def gaussWin2D(shape, sigma=None):
"""
Create a 2D Gaussian window
The shape must have 2 components, namely the vertical and horizontal,
in this order.
"""
# Check input
if len(shape) == 1:
shape = [shape[0] for _ in range(2)]
elif len(shape) > 2:
shape = shape[:2]
shape = [max([1, int(x)]) for x in shape]
if not sigma:
sigma = [x / 2.0 for x in shape]
else:
if len(sigma) == 1:
sigma = [sigma[0] for _ in range(2)]
elif len(sigma) > 2:
sigma = sigma[:2]
sigma = [np.finfo(np.float32).eps if x <= 0 else x for x in sigma]
# Create vertical and horizontal components
v = gaussian(shape[0], sigma[0])
v = np.reshape(v, (-1, 1)) # column
h = gaussian(shape[1], sigma[1])
h = np.reshape(h, (1, -1)) # row
return np.dot(v, h)
def exer21(testImageFolder, saveImageFolder):
"""
Deliverables:
Provide a code snippet and explanation of your solution as well
as illustrations of your solution.
"""
shape = (124, 124)
sigma_blob = 10.0
im = np.ones(shape)
G = gaussian(shape[0], std=sigma_blob)
GG = np.outer(G, G)
blob = im * GG
sigma_scl = [1., 2., 3., 4., 5., 8., 10., 20]
sigma_scale = list(map(lambda x: x**2, sigma_scl))
for i in tqdm(range(len(sigma_scale))):
#create gaussian for scalespace sampling
Gs = gaussian(124, std=sigma_scale[i])
GGs = np.outer(Gs, Gs)
blob_scaled = convolve2d(blob, GGs)
fig = plt.figure()
ax = plt.subplot(1, 1, 1)
ax.imshow(blob_scaled, cmap=plt.cm.gray)
ax.axis('off')
title = r'blob w. $\sigma={}$ scalespace w. $\sigma={}$'.format(
sigma_blob, sigma_scale[i])
ax.set_title(title, fontsize=11)
fig.tight_layout()
filename = "exer21-" + 'blob w sigma={}, scale w sigma={}'.format(
sigma_blob, sigma_scale[i])
plt.savefig(saveImageFolder + filename + '.png')
plt.close
fig = plt.figure()
ax = plt.subplot(1, 1, 1)
ax.imshow(blob, cmap=plt.cm.gray)
ax.axis('off')
title = r'blob w. $\sigma={}$ w. scale = 0'.format(sigma_blob)
ax.set_title(title, fontsize=11)
fig.tight_layout()
filename = "exer21-" + 'blob w sigma={}, scale w sigma=0'.format(
sigma_blob, sigma_scale[i])
plt.savefig(saveImageFolder + filename + '.png')
plt.close
pass
def _smooth_spectral_power(raw_data, wind_len=5):
"""
smoothes the spectral power using a rolling Gaussian window.
Parameters
----------
raw_data : float masked array
The data to smooth.
wind_len : float
Length of the moving window
Returns
-------
data_smooth : float masked array
smoothed data
"""
# we want an odd window
if wind_len % 2 == 0:
wind_len += 1
half_wind = int((wind_len - 1) / 2)
# create window
wind = gaussian(wind_len, std=1.)
wind /= np.sum(wind)
# initialize smoothed data
nrays, ngates, nDoppler = np.shape(raw_data)
data_smooth = np.ma.masked_all((nrays, ngates, nDoppler))
# get rolling window and mask data
data_wind = rolling_window(raw_data, wind_len)
data_smooth[:, :, half_wind:-half_wind] = np.ma.dot(data_wind, wind)
return data_smooth
def smooth_responses(rsps, window_width=50, sigma=0.65):
# Gaussian smoothing
# Values taken from Rajeev's code.
sm_rsps = deepcopy(rsps)
sm_rsps.data = convolve1d(rsps.data, gaussian(window_width, sigma), axis=2)
sm_rsps.data = np.maximum(sm_rsps.data, 0)
return sm_rsps
def gaussian_img_filter(img_h, img_w):
'''
Creates a gaussian filter for images.
Args:
img_h (int): The height of the images.
img_w (int): The width of the images.
