def karcher_calc(beta, q, betamean, mu, basis, mode):
# Compute shooting vector from mu to q_i
w, d = cf.inverse_exp_coord(betamean, beta, mode)
# Project to tangent space of manifold to obtain v_i
if mode == 0:
v = w
else:
v = cf.project_tangent(w, q, basis)
return (v, d)
def karcher_calc(beta, q, betamean, mu, mode=0):
if mode == 1:
basis = cf.find_basis_normal(mu)
# Compute shooting vector from mu to q_i
w, d = cf.inverse_exp_coord(betamean, beta)
# Project to tangent space of manifold to obtain v_i
if mode == 0:
v = w
else:
v = cf.project_tangent(w, q, basis)
return(v, d)
def curve_karcher_cov(betamean, beta, mode='O'):
"""
This claculates the mean of a set of curves
:param betamean: numpy ndarray of shape (n, M) describing the mean curve
:param beta: numpy ndarray of shape (n, M, N) describing N curves
in R^M
:param mode: Open ('O') or closed curve ('C') (default 'O')
:rtype: tuple of numpy array
:return K: Covariance Matrix
"""
n, T, N = beta.shape
modes = ['O', 'C']
mode = [i for i, x in enumerate(modes) if x == mode]
if len(mode) == 0:
mode = 0
else:
mode = mode[0]
# Compute Karcher covariance of uniformly sampled mean
betamean = cf.resamplecurve(betamean, T)
mu = cf.curve_to_q(betamean)
if mode == 1:
mu = cf.project_curve(mu)
basis = cf.find_basis_normal(mu)
v = zeros((n, T, N))
for i in range(0, N):
beta1 = beta[:, :, i]
w, dist = cf.inverse_exp_coord(betamean, beta1)
# Project to the tangent sapce of manifold to obtain v_i
if mode == 0:
v[:, :, i] = w
else:
v[:, :, i] = cf.project_tangent(w, mu, basis)
K = zeros((2*T, 2*T))
for i in range(0, N):
w = v[:, :, i]
wtmp = w.reshape((T*n, 1), order='C')
K = K + wtmp.dot(wtmp.T)
K = K/(N-1)
return(K)
def curve_karcher_cov(betamean, beta, mode='O'):
"""
This claculates the mean of a set of curves
:param betamean: numpy ndarray of shape (n, M) describing the mean curve
:param beta: numpy ndarray of shape (n, M, N) describing N curves
in R^M
:param mode: Open ('O') or closed curve ('C') (default 'O')
:rtype: tuple of numpy array
:return K: Covariance Matrix
"""
n, T, N = beta.shape
modes = ['O', 'C']
mode = [i for i, x in enumerate(modes) if x == mode]
if len(mode) == 0:
mode = 0
else:
mode = mode[0]
# Compute Karcher covariance of uniformly sampled mean
betamean = cf.resamplecurve(betamean, T)
mu = cf.curve_to_q(betamean)
if mode == 1:
mu = cf.project_curve(mu)
basis = cf.find_basis_normal(mu)
v = zeros((n, T, N))
for i in range(0, N):
beta1 = beta[:, :, i]
w, dist = cf.inverse_exp_coord(betamean, beta1)
# Project to the tangent sapce of manifold to obtain v_i
if mode == 0:
v[:, :, i] = w
else:
v[:, :, i] = cf.project_tangent(w, mu, basis)
K = zeros((2*T, 2*T))
for i in range(0, N):
w = v[:, :, i]
wtmp = w.reshape((T*n, 1), order='C')
K = K + wtmp.dot(wtmp.T)
K = K/(N-1)
return(K)
