def fit_ThinPlateSpline_corr(x_nd, y_md, corr_nm, l, rot_reg, x_weights = None):
wt_n = corr_nm.sum(axis=1)
if np.any(wt_n == 0):
inlier = wt_n != 0
x_nd = x_nd[inlier,:]
wt_n = wt_n[inlier,:]
x_weights = x_weights[inlier]
xtarg_nd = (corr_nm[inlier,:]/wt_n[:,None]).dot(y_md)
else:
xtarg_nd = (corr_nm/wt_n[:,None]).dot(y_md)
if x_weights is not None:
if x_weights.ndim > 1:
wt_n=wt_n[:,None]*x_weights
else:
wt_n=wt_n*x_weights
f = fit_ThinPlateSpline(x_nd, xtarg_nd, bend_coef = l, wt_n = wt_n, rot_coef = rot_reg)
f._bend_coef = l
f._wt_n = wt_n
f._rot_coef = rot_reg
f._cost = tps.tps_cost(f.lin_ag, f.trans_g, f.w_ng, f.x_na, xtarg_nd, l, wt_n=wt_n)/wt_n.mean()
return f
def rpm_em_step_stat(x_nd, y_md, l, T, rot_reg, prev_f, vis_cost_xy = None, outlierprior = 1e-2, normalize_iter = 20, T0 = .04, user_data=None):
"""
Statiscal interpretation of the RPM EM step
"""
n,d = x_nd.shape
m,_ = y_md.shape
xwarped_nd = prev_f.transform_points(x_nd)
dist_nm = ssd.cdist(xwarped_nd, y_md, 'sqeuclidean')
outlier_dist_1m = ssd.cdist(xwarped_nd.mean(axis=0)[None,:], y_md, 'sqeuclidean')
outlier_dist_n1 = ssd.cdist(xwarped_nd, y_md.mean(axis=0)[None,:], 'sqeuclidean')
# Note: proportionality constants within a column can be ignored since Sinkorn balancing normalizes the columns first
prob_nm = np.exp( -(dist_nm / (2*T)) + (outlier_dist_1m / (2*T0)) ) / np.sqrt(T) # divide by np.exp( outlier_dist_1m / (2*T0) ) to prevent prob collapsing to zero
if vis_cost_xy != None:
pi = np.exp( -vis_cost_xy )
pi /= pi.sum(axis=0)[None,:] # normalize along columns; these are proper probabilities over j = 1,...,N
prob_nm *= (1. - outlierprior) * pi
else:
prob_nm *= (1. - outlierprior) / float(n)
outlier_prob_1m = outlierprior * np.ones((1,m)) / np.sqrt(T0) # divide by np.exp( outlier_dist_1m / (2*T0) )
outlier_prob_n1 = np.exp( -outlier_dist_n1 / (2*T0) ) / np.sqrt(T0)
prob_NM = np.empty((n+1, m+1), 'f4')
prob_NM[:n, :m] = prob_nm
prob_NM[:n, m][:,None] = outlier_prob_n1
prob_NM[n, :m][None,:] = outlier_prob_1m
prob_NM[n, m] = 0
r_N, c_M = sinkhorn_balance_coeffs(prob_NM, normalize_iter)
prob_NM *= r_N[:,None]
prob_NM *= c_M[None,:]
# prob_NM needs to be row-normalized at this point
corr_nm = prob_NM[:n, :m]
wt_n = corr_nm.sum(axis=1)
# discard points that are outliers (i.e. their total correspondence is smaller than 1e-2)
inlier = wt_n > 1e-2
if np.any(~inlier):
x_nd = x_nd[inlier,:]
wt_n = wt_n[inlier,:]
xtarg_nd = (corr_nm[inlier,:]/wt_n[:,None]).dot(y_md)
else:
xtarg_nd = (corr_nm/wt_n[:,None]).dot(y_md)
f = fit_ThinPlateSpline(x_nd, xtarg_nd, bend_coef = l, wt_n = wt_n, rot_coef = rot_reg)
f._bend_coef = l
f._rot_coef = rot_reg
f._cost = tps.tps_cost(f.lin_ag, f.trans_g, f.w_ng, f.x_na, xtarg_nd, l, wt_n=wt_n)/wt_n.mean()
return f, corr_nm