Returns:
gauss_filter (np.ndarray): Array of shape img_h * img_w.
'''
gauss_mg = np.meshgrid(gaussian(img_w, img_w // 4),
gaussian(img_h, img_h // 4))
return gauss_mg[0] * gauss_mg[1]
def rolling_mean_np(arr, win, center=True, win_type='boxcar'):
import scipy.signal.windows as spwin
df = pd.DataFrame(data=arr.reshape((arr.shape[0], arr[0].size)))
if win_type == 'gaussian':
w_std = win / 3.
print('Performing {} day rolling mean with gaussian window (std={})'
' to get better interannual statistics'.format(win, w_std))
fig, ax = plt.subplots(figsize=(3, 3))
ax.plot(range(-int(win / 2), +round(win / 2 + .49)),
spwin.gaussian(win, w_std))
plt.title('window used for rolling mean')
plt.xlabel('timesteps')
rollmean = df.rolling(win,
center=center,
min_periods=1,
win_type='gaussian').mean(std=w_std)
elif win_type == 'boxcar':
fig, ax = plt.subplots(figsize=(3, 3))
plt.plot(spwin.boxcar(win))
plt.title('window used for rolling mean')
plt.xlabel('timesteps')
rollmean = df.rolling(win,
center=center,
min_periods=1,
win_type='boxcar').mean()
return rollmean.values.reshape((arr.shape))
def createTargetShapeDelayFigure():
gestureLen = 20
gestureSig = np.concatenate([np.zeros((10,3)),np.random.normal(size=(gestureLen,3))*np.atleast_2d(gaussian(20, 3, 0)*2).T,np.zeros((10,3))],0)
target = np.concatenate([np.zeros((10,1)),np.ones((gestureLen,1)),np.zeros((10,1))],0)
target_gaus = np.concatenate([np.zeros((5,1)),np.atleast_2d(gaussian(gestureLen+10,5)).T,np.zeros((5,1))],0)
target_delayed = np.concatenate([np.zeros((28,1)),np.ones((5,1)),np.zeros((7,1))],0)
fig, ax = plt.subplots(1, 3, sharey=True, sharex=True, figsize=(20,5))
plt.ylim(-5,5)
for axn in ax:
axn.plot(gestureSig,label='input signal')
axn.plot([0,40],[0,0],c='black',linewidth=1)
ax[0].plot(target,label='target',c='red',linewidth=2)
ax[0].fill_between(np.arange(0,40),0,target.squeeze(),facecolor='red',alpha=0.5)
ax[0].set_title('(a)')
ax[0].set_xlabel('timestep')
ax[1].plot(target_gaus,label='target',c='red',linewidth=2)
ax[1].fill_between(np.arange(0,40),0,target_gaus.squeeze(),facecolor='red',alpha=0.5)
ax[1].set_title('(b)')
ax[1].set_xlabel('timestep')
ax[2].plot(target_delayed,label='target',c='red',linewidth=2)
ax[2].fill_between(np.arange(0,40),0,target_delayed.squeeze(),facecolor='red',alpha=0.5)
ax[2].set_title('(c)')
ax[2].set_xlabel('timestep')
#plt.legend(bbox_to_anchor=(1., 1.05), loc=1, borderaxespad=0.)
plt.tight_layout()
projectPath = 'C:\Users\Steve\Documents\Uni\BAThesis\\src\\targetShapeDelay2.pdf'
pp = PdfPages(projectPath)
pp.savefig()
pp.close()
def velocity_smoothed(pos, freq, smooth_size=0.03):
"""
Compute wheel velocity from uniformly sampled wheel data
Parameters
----------
pos : array_like
Array of wheel positions
smooth_size : float
Size of Gaussian smoothing window in seconds
freq : float
Sampling frequency of the data
Returns
-------
vel : np.ndarray
Array of velocity values
acc : np.ndarray
Array of acceleration values
"""
# Define our smoothing window with an area of 1 so the units won't be changed
std_samps = np.round(
smooth_size *
freq) # Standard deviation relative to sampling frequency
N = std_samps * 6 # Number of points in the Gaussian covering +/-3 standard deviations
gauss_std = (N - 1) / 6
win = windows.gaussian(N, gauss_std)
win = win / win.sum() # Normalize amplitude
# Convolve and multiply by sampling frequency to restore original units
vel = np.insert(convolve(np.diff(pos), win, mode='same'), 0, 0) * freq
acc = np.insert(convolve(np.diff(vel), win, mode='same'), 0, 0) * freq
return vel, acc
def denoise_sst(sst, bt11, kernel='boxcar', width=20, show=False):
"""
"""
if kernel == 'boxcar':
ker = np.ones((width, width))
elif kernel == 'gaussian':
gau = gaussian(3 * width, width / 2.)
