def get_tag_detections(im, cache_tag):
#
# Because of a bug in the tag detector, it doesn't seem
# to detect tags larger than a certain size. To work-around
# this limitation, we detect tags on two different image
# scales and use the one with more detections
#
assert len(im.shape) == 2
from skimage.transform import rescale as imrescale
im4 = imrescale(im, 1./4)
from skimage.util import img_as_ubyte
im = img_as_ubyte(im)
im4 = img_as_ubyte(im4)
from apriltag import AprilTagDetector, AprilTagDetection
detections1 = AprilTagDetector().detect(im)
detections4 = AprilTagDetector().detect(im4)
for d in detections4:
d.c[0] *= 4.
d.c[1] *= 4.
# note that everything other than the tag center is wrong
# in detections4
if len(detections4) > len(detections1):
return detections4
else:
return detections1
def process(filename):
#
# Conventions:
# a_i, b_i
# are variables in image space, units are pixels
# a_w, b_w
# are variables in world space, units are meters
#
print '\n========================================'
print ' File: ' + filename
print '========================================\n'
im = imread(filename)
im = rgb2gray(im)
im = (im * 255.).astype(np.uint8)
tag_mosaic = TagMosaic(0.0254)
detections = AprilTagDetector().detect(im)
print ' %d tags detected.' % len(detections)
#
# Sort detections by distance to center
#
c_i = np.array([im.shape[1], im.shape[0]]) / 2.
dist = lambda p_i: np.linalg.norm(p_i - c_i)
closer_to_center = lambda d1, d2: int(dist(d1.c) - dist(d2.c))
detections.sort(cmp=closer_to_center)
mosaic_pos = lambda det: tag_mosaic.get_position_meters(det.id)
det_i = np.array([ d.c for d in detections ])
det_w = np.array([ mosaic_pos(d) for d in detections ])
#
# To learn a weighted local homography, we find the weighting
# function parameters that minimize reprojection error across
# leave-one-out validation folds of the data. Since the
# homography is local at the center, we only use 9 nearest
# detections to the center
#
det_i9 = det_i[:9]
det_w9 = det_w[:9]
def local_homography_loocv_error(theta, args):
src, tgt = args
errs = [ local_homography_error(theta, src[t_ix], tgt[t_ix], src[v_ix], tgt[v_ix])
for t_ix, v_ix in LeaveOneOut(len(src)) ]
return np.mean(errs)
def learn_homography_i2w():
result = minimize( local_homography_loocv_error,
x0=[ 50, 1, 1e-3 ],
args=[ det_i9, det_w9 ],
method='Powell',
options={'ftol': 1e-3} )
print '\nHomography: i->w'
print '------------------'
print ' params:', result.x
print ' rmse: %.6f' % sqrt(result.fun)
print '\n Optimization detail:'
print ' ' + str(result).replace('\n', '\n ')
H = create_local_homography_object(*result.x)
for i, w in zip(det_i9, det_w9):
H.add_correspondence(i, w)
return H
def learn_homography_w2i():
result = minimize( local_homography_loocv_error,
x0=[ 0.0254, 1, 1e-3 ],
method='Powell',
args=[ det_w9, det_i9 ],
options={'ftol': 1e-3} )
print '\nHomography: w->i'
print '------------------'
print ' params:', result.x
print ' rmse: %.6f' % sqrt(result.fun)
print '\n Optimization detail:'
print ' ' + str(result).replace('\n', '\n ')
H = create_local_homography_object(*result.x)
for w, i in zip(det_w9, det_i9):
H.add_correspondence(w, i)
return H
#
# We assume that the distortion is zero at the center of
# the image and we are interesting in the word to image
# homography at the center of the image. However, we don't
# know the center of the image in world coordinates.
# So we follow a procedure as explained below:
#
# First, we learn a homography from image to world
# Next, we find where the image center `c_i` maps to in
# world coordinates (`c_w`). Finally, we find the local
# homography `LH0` from world to image at `c_w`
#
H_iw = learn_homography_i2w()
c_i = np.array([im.shape[1], im.shape[0]]) / 2.
