def lstsq_filter(x1, y1, x2, y2, psi=200, order=2, **kwargs):
''' Remove vectors that don't fit the model x1 = f(x2, y2)^n
Fit the model x1 = f(x2, y2)^n using least squares method
Simulate x1 using the model
Compare actual and simulated x1 and remove points where error is too high
Parameters
----------
x1, y1, x2, y2 : coordinates of start and end of displacement [pixels]
psi : threshold error between actual and simulated x1 [pixels]
Returns
-------
x1 : 1D vector - filtered source X coordinates on img1, pix
y1 : 1D vector - filtered source Y coordinates on img1, pix
x2 : 1D vector - filtered destination X coordinates on img2, pix
y2 : 1D vector - filtered destination Y coordinates on img2, pix
'''
if len(x1) == 0:
return map(np.array, [[],[],[],[]])
# interpolate using N-order polynomial
x2sim, y2sim = interpolation_poly(x1, y1, x2, y2, x1, y1, order=order)
# find error between actual and simulated x1
err = np.hypot(x2 - x2sim, y2 - y2sim)
# find pixels with error below psi
gpi = err < psi
print('LSTSQ filter: %d -> %d' % (len(x1), len(gpi[gpi])))
return x1[gpi], y1[gpi], x2[gpi], y2[gpi]
def test_interpolation_poly(self):
keyPoints1, descr1 = find_key_points(self.img1, nFeatures=self.nFeatures)
keyPoints2, descr2 = find_key_points(self.img2, nFeatures=self.nFeatures)
x1, y1, x2, y2 = get_match_coords(keyPoints1, descr1,
keyPoints2, descr2)
x2p1, y2p1 = interpolation_poly(x1, y1, x2, y2, x1, y1, 1)
x2p2, y2p2 = interpolation_poly(x1, y1, x2, y2, x1, y1, 2)
x2p3, y2p3 = interpolation_poly(x1, y1, x2, y2, x1, y1, 3)
plt.subplot(1,2,1)
plt.plot(x2, x2p1, '.')
plt.plot(x2, x2p2, '.')
plt.plot(x2, x2p3, '.')
plt.subplot(1,2,2)
plt.plot(y2, y2p1, '.')
plt.plot(y2, y2p2, '.')
plt.plot(y2, y2p3, '.')
plt.savefig('sea_ice_drift_tests_%s.png' % inspect.currentframe().f_code.co_name)
plt.close('all')
self.assertEqual(len(x2p1), len(x1))
def prepare_first_guess(c2pm1,
r2pm1,
n1,
c1,
r1,
n2,
c2,
r2,
img_size,
min_fg_pts=5,
min_border=20,
max_border=50,
old_border=True,
**kwargs):
''' For the given intial coordinates estimate the approximate final coordinates
Parameters
---------
c2_pm1 : 1D vector, initial PM column on image 2
r2_pm1 : 1D vector, initial PM rows of image 2
n1 : Nansat, the fist image with 2D array
c1 : 1D vector, initial FT columns on img1
r1 : 1D vector, initial FT rows on img2
n2 : Nansat, the second image with 2D array
c2 : 1D vector, final FT columns on img2
r2 : 1D vector, final FT rows on img2
img_size : int, size of template
min_fg_pts : int, minimum number of fist guess points
min_border : int, minimum searching distance
max_border : int, maximum searching distance
old_border : bool, use old border selection algorithm?
**kwargs : parameters for:
x2y2_interpolation_poly
x2y2_interpolation_near
Returns
-------
c2_fg : 1D vector, approximate final PM columns on img2 (first guess)
r2_fg : 1D vector, approximate final PM rows on img2 (first guess)
border : 1D vector, searching distance
'''
n2_shape = n2.shape()
# convert initial FT points to coordinates on image 2
lon1, lat1 = n1.transform_points(c1, r1)
c1n2, r1n2 = n2.transform_points(lon1, lat1, 1)
# interpolate 1st guess using 2nd order polynomial
c2p2, r2p2 = np.round(
interpolation_poly(c1n2, r1n2, c2, r2, c2pm1, r2pm1, **kwargs))
# interpolate 1st guess using griddata
c2fg, r2fg = np.round(
interpolation_near(c1n2, r1n2, c2, r2, c2pm1, r2pm1, **kwargs))
# TODO:
# Now border is proportional to the distance to the point
# BUT it assumes that:
# close to any point error is small, and
# error varies between points
# What if error does not vary with distance from the point?
# Border can be estimated as error of the first guess
# (x2 - x2_predicted_with_polynom) gridded using nearest neighbour.
if old_border:
# find distance to nearest neigbour and create border matrix
border_img = get_distance_to_nearest_keypoint(c2, r2, n2_shape)
border = np.zeros(c2pm1.size) + max_border
gpi = ((c2pm1 >= 0) * (c2pm1 < n2_shape[1]) * (r2pm1 >= 0) *
(r2pm1 < n2_shape[0]))
border[gpi] = border_img[np.round(r2pm1[gpi]).astype(np.int16),
np.round(c2pm1[gpi]).astype(np.int16)]
else:
c2tst, r2tst = interpolation_poly(c1n2, r1n2, c2, r2, c1n2, r1n2,
**kwargs)
c2dif, r2dif = interpolation_near(c1n2, r1n2, c2 - c2tst, r2 - r2tst,
c2pm1, r2pm1, **kwargs)
border = np.hypot(c2dif, r2dif)
# define searching distance
border[border < min_border] = min_border
border[border > max_border] = max_border
border[np.isnan(c2fg)] = max_border
border = np.floor(border)
# define FG based on P2 and GD
c2fg[np.isnan(c2fg)] = c2p2[np.isnan(c2fg)]
r2fg[np.isnan(r2fg)] = r2p2[np.isnan(r2fg)]
return c2fg, r2fg, border