ker = np.outer(gau, gau)
else:
raise Exception('Unknown kernel')
mask = ma.getmaskarray(sst) | ma.getmaskarray(bt11)
sst.data[mask] = 0.
bt11.data[mask] = 0.
corr = convolve((sst - 273.15) * 0.9 + 273.15 - bt11, ker)
#corr = convolve(sst - bt11, ker)
#corr = convolve((sst - 273) * 0.9 + 273 - bt11, ker)
norm = convolve(1. - mask, ker)
corr[mask] = 0
corr[~mask] /= norm[~mask]
denoised_sst = bt11 + corr
denoised_sst.mask = mask
if show == True:
import matplotlib.pyplot as plt
vmin = min([bt11.min(), sst.min(), denoised_sst.min()])
vmax = max([bt11.max(), sst.max(), denoised_sst.max()])
corr = ma.MaskedArray(corr, mask=mask)
for ivar, var in enumerate([sst, bt11, corr, denoised_sst]):
plt.figure()
if ivar == 2:
plt.imshow(var, interpolation='nearest')
else:
plt.imshow(var, vmin=vmin, vmax=vmax, interpolation='nearest')
plt.colorbar()
plt.show()
return denoised_sst
def smooth_responses(rsps, window_width=50, sigma=0.65):
# Gaussian smoothing
# Values taken from Rajeev's code.
sm_rsps = deepcopy(rsps)
sm_rsps.data = convolve1d(rsps.data, gaussian(window_width, sigma), axis=2)
sm_rsps.data = np.maximum(sm_rsps.data, 0)
return sm_rsps
def edge_detector(
gammatone: NDVar,
c: float = 0,
name: str = None,
):
"""Neural model for auditory edge-detection, as described by [1]_ and used in [2]_
Parameters
----------
gammatone
Gammatone spectrogram.
c
Saturation parameter (see [1]_).
name
Name for the returned :class:`NDVar`.
References
----------
.. [1] Fishbach, A., Nelken, I., & Yeshurun, Y. (2001). Auditory Edge Detection: A Neural Model for Physiological and Psychoacoustical Responses to Amplitude Transients. Journal of Neurophysiology, 85(6), 2303–2323. https://doi.org/10.1152/jn.2001.85.6.2303
.. [2] Brodbeck, C., Jiao, A., Hong, L. E., & Simon, J. Z. (2020). Neural speech restoration at the cocktail party: Auditory cortex recovers masked speech of both attended and ignored speakers. PLOS Biology, 18(10), e3000883. https://doi.org/10.1371/journal.pbio.3000883
"""
taus = np.linspace(3, 5, 10)
ws = np.diff(gaussian(11, 2))
rfs = [delay_rf(tau) for tau in taus]
xs_d = [apply_receptive_field(gammatone, rf) for rf in rfs]
if c:
xs_d = [saturate(x, c) for x in xs_d]
return sum([w * x for w, x in zip(ws, xs_d)]).clip(0, name=name)
def gaussian(t, std=1):
r"""Ricker wavelet
Create a Gaussian wavelet given time axis ``t`` and standard deviation ``std``
using :py:func:`scipy.signal.gaussian`.
