PsiQ
else:
path = 0
if Disp_registration_between_curves:
centroid1 = fs.calculatecentroid(beta1)
beta1 = beta1 - np.tile(centroid1, [T, 1]).T
eps = np.finfo(np.double).eps
gam = np.linspace(0, 1, TT)
psi = np.sqrt(np.abs(np.gradient(gam, binsize)) + eps)
gam_old = gam
psi_old = psi
itr = 0
max_val = np.zeros(max_itr + 1)
while itr <= max_itr:
A = np.zeros(m)
Adiff = np.zeros((TT, m))
qtmp = np.interp((time[-1] - time[0]) * gam_old + time[0], time, q)
qtmp_diff = np.interp((time[-1] - time[0]) * gam_old + time[0], time,
np.gradient(q, binsize))
for i in range(0, m):
A[i] = fs.innerprod_q(time, qtmp * psi_old, beta[:, i])
tmp1 = trapz(qtmp_diff * psi_old * beta[:, i], time)
tmp2 = cumtrapz(qtmp_diff * psi_old * beta[:, i], time, initial=0)
tmp = tmp1 - tmp2
Adiff[:, i] = 2 * psi_old * tmp + qtmp * beta[:, i]
tmp1 = np.sum(np.exp(alpha + A))
tmp2 = np.sum(np.exp(alpha + A) * Adiff, axis=1)
h = np.sum(y * Adiff, axis=1) - (tmp2 / tmp1)
tmp = fs.innerprod_q(time, h, psi_old)
vec = h - tmp * psi_old
vecnorm = norm(vec) * binsize
costmp = np.cos(delta * vecnorm) * psi_old
sintmp = np.sin(delta * vecnorm) * (vec / vecnorm)
psi_new = costmp + sintmp