c_w = H_iw.map(c_i)[:2]
H_wi = learn_homography_w2i()
LH0 = H_wi.get_homography_at(c_w)
print '\nHomography at center'
print '----------------------'
print ' c_w =', c_w
print ' c_i =', c_i
print 'LH0 * c_w =', H_wi.map(c_w)
#
# Obtain distortion estimate
# detected + undistortion = mapped
# (or) undistortion = mapped - detected
#
def homogeneous_coords(arr):
return np.hstack([ arr, np.ones((len(arr), 1)) ])
mapped_i = LH0.dot(homogeneous_coords(det_w).T).T
mapped_i = np.array([ p / p[2] for p in mapped_i ])
mapped_i = mapped_i[:,:2]
undistortion = mapped_i - det_i # image + undistortion = mapped
max_distortion = np.max([np.linalg.norm(u) for u in undistortion])
print '\nMaximum distortion is %.2f pixels' % max_distortion
#
# Fit non-parametric model to the observations
#
model = GPModel(det_i, undistortion)
print '\nGP Hyper-parameters'
print '---------------------'
print ' x: ', model._gp_x._covf.theta
print ' log-likelihood: %.4f' % model._gp_x.model_evidence()
print ' y: ', model._gp_y._covf.theta
print ' log-likelihood: %.4f' % model._gp_y.model_evidence()
print ''
print ' Optimization detail:'
print ' [ x ]'
print ' ' + str(model._gp_x.fit_result).replace('\n', '\n ')
print ' [ y ]'
print ' ' + str(model._gp_y.fit_result).replace('\n', '\n ')
#
# Visualization
#
from skimage.filters import scharr
from matplotlib import pyplot as plt
plt.style.use('ggplot')
plt.figure(figsize=(16,10))
#__1__
plt.subplot(221)
plt.title(filename.split('/')[-1])
plt.imshow(im, cmap='gray')
plt.plot(det_i[:,0], det_i[:,1], 'o')
for i, d in enumerate(detections):
plt.text(d.c[0], d.c[1], str(i),
fontsize=8, color='white', bbox=dict(facecolor='maroon', alpha=0.75))
plt.grid()
plt.axis('equal')
#__2__
plt.subplot(222)
plt.title('Non-linear Homography')
if False:
plt.imshow(1.-scharr(im), cmap='bone', interpolation='gaussian')
from collections import defaultdict
row_groups = defaultdict(list)
col_groups = defaultdict(list)
for d in detections:
row, col = tag_mosaic.get_row(d.id), tag_mosaic.get_col(d.id)
row_groups[row] += [ d.id ]
col_groups[col] += [ d.id ]
for k, v in row_groups.iteritems():
a = tag_mosaic.get_position_meters(np.min(v))
b = tag_mosaic.get_position_meters(np.max(v))
x_coords = np.linspace(a[0], b[0], 100)
points = np.array([ H_wi.map([x, a[1]]) for x in x_coords ])
plt.plot(points[:,0], points[:,1], '-',color='#CF4457', linewidth=2)
for k, v in col_groups.iteritems():
a = tag_mosaic.get_position_meters(np.min(v))
b = tag_mosaic.get_position_meters(np.max(v))
y_coords = np.linspace(a[1], b[1], 100)
points = np.array([ H_wi.map([a[0], y]) for y in y_coords ])
plt.plot(points[:,0], points[:,1], '-',color='#CF4457', linewidth=2)
plt.plot(det_i[:,0], det_i[:,1], 'kx')
plt.grid()
plt.axis('equal')
#__3__
plt.subplot(223)
plt.title('Qualitative Estimates')
for i, d in enumerate(detections):
plt.text(d.c[0], d.c[1], str(i), fontsize=8, color='#999999')
X, Y = det_i[:,0], det_i[:,1]
U, V = undistortion[:,0], undistortion[:,1]
plt.quiver(X, Y, U, -V, units='dots')
# plt.quiver(X, Y, U, -V, angles='xy', scale_units='xy', scale=1) # plot exact
plt.text( 0.5, 0, 'max observed distortion: %.2f px' % max_distortion, color='#CF4457', fontsize=10,
horizontalalignment='center', verticalalignment='bottom', transform=plt.gca().transAxes)
plt.gca().invert_yaxis()
plt.axis('equal')
#__4__
plt.subplot(224)
plt.title('Qualitative Undistortion')
H, W = im.shape
grid = np.array([[x, y] for y in xrange(0, H, 80) for x in xrange(0, W, 80)])
predicted = model.predict(grid)
X, Y = grid[:,0], grid[:,1]
U, V = predicted[:,0], predicted[:,1]
plt.quiver(X, Y, U, -V, units='dots')