Parameters
----------
t : :obj:`numpy.ndarray`
Time axis (positive part including zero sample)
std : :obj:`float`, optional
Standard deviation of gaussian
Returns
-------
w : :obj:`numpy.ndarray`
Wavelet
t : :obj:`numpy.ndarray`
Symmetric time axis
wcenter : :obj:`int`
Index of center of wavelet
"""
if len(t) % 2 == 0:
t = t[:-1]
warnings.warn('one sample removed from time axis...')
w = gaussian(len(t) * 2 - 1, std=std)
t = np.concatenate((np.flipud(-t[1:]), t), axis=0)
wcenter = np.argmax(np.abs(w))
return w, t, wcenter
def add_background_fluctuation(sinogram, strength_ratio=0.2):
"""
Fluctuate the background of a sinogram image using a Gaussian profile beam.
Parameters
----------
sinogram : array_like
2D array. Sinogram image.
strength_ratio : float
To define the strength of the variation. The value is in the range of
[0.0, 1.0].
Returns
-------
array_like
"""
sinogram = np.copy(sinogram)
(nrow, ncol) = sinogram.shape
list_fact = 1.0 - np.random.rand(nrow) * strength_ratio
list_shift = np.int16(
(0.5 - np.random.rand(nrow)) * strength_ratio * ncol * 0.5)
for i in range(nrow):
sinogram[i] = sinogram[i] * np.roll(
win.gaussian(ncol, 0.5 * list_fact[i] * ncol), list_shift[i])
return sinogram
def test_basic(self):
assert_allclose(windows.gaussian(6, 1.0),
[0.04393693362340742, 0.3246524673583497,
0.8824969025845955, 0.8824969025845955,
0.3246524673583497, 0.04393693362340742])
assert_allclose(windows.gaussian(7, 1.2),
[0.04393693362340742, 0.2493522087772962,
0.7066482778577162, 1.0, 0.7066482778577162,
0.2493522087772962, 0.04393693362340742])
assert_allclose(windows.gaussian(7, 3),
[0.6065306597126334, 0.8007374029168081,
0.9459594689067654, 1.0, 0.9459594689067654,
0.8007374029168081, 0.6065306597126334])
assert_allclose(windows.gaussian(6, 3, False),
[0.6065306597126334, 0.8007374029168081,
0.9459594689067654, 1.0, 0.9459594689067654,
0.8007374029168081])
def gauss(n):
"""
creates a 1d gaussian low pass filter with unit
standard deviation.
:param n: number of desired filter components
"""
kernel = gaussian(n, 1).reshape(1, n)
return kernel/np.sum(kernel)
def test_basic(self):
assert_allclose(windows.gaussian(6, 1.0),
[0.04393693362340742, 0.3246524673583497,
0.8824969025845955, 0.8824969025845955,
0.3246524673583497, 0.04393693362340742])
assert_allclose(windows.gaussian(7, 1.2),
[0.04393693362340742, 0.2493522087772962,
0.7066482778577162, 1.0, 0.7066482778577162,
0.2493522087772962, 0.04393693362340742])
assert_allclose(windows.gaussian(7, 3),
[0.6065306597126334, 0.8007374029168081,
0.9459594689067654, 1.0, 0.9459594689067654,
0.8007374029168081, 0.6065306597126334])
assert_allclose(windows.gaussian(6, 3, False),
[0.6065306597126334, 0.8007374029168081,
0.9459594689067654, 1.0, 0.9459594689067654,
0.8007374029168081])
def smooth(data, window_type='hann', filter_width=11, sigma=2, plot_on=1):
"""
Smooth 1d data with moving window (uses filtfilt to have zero phase distortion)
Wrapper for scipy.signal.filtfilt
To do: consider replacing with sosfiltfilt
Inputs:
data: numpy array
window_type ('hann'): string ('boxcar', 'gaussian', 'hann', 'bartlett', 'blackman')
filter_width (11): int (wider is more smooth) odd is ideal
sigma (2.): scalar std deviation only used for gaussian
plot_on (1): int determines plotting. 0 none, 1 plot signal, 2: also plot filter
Outputs
data_smoothed: signal after being smoothed
filter_window: the window used for smoothing
Notes:
Uses gustaffson's method to handle edge artifacts
Currently accepted window_type options:
