def solve_photometric(frame_reference,
frame_target,
max_its,
eps,
alpha_step,
use_ndc=False,
debug=False):
# init
# array for twist values x, y, z, roll, pitch, yaw
t_est = np.array([0, 0, 0], dtype=matrix_data_type).reshape((3, 1))
#R_est = np.array([[0.0, -1.0, 0],
# [1.0, 0.0, 0],
# [0, 0, 1]], dtype=matrix_data_type)
R_est = np.identity(3, dtype=matrix_data_type)
I_3 = np.identity(3, dtype=matrix_data_type)
(height, width) = frame_target.pixel_image.shape
N = height * width
position_vector_size = 3
twist_size = 6
stacked_obs_size = position_vector_size * N
homogeneous_se3_padding = Utils.homogenous_for_SE3()
# Step Factor
#alpha = 0.125
Gradient_step_manager = GradientStepManager.GradientStepManager(
alpha_start=alpha_step,
alpha_min=-0.7,
alpha_step=-0.01,
alpha_change_rate=0,
gradient_monitoring_window_start=3,
gradient_monitoring_window_size=0)
v_mean = -10000
v_mean_abs = -10000
it = -1
std = math.sqrt(0.4)
image_range_offset = 10
#depth_factor = 1.0
#depth_factor = 1000 # 0.001 # ZR300
SE_3_est = np.append(np.append(R_est, t_est, axis=1),
Utils.homogenous_for_SE3(),
axis=0)
SE_3_est_orig = np.append(np.append(R_est, t_est, axis=1),
Utils.homogenous_for_SE3(),
axis=0)
SE_3_est_last_valid = np.append(np.append(R_est, t_est, axis=1),
Utils.homogenous_for_SE3(),
axis=0)
generator_x = Lie.generator_x_3_4()
generator_y = Lie.generator_y_3_4()
generator_z = Lie.generator_z_3_4()
generator_roll = Lie.generator_roll_3_4()
generator_pitch = Lie.generator_pitch_3_4()
generator_yaw = Lie.generator_yaw_3_4()
X_back_projection = np.ones((4, N), Utils.matrix_data_type)
X_back_projection_last_valid = np.ones((4, N), Utils.matrix_data_type)
valid_measurements_reference = np.full(N, False)
valid_measurements_last = np.full(N, False)
valid_measurements_target = np.full(N, False)
valid_measurements = valid_measurements_reference
# Precompute back projection of pixels
GaussNewtonRoutines.back_project_image(width, height, image_range_offset,
frame_reference.camera,
frame_reference.pixel_depth,
X_back_projection,
valid_measurements, use_ndc)
if debug:
Plot3D.save_projection_of_back_projected(height, width,
frame_reference,
X_back_projection)
# Precompute the Jacobian of SE3 around the identity
J_lie = JacobianGenerator.get_jacobians_lie(generator_x,
generator_y,
generator_z,
generator_yaw,
generator_pitch,
generator_roll,
X_back_projection,
N,
stacked_obs_size,
coefficient=2.0)
# Precompute the Jacobian of the projection function
J_pi = JacobianGenerator.get_jacobian_camera_model(
frame_reference.camera.intrinsic, X_back_projection)
# count the number of true
#valid_measurements_total = np.logical_and(valid_measurements_reference,valid_measurements_target)
#number_of_valid_reference = np.sum(valid_measurements_reference)
#number_of_valid_total = np.sum(valid_measurements_total)
#number_of_valid_measurements = number_of_valid_reference
for it in range(0, max_its, 1):
start = time.time()
# accumulators
#TODO: investigate preallocate and clear in a for loop
J_v = np.zeros((twist_size, 1))
normal_matrix = np.zeros((twist_size, twist_size))
# Warp with the current SE3 estimate
Y_est = np.matmul(SE_3_est, X_back_projection)
v = np.zeros((N, 1), dtype=matrix_data_type, order='F')
target_index_projections = frame_target.camera.apply_perspective_pipeline(
Y_est)
v_sum = GaussNewtonRoutines.compute_residual(
width, height, target_index_projections, valid_measurements,
