def tps_rpm_bij(x_nd,
y_md,
fsolve,
gsolve,
n_iter=20,
reg_init=.1,
reg_final=.001,
rad_init=.1,
rad_final=.005,
rot_reg=1e-3,
outlierprior=1e-1,
outlierfrac=2e-1,
vis_cost_xy=None,
return_corr=False,
check_solver=False):
"""
tps-rpm algorithm mostly as described by chui and rangaran
reg_init/reg_final: regularization on curvature
rad_init/rad_final: radius for correspondence calculation (meters)
plotting: 0 means don't plot. integer n means plot every n iterations
"""
_, d = x_nd.shape
regs = np.around(loglinspace(reg_init, reg_final, n_iter),
BEND_COEF_DIGITS)
rads = loglinspace(rad_init, rad_final, n_iter)
f = ThinPlateSpline(d)
scale = (np.max(y_md, axis=0) - np.min(y_md, axis=0)) / (
np.max(x_nd, axis=0) - np.min(x_nd, axis=0))
f.lin_ag = np.diag(scale) # align the mins and max
f.trans_g = np.median(
y_md, axis=0) - np.median(x_nd, axis=0) * scale # align the medians
g = ThinPlateSpline(d)
g.lin_ag = np.diag(1. / scale)
g.trans_g = -np.diag(1. / scale).dot(f.trans_g)
# r_N = None
for i in xrange(n_iter):
xwarped_nd = f.transform_points(x_nd)
ywarped_md = g.transform_points(y_md)
fwddist_nm = ssd.cdist(xwarped_nd, y_md, 'euclidean')
invdist_nm = ssd.cdist(x_nd, ywarped_md, 'euclidean')
r = rads[i]
prob_nm = np.exp(-(fwddist_nm + invdist_nm) / (2 * r))
corr_nm, r_N, _ = balance_matrix(prob_nm, 10, outlierprior,
outlierfrac)
corr_nm += 1e-9
wt_n = corr_nm.sum(axis=1)
wt_m = corr_nm.sum(axis=0)
xtarg_nd = (corr_nm / wt_n[:, None]).dot(y_md)
ytarg_md = (corr_nm / wt_m[None, :]).T.dot(x_nd)
fsolve.solve(wt_n, xtarg_nd, regs[i], rot_reg, f)
gsolve.solve(wt_m, ytarg_md, regs[i], rot_reg, g)
if check_solver:
f_test = fit_ThinPlateSpline(x_nd,
xtarg_nd,
bend_coef=regs[i],
wt_n=wt_n,
rot_coef=rot_reg)
g_test = fit_ThinPlateSpline(y_md,
ytarg_md,
bend_coef=regs[i],
wt_n=wt_m,
rot_coef=rot_reg)
tol = 1e-4
assert np.allclose(f.trans_g, f_test.trans_g, atol=tol)
assert np.allclose(f.lin_ag, f_test.lin_ag, atol=tol)
assert np.allclose(f.w_ng, f_test.w_ng, atol=tol)
assert np.allclose(g.trans_g, g_test.trans_g, atol=tol)
assert np.allclose(g.lin_ag, g_test.lin_ag, atol=tol)
assert np.allclose(g.w_ng, g_test.w_ng, atol=tol)
f._cost = tps.tps_cost(
f.lin_ag, f.trans_g, f.w_ng, f.x_na, xtarg_nd, regs[i],
wt_n=wt_n) / wt_n.mean()
g._cost = tps.tps_cost(
g.lin_ag, g.trans_g, g.w_ng, g.x_na, ytarg_md, regs[i],
wt_n=wt_m) / wt_m.mean()
if return_corr:
return (f, g), corr_nm
return f, g
def test_batch_tps_rpm_bij(
src_ctx,
tgt_ctx,
T_init=1e-1,
T_final=5e-3,
outlierfrac=1e-2,
outlierprior=1e-1,
outliercutoff=0.5,
em_iter=EM_ITER_CHEAP,
test_ind=0,
):
from lfd.tpsopt.transformations import ThinPlateSpline, set_ThinPlateSpline
n_iter = len(src_ctx.bend_coefs)
T_vals = loglinspace(T_init, T_final, n_iter)
x_nd = src_ctx.pts[test_ind].get()[: src_ctx.dims[test_ind]]
y_md = tgt_ctx.pts[0].get()[: tgt_ctx.dims[0]]
(n, d) = x_nd.shape
(m, _) = y_md.shape
f = ThinPlateSpline(d)
g = ThinPlateSpline(d)
src_ctx.reset_tps_params()
tgt_ctx.reset_tps_params()
for i, b in enumerate(src_ctx.bend_coefs):
T = T_vals[i]
for _ in range(em_iter):
src_ctx.transform_points()
tgt_ctx.transform_points()