#plt.quiver(X, Y, U, -V, angles='xy', scale_units='xy', scale=1)) # plot exact
plt.gca().invert_yaxis()
plt.axis('equal')
plt.tight_layout()
plt.gcf().patch.set_facecolor('#dddddd')
#plt.show()
plt.savefig(filename + '.svg', bbox_inches='tight')
def main():
im = imread(sys.argv[1])
im = img_as_ubyte(im)
tagdetector = AprilTagDetector()
print "\n".join([str((d.id, d.c)) for d in tagdetector.detect(im)])
def process(filename, options):
#
# Conventions:
# a_i, b_i
# are variables in image space, units are pixels
# a_w, b_w
# are variables in world space, units are meters
#
print('\n========================================')
print(' File: ' + filename)
print('========================================\n')
from skimage.io import imread
im = imread(filename)
from skimage.color import rgb2gray
im = rgb2gray(im)
im = img_as_ubyte(im)
from apriltag import AprilTagDetector
detections = AprilTagDetector().detect(im)
print(' %d tags detected.' % len(detections))
#
# Sort detections by distance to center
#
c_i = np.array([im.shape[1], im.shape[0]]) / 2.
dist = lambda p_i: np.linalg.norm(p_i - c_i)
closer_to_center = lambda d1, d2: int(dist(d1.c) - dist(d2.c))
import functools
detections.sort(key=functools.cmp_to_key(closer_to_center))
from apriltag.tag_mosaic import Tag36h11Mosaic
tag_mosaic = Tag36h11Mosaic(0.0254)
mosaic_pos = lambda det: tag_mosaic.get_position_meters(det.id)
det_i = np.array([d.c for d in detections])
det_w = np.array([mosaic_pos(d) for d in detections])
#
# To learn a weighted local homography, we find the weighting
# function parameters that minimize reprojection error across
# leave-one-out validation folds of the data. Since the
# homography is local at the center, we only use 36 nearest
# detections to the center
#
det_i36 = det_i[:36]
det_w36 = det_w[:36]
from sklearn.model_selection import LeaveOneOut
from scipy.optimize import minimize
def local_homography_loocv_error(theta, args):
src, tgt = args
errs = [
local_homography_error(theta, src[t_ix], tgt[t_ix], src[v_ix],
tgt[v_ix])
for t_ix, v_ix in LeaveOneOut().split(range(len(src)))
]
return np.mean(errs)
def learn_homography_i2w():
result = minimize(local_homography_loocv_error,
x0=[50, 1, 1e-3],
args=[det_i36, det_w36],
method='Powell',
options={'ftol': 1e-3})
print('\nHomography: i->w')
print('------------------')
print(' params:', result.x)
print(' rmse: %.6f' % sqrt(result.fun))
print('\n Optimization detail:')
print(' ' + str(result).replace('\n', '\n '))
H = create_local_homography_object(*result.x)
for i, w in zip(det_i36, det_w36):
H.add_correspondence(i, w)
return H
def learn_homography_w2i():
result = minimize(local_homography_loocv_error,
x0=[0.0254, 1, 1e-3],
method='Powell',
args=[det_w36, det_i36],
options={'ftol': 1e-3})
print('\nHomography: w->i')
print('------------------')
print(' params:', result.x)
print(' rmse: %.6f' % sqrt(result.fun))
print('\n Optimization detail:')
print(' ' + str(result).replace('\n', '\n '))
H = create_local_homography_object(*result.x)
for w, i in zip(det_w36, det_i36):
H.add_correspondence(w, i)
return H
#
# We assume that the distortion is zero at the center of
# the image and we are interested in the world to image
# homography at the center of the image. However, we don't
# know the center of the image in world coordinates.
# So we follow a procedure as explained below:
#
# First, we learn a homography from image to world
# Next, we find where the image center `c_i` maps to in
# world coordinates (`c_w`). Finally, we find the local
# homography `LH0` from world to image at `c_w`
#
H_iw = learn_homography_i2w()
c_i = np.array([im.shape[1], im.shape[0]]) / 2.