frame_target.pixel_image, frame_reference.pixel_image, v,
image_range_offset)
number_of_valid_measurements = np.sum(valid_measurements_reference)
Gradient_step_manager.save_previous_mean_error(v_mean_abs, it)
v_mean = v_sum / number_of_valid_measurements
valid_pixel_ratio = number_of_valid_measurements / N
#v_mean_abs = np.abs(v_mean)
#v_mean_abs = v_mean
# TODO put this in gradient step manager
#if valid_pixel_ratio< 0.8:
# print('Too many pixels are marked invalid')
# Gradient_step_manager.current_alpha+=0.1
# SE_3_est = SE_3_est_last_valid
# valid_measurements = valid_measurements_last
#else:
# SE_3_est_last_valid = SE_3_est
# valid_measurements_last = valid_measurements
Gradient_step_manager.track_gradient(v_mean_abs, it)
if v_mean < eps:
print('done, mean error:', v_mean)
break
Gradient_step_manager.analyze_gradient_history(it)
#Gradient_step_manager.analyze_gradient_history_instantly(v_mean_abs)
# See Kerl et al. ensures error decreases ( For pyramid levels )
#if(v_mean > Gradient_step_manager.last_error_mean_abs):
#continue
GaussNewtonRoutines.gauss_newton_step(width, height,
valid_measurements, J_pi, J_lie,
frame_target.grad_x,
frame_target.grad_y, v, J_v,
normal_matrix,
image_range_offset)
# TODO: Investigate faster inversion with QR
try:
pseudo_inv = linalg.inv(normal_matrix)
#(Q,R) = linalg.qr(normal_matrix)
#Q_t = np.transpose(Q)
#R_inv = linalg.inv(R)
#pseudo_inv = np.multiply(R_inv,Q_t)
except:
print('Cant invert')
return SE_3_est
w = np.matmul(pseudo_inv, J_v)
# Apply Step Factor
w = Gradient_step_manager.current_alpha * w
w_transpose = np.transpose(w)
w_x = Utils.skew_symmetric(w[3], w[4], w[5])
w_x_squared = np.matmul(w_x, w_x)
# closed form solution for exponential map
theta = math.sqrt(np.matmul(w_transpose, w))
theta_sqred = math.pow(theta, 2)
# TODO use Taylor Expansion when theta_sqred is small
try:
A = math.sin(theta) / theta
B = (1 - math.cos(theta)) / theta_sqred
C = (1 - A) / theta_sqred
except:
print('bad theta')
return SE_3_est
u = np.array([w[0], w[1], w[2]]).reshape((3, 1))
R_new = I_3 + np.multiply(A, w_x) + np.multiply(B, w_x_squared)
V = I_3 + np.multiply(B, w_x) + np.multiply(C, w_x_squared)
t_est += +np.matmul(V, u)
R_est = np.matmul(R_new, R_est)
SE_3_est = np.append(np.append(R_est, t_est, axis=1),
homogeneous_se3_padding,
axis=0)
end = time.time()
print('mean error:', v_mean, 'iteration: ', it, 'valid pixel ratio: ',
valid_pixel_ratio, 'runtime: ', end - start)
return SE_3_est
def solve_photometric(frame_reference,
frame_target,
threadLock,
pose_estimate_list,
max_its,
eps,
alpha_step,
gradient_monitoring_window_start,
image_range_offset_start,
max_depth,
twist_prior=None,
motion_cov_inv_in=None,
use_ndc=False,
use_robust=False,
track_pose_estimates=False,
use_motion_prior=False,
ackermann_pose_prior=None,
use_ackermann=False,
debug=False):
if track_pose_estimates and (threadLock == None
or pose_estimate_list == None):
raise RuntimeError(
'Visualization Flag is set, but no list and lock are supplied')
# init
# array for twist values x, y, z, roll, pitch, yaw
t_est = np.array([0, 0, 0], dtype=matrix_data_type).reshape((3, 1))
#R_est = np.array([[0.0, -1.0, 0],
# [1.0, 0.0, 0],
# [0, 0, 1]], dtype=matrix_data_type)
R_est = np.identity(3, dtype=matrix_data_type)
I_3 = np.identity(3, dtype=matrix_data_type)
I_4 = np.identity(4, dtype=matrix_data_type)
I_6 = np.identity(6, dtype=matrix_data_type)
