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# ----------------------------------------------------------------------------
# - Open3D: www.open3d.org -
# ----------------------------------------------------------------------------
# The MIT License (MIT)
#
# Copyright (c) 2018-2021 www.open3d.org
#
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in
# all copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
# IN THE SOFTWARE.
# ----------------------------------------------------------------------------
# examples/python/reconstruction_system/opencv_pose_estimation.py
# following code is tested with OpenCV 3.2.0 and Python2.7
# how to install opencv
# conda create --prefix py27opencv python=2.7
# source activate py27opencv
# conda install -c conda-forge opencv
# conda install -c conda-forge openblas (if openblas conflicts)
import numpy as np
import cv2
from matplotlib import pyplot as plt # for visualizing feature matching
import copy
def pose_estimation(source_rgbd_image, target_rgbd_image,
pinhole_camera_intrinsic, debug_draw_correspondences):
success = False
trans = np.identity(4)
# transform double array to unit8 array
color_cv_s = np.uint8(np.asarray(source_rgbd_image.color) * 255.0)
color_cv_t = np.uint8(np.asarray(target_rgbd_image.color) * 255.0)
orb = cv2.ORB_create(scaleFactor=1.2,
nlevels=8,
edgeThreshold=31,
firstLevel=0,
WTA_K=2,
scoreType=cv2.ORB_HARRIS_SCORE,
nfeatures=100,
patchSize=31) # to save time
[kp_s, des_s] = orb.detectAndCompute(color_cv_s, None)
[kp_t, des_t] = orb.detectAndCompute(color_cv_t, None)
if len(kp_s) == 0 or len(kp_t) == 0:
return success, trans
bf = cv2.BFMatcher(cv2.NORM_HAMMING, crossCheck=True)
matches = bf.match(des_s, des_t)
pts_s = []
pts_t = []
for match in matches:
pts_t.append(kp_t[match.trainIdx].pt)
pts_s.append(kp_s[match.queryIdx].pt)
pts_s = np.asarray(pts_s)
pts_t = np.asarray(pts_t)
# inlier points after initial BF matching
if debug_draw_correspondences:
draw_correspondences(np.asarray(source_rgbd_image.color),
np.asarray(target_rgbd_image.color), pts_s, pts_t,
np.ones(pts_s.shape[0]), "Initial BF matching")
focal_input = (pinhole_camera_intrinsic.intrinsic_matrix[0, 0] +
pinhole_camera_intrinsic.intrinsic_matrix[1, 1]) / 2.0
pp_x = pinhole_camera_intrinsic.intrinsic_matrix[0, 2]
pp_y = pinhole_camera_intrinsic.intrinsic_matrix[1, 2]
# Essential matrix is made for masking inliers
pts_s_int = np.int32(pts_s + 0.5)
pts_t_int = np.int32(pts_t + 0.5)
[E, mask] = cv2.findEssentialMat(pts_s_int,
pts_t_int,
focal=focal_input,
pp=(pp_x, pp_y),
method=cv2.RANSAC,
prob=0.999,
threshold=1.0)
if mask is None:
return success, trans
# inlier points after 5pt algorithm
if debug_draw_correspondences:
draw_correspondences(np.asarray(source_rgbd_image.color),
np.asarray(target_rgbd_image.color), pts_s, pts_t,
mask, "5-pt RANSAC")
# make 3D correspondences
depth_s = np.asarray(source_rgbd_image.depth)
depth_t = np.asarray(target_rgbd_image.depth)
pts_xyz_s = np.zeros([3, pts_s.shape[0]])
pts_xyz_t = np.zeros([3, pts_s.shape[0]])
cnt = 0
for i in range(pts_s.shape[0]):
if mask[i]:
xyz_s = get_xyz_from_pts(pts_s[i, :], depth_s, pp_x, pp_y,
focal_input)
pts_xyz_s[:, cnt] = xyz_s
xyz_t = get_xyz_from_pts(pts_t[i, :], depth_t, pp_x, pp_y,
focal_input)
pts_xyz_t[:, cnt] = xyz_t
cnt = cnt + 1
pts_xyz_s = pts_xyz_s[:, :cnt]
pts_xyz_t = pts_xyz_t[:, :cnt]
success, trans, inlier_id_vec = estimate_3D_transform_RANSAC(
pts_xyz_s, pts_xyz_t)
if debug_draw_correspondences:
pts_s_new = np.zeros(shape=(len(inlier_id_vec), 2))
pts_t_new = np.zeros(shape=(len(inlier_id_vec), 2))
mask = np.ones(len(inlier_id_vec))
cnt = 0
for i in inlier_id_vec:
u_s, v_s = get_uv_from_xyz(pts_xyz_s[0, i], pts_xyz_s[1, i],
pts_xyz_s[2, i], pp_x, pp_y, focal_input)
u_t, v_t = get_uv_from_xyz(pts_xyz_t[0, i], pts_xyz_t[1, i],
pts_xyz_t[2, i], pp_x, pp_y, focal_input)
pts_s_new[cnt, :] = [u_s, v_s]