xwarped_nd = f.transform_points(x_nd)
ywarped_md = g.transform_points(y_md)
gpu_xw = src_ctx.pts_w[test_ind].get()[:n, :]
gpu_yw = tgt_ctx.pts_w[test_ind].get()[:m, :]
assert np.allclose(xwarped_nd, gpu_xw, atol=1e-5)
assert np.allclose(ywarped_md, gpu_yw, atol=1e-5)
xwarped_nd = gpu_xw
ywarped_md = gpu_yw
src_ctx.get_target_points(tgt_ctx, outlierprior, outlierfrac, outliercutoff, T)
fwddist_nm = ssd.cdist(xwarped_nd, y_md, "euclidean")
invdist_nm = ssd.cdist(x_nd, ywarped_md, "euclidean")
prob_nm = outlierprior * np.ones((n + 1, m + 1), np.float32)
prob_nm[:n, :m] = np.exp(-(fwddist_nm + invdist_nm) / float(2 * T))
prob_nm[n, m] = outlierfrac * np.sqrt(n * m)
gpu_corr = src_ctx.corr_rm[test_ind].get()
gpu_corr = gpu_corr.flatten()
gpu_corr = gpu_corr[: (n + 1) * (m + 1)].reshape(n + 1, m + 1).astype(np.float32)
assert np.allclose(prob_nm[:n, :m], gpu_corr[:n, :m], atol=1e-5)
save_prob_nm = np.array(prob_nm)
save_gpu_corr = np.array(gpu_corr)
prob_nm[:n, :m] = gpu_corr[:n, :m]
r_coefs = np.ones(n + 1, np.float32)
c_coefs = np.ones(m + 1, np.float32)
a_N = np.ones((n + 1), dtype=np.float32)
a_N[n] = m * outlierfrac
b_M = np.ones((m + 1), dtype=np.float32)
b_M[m] = n * outlierfrac
for norm_iter_i in range(DEFAULT_NORM_ITERS):
r_coefs = a_N / prob_nm.dot(c_coefs)
rn_c_coefs = c_coefs
c_coefs = b_M / r_coefs.dot(prob_nm)
gpu_r_coefs = src_ctx.r_coefs[test_ind].get()[: n + 1].reshape(n + 1)
gpu_c_coefs_cn = src_ctx.c_coefs_cn[test_ind].get()[: m + 1].reshape(m + 1)
gpu_c_coefs_rn = src_ctx.c_coefs_rn[test_ind].get()[: m + 1].reshape(m + 1)
r_diff = np.abs(r_coefs - gpu_r_coefs)
rn_diff = np.abs(rn_c_coefs - gpu_c_coefs_rn)
cn_diff = np.abs(c_coefs - gpu_c_coefs_cn)
assert np.allclose(r_coefs, gpu_r_coefs, atol=1e-5)
assert np.allclose(c_coefs, gpu_c_coefs_cn, atol=1e-5)
assert np.allclose(rn_c_coefs, gpu_c_coefs_rn, atol=1e-5)
prob_nm = prob_nm[:n, :m]
prob_nm *= gpu_r_coefs[:n, None]
rn_p_nm = prob_nm * gpu_c_coefs_rn[None, :m]
cn_p_nm = prob_nm * gpu_c_coefs_cn[None, :m]
wt_n = rn_p_nm.sum(axis=1)
gpu_corr_cm = src_ctx.corr_cm[test_ind].get().flatten()[: (n + 1) * (m + 1)]
gpu_corr_cm = gpu_corr_cm.reshape(m + 1, n + 1) ## b/c it is column major
assert np.allclose(wt_n, gpu_corr_cm[m, :n], atol=1e-4)
inlier = wt_n > outliercutoff
xtarg_nd = np.empty((n, DATA_DIM), np.float32)
xtarg_nd[inlier, :] = rn_p_nm.dot(y_md)[inlier, :]
xtarg_nd[~inlier, :] = xwarped_nd[~inlier, :]
wt_m = cn_p_nm.sum(axis=0)
assert np.allclose(wt_m, gpu_corr[n, :m], atol=1e-4)
inlier = wt_m > outliercutoff
ytarg_md = np.empty((m, DATA_DIM), np.float32)
ytarg_md[inlier, :] = cn_p_nm.T.dot(x_nd)[inlier, :]
ytarg_md[~inlier, :] = ywarped_md[~inlier, :]
xt_gpu = src_ctx.pts_t[test_ind].get()[:n, :]
yt_gpu = tgt_ctx.pts_t[test_ind].get()[:m, :]
assert np.allclose(xtarg_nd, xt_gpu, atol=1e-4)
assert np.allclose(ytarg_md, yt_gpu, atol=1e-4)
src_ctx.update_transform(b)
tgt_ctx.update_transform(b)
f_p_mat = src_ctx.proj_mats[b][test_ind].get()[: n + d + 1, :n]
f_o_mat = src_ctx.offset_mats[b][test_ind].get()[: n + d + 1]
b_p_mat = tgt_ctx.proj_mats[b][0].get()[: m + d + 1, :m]
