def sub_mean(img, mean_img, scale=1.0):
"""
Subtract the pixelwise mean from each
frame.
"""
return set_neg_to_zero(img-scale*mean_img)
def sub_min(img, min_img, scale=1.0):
"""
Subtract a pixelwise minimum from each
frame.
"""
return set_neg_to_zero(img-scale*min_img)
def sub_median(img, median_img, scale=1.0):
"""
Subtract the movie's median with respect to
time from the frame.
"""
return set_neg_to_zero(img-scale*median_img)
def sub_gauss_filt_mean(img, mean_img, k=2.0,
scale=1.0):
"""
Subtract a Gaussian-filtered mean image
from the present image.
"""
return set_neg_to_zero(img - scale * \
ndi.gaussian_filter(mean_img, k))
def centroid(psf_img, sub_bg=False, camera_offset=0.0, camera_gain=1.0):
"""
Localize with center-of-mass.
args
----
psf_img : 2D ndarray
sub_bg : bool, subtract BG before
taking centroid
camera_offset : float, offset of
camera
camera_gain : float, gain of
camera
returns
-------
dict : {
'y0': y centroid in pixels,
'x0': x centroid in pixels
'I': integrated intensity above background;
'amp': the intensity of the brightest pixel;
'bg': the estimated background level;
'snr': the estimated signal-to-noise ratio
based on the amplitude
}
"""
# Subtract BG and divide out gain
psf_img = utils.rescale_img(psf_img,
camera_offset=camera_offset,
camera_gain=camera_gain)
# Estimate background
bg = utils.ring_mean(psf_img)
# Subtract background
psf_sub_bg = utils.set_neg_to_zero(psf_img - bg)
# Integrate intensity above background
I = psf_sub_bg.sum()
# Take the brightest pixel above background as
# the amplitude
amp = utils.amp_from_I(I, sigma=1.0)
# Find spot centers
if sub_bg:
y0, x0 = ndi.center_of_mass(psf_sub_bg)
else:
y0, x0 = ndi.center_of_mass(psf_img)
# Estimate signal-to-noise
snr = utils.estimate_snr(psf_img, amp)
return dict((('bg', bg), ('I', I), ('amp', amp), ('y0', y0), ('x0', x0),
('snr', snr)))
def dou_filter(img, k0=3, k1=9, t=None,
return_filt=True):
"""
Find spots by difference of uniforming-
filtering.
args
----
img : 2D ndarray
k0 : float, spot kernel width
k1 : float, BG kernel width
t : float, threshold (if None,
defaults to Otsu)
return_filt : bool. In addition to
the spot positions, also return
the filtered and binary images
returns
-------
If *return_filt*:
(
2D ndarray, filtered image;
2D ndarray, binary image;
2D ndarray of shape (n_spots, 2),
coordinates of spots
)
else:
2D ndarray of shape (n_spots, 2),
coordinates of spots
"""
img = img.astype('float64')
# Filter
img_filt = utils.set_neg_to_zero(
ndi.uniform_filter(img, k0) - \
ndi.uniform_filter(img, k1)
)
# Threshold
if t is None:
t = threshold_otsu(img_filt)
img_bin = img_filt > t
# Find spots
positions = utils.label_binary_spots(img_bin,
img_int=img_filt)
if return_filt:
return img_filt, img_bin, positions
else:
return positions
def ls_log_gaussian(psf_img, sigma=1.0, camera_bg=0.0, camera_gain=1.0):
"""
Find the least-squares estimate for the
parameters of a pointwise 2D Gaussian PSF
model, assuming noise is log-normally distributed.
While this noise model is fairly unrealistic,
it admits a linear LS estimator for the
parabolic log intensities of a pointwise
Gaussian. As a result, it is very fast.
However, it has the issue that it is biased-
the log normality assumption tends to make
it biased toward the center of the fitting
window. Use at your own risk.
args
----
psf_img : 2D ndarray
sigma : float, the width of the Gaussian
model
returns
-------
dict : {
'y0': estimated y center,
'x0': estimated x center,
'I': estimated PSF intensity,
'bg': estimated background intensity,
'amp': estimated peak PSF amplitude,
'snr': estimated SNR
}
"""
# Subtract BG and divide out gain
psf_img = utils.rescale_img(psf_img,
camera_offset=camera_offset,
camera_gain=camera_gain)
# Common factors
V = sigma**2
V2 = V * 2
# Estimate background by taking the mean
# of the outer ring of pixels
bg = utils.ring_mean(psf_img)
# Subtract background
psf_img_sub = utils.set_neg_to_zero(psf_img - bg)
# Avoid taking log of zero pixels
nonzero = psf_img_sub > 0.0
# Pixel indices
Y, X = np.indices(psf_img.shape)
Y = Y[nonzero]
X = X[nonzero]
# Log PSF above background
log_psf = np.log(psf_img_sub[nonzero])
# Response vector in LS problem
R = log_psf + np.log(V2 * np.pi) + (Y**2 + X**2) / V2
# Independent matrix in LS problem
M = np.asarray([np.ones(nonzero.sum()), V * Y, V * X]).T
# Compute the LS parameter estimate
ls_pars = utils.pinv(M) @ R
# Use the LS parameters to the find the
# spot center
y0 = ls_pars[1]
x0 = ls_pars[2]
I = np.exp(ls_pars[0] + (y0**2 + x0**2) / V2)
# Estimate peak Gaussian amplitude
amp = utils.amp_from_I(I, sigma=sigma)
# Estimate SNR
snr = utils.estimate_snr(psf_img, amp)
return dict((('y0', y0), ('x0', x0), ('I', I), ('bg', bg), ('amp', amp),
('snr', snr)))