pts_t_new[cnt, :] = [u_t, v_t]
cnt = cnt + 1
draw_correspondences(np.asarray(source_rgbd_image.color),
np.asarray(target_rgbd_image.color), pts_s_new,
pts_t_new, mask, "5-pt RANSAC + 3D Rigid RANSAC")
return success, trans
def draw_correspondences(img_s, img_t, pts_s, pts_t, mask, title):
ha, wa = img_s.shape[:2]
hb, wb = img_t.shape[:2]
total_width = wa + wb
new_img = np.zeros(shape=(ha, total_width))
new_img[:ha, :wa] = img_s
new_img[:hb, wa:wa + wb] = img_t
fig = plt.figure()
fig.canvas.set_window_title(title)
for i in range(pts_s.shape[0]):
if mask[i]:
sx = pts_s[i, 0]
sy = pts_s[i, 1]
tx = pts_t[i, 0] + wa
ty = pts_t[i, 1]
plt.plot([sx, tx], [sy, ty],
color=np.random.random(3) / 2 + 0.5,
lw=1.0)
plt.imshow(new_img)
plt.pause(0.5)
plt.close()
def estimate_3D_transform_RANSAC(pts_xyz_s, pts_xyz_t):
max_iter = 1000
max_distance = 0.05
n_sample = 5
n_points = pts_xyz_s.shape[1]
Transform_good = np.identity(4)
max_inlier = n_sample
inlier_vec_good = []
success = False
if n_points < n_sample:
return False, np.identity(4), []
for i in range(max_iter):
# sampling
rand_idx = np.random.randint(n_points, size=n_sample)
sample_xyz_s = pts_xyz_s[:, rand_idx]
sample_xyz_t = pts_xyz_t[:, rand_idx]
R_approx, t_approx = estimate_3D_transform(sample_xyz_s, sample_xyz_t)
# evaluation
diff_mat = pts_xyz_t - (np.matmul(R_approx, pts_xyz_s) +
np.tile(t_approx, [1, n_points]))
diff = [np.linalg.norm(diff_mat[:, i]) for i in range(n_points)]
n_inlier = len([1 for diff_iter in diff if diff_iter < max_distance])
# note: diag(R_approx) > 0 prevents ankward transformation between
# RGBD pair of relatively small amount of baseline.
if (n_inlier > max_inlier) and (np.linalg.det(R_approx) != 0.0) and \
(R_approx[0,0] > 0 and R_approx[1,1] > 0 and R_approx[2,2] > 0):
Transform_good[:3, :3] = R_approx
Transform_good[:3, 3] = [t_approx[0], t_approx[1], t_approx[2]]
max_inlier = n_inlier
inlier_vec = [id_iter for diff_iter, id_iter \
in zip(diff, range(n_points)) \
if diff_iter < max_distance]
inlier_vec_good = inlier_vec
success = True
return success, Transform_good, inlier_vec_good
# singular value decomposition approach
# based on the description in the sec 3.1.2 in
# http://graphics.stanford.edu/~smr/ICP/comparison/eggert_comparison_mva97.pdf
def estimate_3D_transform(input_xyz_s, input_xyz_t):
# compute H
xyz_s = copy.copy(input_xyz_s)
xyz_t = copy.copy(input_xyz_t)
n_points = xyz_s.shape[1]
mean_s = np.mean(xyz_s, axis=1)
mean_t = np.mean(xyz_t, axis=1)
mean_s.shape = (3, 1)
mean_t.shape = (3, 1)
xyz_diff_s = xyz_s - np.tile(mean_s, [1, n_points])
xyz_diff_t = xyz_t - np.tile(mean_t, [1, n_points])
H = np.matmul(xyz_diff_s, xyz_diff_t.transpose())
# solve system
U, s, V = np.linalg.svd(H)
R_approx = np.matmul(V.transpose(), U.transpose())
if np.linalg.det(R_approx) < 0.0:
det = np.linalg.det(np.matmul(U, V))
D = np.identity(3)
D[2, 2] = det
R_approx = np.matmul(U, np.matmul(D, V))
t_approx = mean_t - np.matmul(R_approx, mean_s)
return R_approx, t_approx
def get_xyz_from_pts(pts_row, depth, px, py, focal):
u = pts_row[0]
v = pts_row[1]
u0 = int(u)
v0 = int(v)
height = depth.shape[0]
width = depth.shape[1]
# bilinear depth interpolation
if u0 > 0 and u0 < width - 1 and v0 > 0 and v0 < height - 1:
up = pts_row[0] - u0
vp = pts_row[1] - v0
d0 = depth[v0, u0]
d1 = depth[v0, u0 + 1]
d2 = depth[v0 + 1, u0]
d3 = depth[v0 + 1, u0 + 1]
d = (1 - vp) * (d1 * up + d0 * (1 - up)) + vp * (d3 * up + d2 *
(1 - up))
return get_xyz_from_uv(u, v, d, px, py, focal)
else:
return [0, 0, 0]
def get_xyz_from_uv(u, v, d, px, py, focal):
if focal != 0:
x = (u - px) / focal * d
y = (v - py) / focal * d
else:
x = 0
y = 0
return np.array([x, y, d]).transpose()
def get_uv_from_xyz(x, y, z, px, py, focal):
if z != 0:
u = focal * x / z + px
v = focal * y / z + py
else:
u = 0
v = 0
return u, v
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