zero_cov = np.zeros((6, 6), dtype=matrix_data_type)
#SE3_best = np.identity(4,dtype=matrix_data_type)
(height, width) = frame_target.pixel_image.shape
N = height * width
position_vector_size = 3
twist_size = 6
stacked_obs_size = position_vector_size * N
homogeneous_se3_padding = Utils.homogenous_for_SE3()
variance = -1
v_mean = maxsize
image_range_offset = image_range_offset_start
degrees_of_freedom = 5.0 # empirically derived: see paper
normal_matrix_ret = np.identity(6, dtype=Utils.matrix_data_type)
motion_cov_inv = motion_cov_inv_in
#motion_cov_inv = np.linalg.inv(motion_cov_inv_in)
w = np.zeros((twist_size, 1), dtype=Utils.matrix_data_type)
w_empty = np.zeros((twist_size, 1), dtype=Utils.matrix_data_type)
w_prev = np.zeros((twist_size, 1), dtype=Utils.matrix_data_type)
w_acc = np.zeros((twist_size, 1), dtype=Utils.matrix_data_type)
v_id = np.zeros((N, 1), dtype=matrix_data_type, order='F')
pseudo_inv = np.identity(twist_size, dtype=matrix_data_type)
not_better = False
valid_pixel_ratio = 1.0
motion_cov_inv_norm = Utils.norm_covariance_row(motion_cov_inv_in)
fx = frame_reference.camera.intrinsic.extract_fx()
fy = frame_reference.camera.intrinsic.extract_fy()
depth_factor = np.sign(fx)
#depth_factor = -np.sign(fx)
Gradient_step_manager = GradientStepManager.GradientStepManager(
alpha_start=alpha_step,
alpha_min=-0.7,
alpha_step=-0.01,
alpha_change_rate=0,
gradient_monitoring_window_start=gradient_monitoring_window_start,
gradient_monitoring_window_size=0)
SE_3_est = np.append(np.append(R_est, t_est, axis=1),
Utils.homogenous_for_SE3(),
axis=0)
SE_3_prev = np.append(np.append(R_est, t_est, axis=1),
Utils.homogenous_for_SE3(),
axis=0)
#SE_3_est_orig = np.append(np.append(R_est, t_est, axis=1), Utils.homogenous_for_SE3(), axis=0)
#SE_3_est_last_valid = np.append(np.append(R_est, t_est, axis=1), Utils.homogenous_for_SE3(), axis=0)
generator_x = Lie.generator_x_3_4()
#generator_x = Lie.generator_x_3_4_neg()
generator_y = Lie.generator_y_3_4()
#generator_y = Lie.generator_y_3_4_neg()
#generator_z = Lie.generator_z_3_4()
generator_z = Lie.generator_z_3_4_neg()
# Depth factor of -1.0 leads to inverted roll and pitch when displaying
# Why?: Generator defines the direction of increase (My thoughts)
generator_roll = Lie.generator_roll_3_4()
#generator_roll = Lie.generator_roll_3_4_neg()
#generator_pitch = Lie.generator_pitch_3_4()
generator_pitch = Lie.generator_pitch_3_4_neg()
generator_yaw = Lie.generator_yaw_3_4()
#generator_yaw = Lie.generator_yaw_3_4_neg()
X_back_projection = depth_factor * np.ones((4, N), Utils.matrix_data_type)
X_back_projection[3, :] = 1.0
#X_back_projection_last_valid = np.ones((4, N), Utils.matrix_data_type)
valid_measurements_reference = np.full(N, False)
valid_measurements_target = np.full(N, False)
#valid_measurements_last = np.full(N,False)
#valid_measurements_target = np.full(N,False)
valid_measurements = valid_measurements_reference
number_of_valid_measurements = N
#v = np.zeros((N, 1), dtype=matrix_data_type, order='F')
# Precompute back projection of pixels
GaussNewtonRoutines.back_project_image(
width, height, image_range_offset, frame_reference.camera,
frame_reference.pixel_depth, frame_target.pixel_depth,
X_back_projection, valid_measurements, valid_measurements_target,
use_ndc, depth_factor, max_depth)
count = np.sum(valid_measurements)
count_target = np.sum(valid_measurements_target)
z_rot = SE3.makeS03(0, 0, math.pi)