c_w = H_iw.map(c_i)[:2]
H_wi = learn_homography_w2i()
LH0 = H_wi.get_homography_at(c_w)
print('\nHomography at center')
print('----------------------')
print(' c_w =', c_w)
print(' c_i =', c_i)
print('LH0 * c_w =', H_wi.map(c_w))
#
# Obtain distortion estimate
# mapped + distortion = detected
# (or) distortion = detected - mapped
#
def homogeneous_coords(arr):
return np.hstack([arr, np.ones((len(arr), 1))])
subset_step = int(options.subset_step)
if subset_step == 1:
print('\nUsing all observed correspondences for training model ...')
else:
print(
'\nUsing every %d-th observed correspondence for training model ...'
% subset_step)
det_i = det_i[::subset_step]
det_w = det_w[::subset_step]
mapped_i = LH0.dot(homogeneous_coords(det_w).T).T
mapped_i = np.array([p / p[2] for p in mapped_i])
mapped_i = mapped_i[:, :2]
distortion = det_i - mapped_i # image + distortion = mapped
max_distortion = np.max([np.linalg.norm(u) for u in distortion])
print('\nMaximum observed distortion is %.2f pixels' % max_distortion)
#
# Fit non-parametric model to the observations
#
model = GPModel(mapped_i, distortion)
print('\nGP Hyper-parameters')
print('---------------------')
print(' x: ', model._gp_x._covf.theta)
print(' log-likelihood: %.4f' % model._gp_x.model_evidence())
print(' y: ', model._gp_y._covf.theta)
print(' log-likelihood: %.4f' % model._gp_y.model_evidence())
print('')
print(' Optimization detail:')
print(' [ x ]')
print(' ' + str(model._gp_x.fit_result).replace('\n', '\n '))
print(' [ y ]')
print(' ' + str(model._gp_y.fit_result).replace('\n', '\n '))
#
# Use the non-parametric model to compute the source map
# we compute the map in blocks to reduce our memory requirements
#
print('\nComputing source map')
print('----------------------')
H, W = im.shape
center = np.array([W / 2., H / 2.])
def scale_coords(xy):
return (xy - center) * float(options.output_scale) + center
source_map = np.zeros((2, H, W))
B = 50 # Block size is 50x50
for sy in range(0, H, B):
sys.stdout.write(' ')
for sx in range(0, W, B):
ty, tx = min(sy + B, H), min(sx + B, W)
dst_coords = np.array([[x, y] for y in range(sy, ty)
for x in range(sx, tx)])
dst_coords = scale_coords(dst_coords)
src_coords = dst_coords + model.predict(dst_coords)
source_map[1, sy:ty, sx:tx] = src_coords[:, 0].reshape(
(ty - sy, tx - sx))
source_map[0, sy:ty, sx:tx] = src_coords[:, 1].reshape(
(ty - sy, tx - sx))
sys.stdout.write('. ')
sys.stdout.flush()
sys.stdout.write('\n')
#
# output undistortion table if requested
#
if not options.no_write_table:
table_filename = filename + '.table'
print('\nWriting undistortion table to %s' % table_filename)
import struct
with open(table_filename, 'wb') as f:
f.write(struct.pack('<II', H, W))
for y in range(H):
for x in range(W):
f.write(struct.pack('<dd', *source_map[:, y, x]))
#
# undistorted image if requested
#
if not options.no_write_image:
import os.path
render_filename = os.path.splitext(filename)[0] + '.fixed.png'
print('\nRendering undistorted image: %s' % render_filename)
from skimage.transform import warp
im_fixed = img_as_ubyte(warp(im, source_map))
from skimage.io import imsave
imsave(render_filename, im_fixed)
def main():
im = imread(sys.argv[1])
im = img_as_ubyte(im)
tagdetector = AprilTagDetector()
print "\n".join([ str((d.id, d.c)) for d in tagdetector.detect(im) ])