b_o_mat = tgt_ctx.offset_mats[b][0].get()[: m + d + 1]
f_params = f_p_mat.dot(xtarg_nd) + f_o_mat
g_params = b_p_mat.dot(ytarg_md) + b_o_mat
gpu_fparams = src_ctx.tps_params[test_ind].get()[: n + d + 1]
gpu_gparams = tgt_ctx.tps_params[test_ind].get()[: m + d + 1]
assert np.allclose(f_params, gpu_fparams, atol=1e-4)
assert np.allclose(g_params, gpu_gparams, atol=1e-4)
set_ThinPlateSpline(f, x_nd, gpu_fparams)
set_ThinPlateSpline(g, y_md, gpu_gparams)
f._cost = tps.tps_cost(f.lin_ag, f.trans_g, f.w_ng, f.x_na, xtarg_nd, 1)
g._cost = tps.tps_cost(g.lin_ag, g.trans_g, g.w_ng, g.x_na, ytarg_md, 1)
gpu_cost = src_ctx.bidir_tps_cost(tgt_ctx)
cpu_cost = f._cost + g._cost
assert np.isclose(gpu_cost[test_ind], cpu_cost, atol=1e-4)
def tps_rpm_bij(x_nd, y_md, fsolve, gsolve,n_iter = 20, reg_init = .1, reg_final = .001, rad_init = .1,
rad_final = .005, rot_reg = 1e-3, outlierprior=1e-1, outlierfrac=2e-1, vis_cost_xy=None,
return_corr=False, check_solver=False):
"""
tps-rpm algorithm mostly as described by chui and rangaran
reg_init/reg_final: regularization on curvature
rad_init/rad_final: radius for correspondence calculation (meters)
plotting: 0 means don't plot. integer n means plot every n iterations
"""
_,d=x_nd.shape
regs = np.around(loglinspace(reg_init, reg_final, n_iter), BEND_COEF_DIGITS)
rads = loglinspace(rad_init, rad_final, n_iter)
f = ThinPlateSpline(d)
scale = (np.max(y_md,axis=0) - np.min(y_md,axis=0)) / (np.max(x_nd,axis=0) - np.min(x_nd,axis=0))
f.lin_ag = np.diag(scale) # align the mins and max
f.trans_g = np.median(y_md,axis=0) - np.median(x_nd,axis=0) * scale # align the medians
g = ThinPlateSpline(d)
g.lin_ag = np.diag(1./scale)
g.trans_g = -np.diag(1./scale).dot(f.trans_g)
# r_N = None
for i in xrange(n_iter):
xwarped_nd = f.transform_points(x_nd)
ywarped_md = g.transform_points(y_md)
fwddist_nm = ssd.cdist(xwarped_nd, y_md,'euclidean')
invdist_nm = ssd.cdist(x_nd, ywarped_md,'euclidean')
r = rads[i]
prob_nm = np.exp( -(fwddist_nm + invdist_nm) / (2*r) )
corr_nm, r_N, _ = balance_matrix(prob_nm, 10, outlierprior, outlierfrac)
corr_nm += 1e-9
wt_n = corr_nm.sum(axis=1)
wt_m = corr_nm.sum(axis=0)
xtarg_nd = (corr_nm/wt_n[:,None]).dot(y_md)
ytarg_md = (corr_nm/wt_m[None,:]).T.dot(x_nd)
fsolve.solve(wt_n, xtarg_nd, regs[i], rot_reg, f)
gsolve.solve(wt_m, ytarg_md, regs[i], rot_reg, g)
if check_solver:
f_test = fit_ThinPlateSpline(x_nd, xtarg_nd, bend_coef = regs[i], wt_n=wt_n, rot_coef = rot_reg)
g_test = fit_ThinPlateSpline(y_md, ytarg_md, bend_coef = regs[i], wt_n=wt_m, rot_coef = rot_reg)
tol = 1e-4
assert np.allclose(f.trans_g, f_test.trans_g, atol=tol)
assert np.allclose(f.lin_ag, f_test.lin_ag, atol=tol)
assert np.allclose(f.w_ng, f_test.w_ng, atol=tol)
assert np.allclose(g.trans_g, g_test.trans_g, atol=tol)
assert np.allclose(g.lin_ag, g_test.lin_ag, atol=tol)
assert np.allclose(g.w_ng, g_test.w_ng, atol=tol)
f._cost = tps.tps_cost(f.lin_ag, f.trans_g, f.w_ng, f.x_na, xtarg_nd, regs[i], wt_n=wt_n)/wt_n.mean()
g._cost = tps.tps_cost(g.lin_ag, g.trans_g, g.w_ng, g.x_na, ytarg_md, regs[i], wt_n=wt_m)/wt_m.mean()
if return_corr:
return (f, g), corr_nm
return f,g