se3_rot = np.identity(4, dtype=matrix_data_type)
se3_rot[0:3, 0:3] = z_rot
#X_back_projection = np.matmul(se3_rot,X_back_projection)
if debug:
Plot3D.save_projection_of_back_projected(height, width,
frame_reference,
X_back_projection)
# Precompute the Jacobian of SE3 around the identity
J_lie = JacobianGenerator.get_jacobians_lie(generator_x,
generator_y,
generator_z,
generator_yaw,
generator_pitch,
generator_roll,
X_back_projection,
N,
stacked_obs_size,
coefficient=1.0)
# Precompute the Jacobian of the projection function
J_pi = JacobianGenerator.get_jacobian_camera_model(
frame_reference.camera.intrinsic, X_back_projection)
# count the number of true
#valid_measurements_total = np.logical_and(valid_measurements_reference,valid_measurements_target)
#number_of_valid_reference = np.sum(valid_measurements_reference)
#number_of_valid_total = np.sum(valid_measurements_total)
#number_of_valid_measurements = number_of_valid_reference
#target_index_projections_id = frame_target.camera.apply_perspective_pipeline(I_4)
target_index_projections = frame_target.camera.apply_perspective_pipeline(
X_back_projection, use_ndc, width, height)
GaussNewtonRoutines.compute_residual(
width, height, target_index_projections, valid_measurements,
valid_measurements_target, frame_target.pixel_image,
frame_reference.pixel_image, frame_target.pixel_depth,
frame_reference.pixel_depth, v_id, image_range_offset)
v = np.copy(v_id)
W = np.ones((1, N), dtype=matrix_data_type, order='F')
for it in range(0, max_its, 1):
start = time.time()
# accumulators
#TODO: investigate preallocate and clear in a for loop
g = np.zeros((twist_size, 1))
normal_matrix = np.identity(twist_size, dtype=matrix_data_type)
# TODO investigate performance impact
if track_pose_estimates:
threadLock.acquire()
pose_estimate_list.append(SE_3_est)
threadLock.release()
#v_diff = math.fabs(Gradient_step_manager.last_error_mean_abs - v_mean)
#v_diff = Gradient_step_manager.last_error_mean_abs - v_mean
#Gradient_step_manager.track_gradient(v_mean,it)
# TODO investigate absolute error threshold aswel?
#if ((v_diff <= eps)) and Gradient_step_manager.check_iteration(it) :
# print('done, mean error:', v_mean, 'diff: ', v_diff, 'pixel ratio:', valid_pixel_ratio)
# break
# no if statement means solver 2
#if v_mean <= Gradient_step_manager.last_error_mean_abs:
not_better = False
prior_empty = False
if twist_prior[0] == 0 and twist_prior[1] == 0 and twist_prior[2] == 0 and twist_prior[3] == 0 and \
twist_prior[4] == 0 and twist_prior[5] == 0:
prior_empty = True
if use_motion_prior:
converged = GaussNewtonRoutines.gauss_newton_step_motion_prior(
width, height, valid_measurements, valid_measurements_target,
W, J_pi, J_lie, frame_target.grad_x, frame_target.grad_y, v, g,
normal_matrix, motion_cov_inv, twist_prior, w,
image_range_offset)
else:
converged = GaussNewtonRoutines.gauss_newton_step(
width, height, valid_measurements, valid_measurements_target,
W, J_pi, J_lie, frame_target.grad_x, frame_target.grad_y, v, g,
normal_matrix, image_range_offset)
normal_matrix_ret = normal_matrix
#try:
# pseudo_inv = linalg.inv(normal_matrix)
#except:
# print('Cant invert')
# return SE_3_est
#w_new = np.matmul(pseudo_inv, g)
try:
w_new = linalg.solve(normal_matrix, g)
except:
print('Cant solve')
return SE_3_est
# initial step with empty motion prior seems to be quite large
#if use_motion_prior and prior_empty:
# w_new = np.multiply(Gradient_step_manager.current_alpha/2.0, w_new)
#else:
w_new = np.multiply(Gradient_step_manager.current_alpha, w_new)
# For using ackermann motion
if use_ackermann:
# V1
# inc = ackermann_pose_prior - w
# w_new += np.matmul(motion_cov_inv,inc)
# w_new += inc
# V2
#factor = 0.1*Gradient_step_manager.current_alpha
factor = 0.1
#factor = math.pow(Gradient_step_manager.current_alpha,it)
# ack_prior = np.multiply(Gradient_step_manager.current_alpha,ackermann_pose_prior)
ack_prior = ackermann_pose_prior
w_new += Lie.lie_ackermann_correction(factor, motion_cov_inv,
ack_prior, w, twist_size)
#else:
# not_better = True
# w_new = w_empty
R_cur, t_cur = Lie.exp(w, twist_size)
R_new, t_new = Lie.exp(w_new, twist_size)
# C_new . C_cur
#t_est = np.add(np.matmul(R_new, t_cur), t_new)
#R_est = np.matmul(R_new, R_cur)
# C_Cur . C_new
t_est = np.add(np.matmul(R_cur, t_new), t_cur)
R_est = np.matmul(R_cur, R_new)
w = Lie.ln(R_est, t_est, twist_size)
#SE_3_current = np.append(np.append(R_cur, t_cur, axis=1), homogeneous_se3_padding, axis=0)
SE_3_est = np.append(np.append(R_est, t_est, axis=1),
homogeneous_se3_padding,
axis=0)
#debug_list = [i for i, x in enumerate(valid_measurements) if x]
Y_est = np.matmul(SE_3_est, X_back_projection)
target_index_projections = frame_target.camera.apply_perspective_pipeline(
Y_est, use_ndc, width, height)
#target_index_projections[2,:] -= depth_factor*1
v = GaussNewtonRoutines.compute_residual(
width, height, target_index_projections, valid_measurements,
valid_measurements_target, frame_target.pixel_image,
frame_reference.pixel_image, frame_target.pixel_depth,
frame_reference.pixel_depth, v, image_range_offset)
number_of_valid_measurements = np.sum(valid_measurements)
valid_pixel_ratio = number_of_valid_measurements / N
if number_of_valid_measurements <= 0 and Gradient_step_manager.check_iteration(
it):
print('pixel ratio break')
print('done, mean error:', v_mean, 'diff: ', v_diff,
'pixel ratio:', valid_pixel_ratio)
#SE_3_est = SE3_best
break
if use_robust:
variance = GaussNewtonRoutines.compute_t_dist_variance(
v,
degrees_of_freedom,
N,
valid_measurements,
valid_measurements_target,
number_of_valid_measurements,
variance_min=1000,
eps=0.001)
if variance > 0.0:
# clear old weights
for i in range(0, N):
W[0, i] = 1
GaussNewtonRoutines.generate_weight_matrix(
W, v, variance, degrees_of_freedom, N)
v_weighted = np.copy(v)
GaussNewtonRoutines.multiply_v_by_diagonal_matrix(
W, v_weighted, N, valid_measurements)
v_sum = np.matmul(np.transpose(v), v_weighted)[0][0]
end = time.time()
#if v_mean < Gradient_step_manager.last_error_mean_abs:
# SE3_best = np.copy(SE_3_est)
#if not not_better: # solver 6
Gradient_step_manager.save_previous_mean_error(v_mean)
if number_of_valid_measurements > 0:
v_mean = v_sum / number_of_valid_measurements
else:
v_mean = maxsize
v_diff = math.fabs(Gradient_step_manager.last_error_mean_abs - v_mean)
print('mean error:', v_mean, 'error diff: ', v_diff, 'iteration: ', it,
'valid pixel ratio: ', valid_pixel_ratio, 'runtime: ',
end - start, 'variance: ', variance)
#v_diff = Gradient_step_manager.last_error_mean_abs - v_mean
#Gradient_step_manager.track_gradient(v_mean,it)
# TODO investigate absolute error threshold aswel?
if ((v_diff <= eps)) and Gradient_step_manager.check_iteration(it):
print('done, mean error:', v_mean, 'diff: ', v_diff,
'pixel ratio:', valid_pixel_ratio)
break
motion_cov_inv = normal_matrix_ret
return SE_3_est, w, motion_cov_inv