hann (default) - cosine bump filter_width is only param
blackman - more narrowly peaked bump than hann
boxcar - flat-top of length filter_width
bartlett - triangle
gaussian - sigma determines width
"""
if window_type == 'boxcar':
filter_window = windows.boxcar(filter_width)
elif window_type == 'hann':
filter_window = windows.hann(filter_width)
elif window_type == 'bartlett':
filter_window = windows.bartlett(filter_width)
elif window_type == 'blackman':
filter_window = windows.blackman(filter_width)
elif window_type == 'gaussian':
filter_window = windows.gaussian(filter_width, sigma)
filter_window = filter_window / np.sum(filter_window)
data_smoothed = signal.filtfilt(filter_window, 1, data,
method="gust") # pad
if plot_on:
if plot_on > 1:
plt.plot(filter_window)
plt.title(f'{window_type} filter')
plt.figure('signal', figsize=(10, 5))
plt.plot(data,
color=(0.7, 0.7, 0.7),
label='noisy signal',
linewidth=1)
plt.plot(data_smoothed, color='r', label='smoothed signal')
plt.xlim(0, len(data_smoothed))
plt.xlabel('sample')
plt.grid(True)
plt.legend()
return data_smoothed, filter_window
def compute_mute_flag(s0):
a = s0[:]
a = a.astype('float32') / np.max(a)
s = a**2 * 0.25
w = gaussian(32, 1)
s = convolve(s, w)
# plt.plot(s[:102400*5])
s[0] = 0
flag = np.array(s > 0.030, 'uint8')
return flag
def accumulate_signal_energy_gaussian(array : np.array) -> np.array:
"""
Computes the cumulative energy from an array considering a Gaussian
weighted window. This is equivalent to a Gaussian filtered signal
Parameters of the window: 100 points, std=7
"""
# TODO: optimize window based on noise/NN
gaussian_window = window.gaussian(100, std=2)
gaussian_window = gaussian_window/np.sum(gaussian_window)
filtered = signal.convolve(array, gaussian_window)
return np.cumsum(filtered ** 2, axis=0)
def rolling_mean_np(arr, win, center=True):
import scipy.signal.windows as spwin
plt.plot(range(-int(win/2),+int(win/2)+1), spwin.gaussian(win, win/2))
plt.title('window used for rolling mean')
plt.xlabel('timesteps')
df = pd.DataFrame(data=arr.reshape( (arr.shape[0], arr[0].size)))
rollmean = df.rolling(win, center=center, min_periods=1,
win_type='gaussian').mean(std=win/2.)
return rollmean.values.reshape( (arr.shape))
def _f_calc_weighted_percentage(roi):
"""
特徴量計算: 「端点」「分岐点」の重み付け割合
- ガウシアンカーネルによる重み付けを行う
Parameters
----------
roi : numpy.ndarray
局所領域画像
Returns
-------
value : np.float
特徴量値
"""
LABELS = EdgeLineFeatures.LABELS
BG = LABELS["BG"]
ENDPOINT = LABELS["endpoint"]
BRANCH = LABELS["branch"]
sigma = roi.shape[0] / 3
# Generate Gaussian kernel
gaussian_kernel = np.outer(gaussian(roi.shape[0], std=sigma),
gaussian(roi.shape[1], std=sigma))
# TODO: 分母の値は「領域サイズ」？それとも「エッジ画素数」？
# w_n_edges = np.sum(gaussian_kernel) - np.sum(gaussian_kernel[roi == BG])
w_n_edges = np.sum(gaussian_kernel)
if w_n_edges == 0:
return 0
w_n_endpoint = np.sum(gaussian_kernel[roi == ENDPOINT])
w_n_branch = np.sum(gaussian_kernel[roi == BRANCH])
value = (w_n_endpoint + w_n_branch) / w_n_edges
return value
def do_smooth_with_gaussian(hist_dat, std):
window_len = int(4*std)+1
if window_len>2*hist_dat.size-1:
raise Exception('Whoa buddy!')
kern = gaussian(window_len,std)
kern /= np.sum(kern)
ys1 = hist_dat
ys1 = np.r_[ys1[(window_len-1)//2:0:-1],ys1,ys1[-2:(-window_len-3)//2:-1]]
ys1 = np.convolve(ys1,kern,'valid')
return ys1
def convolute(self: 'Frame2D',
radius: int,
method: str = 'nearest') -> Frame2D:
""" Convolutes the Frame.
:param radius: The radius of the convolution.
:param method: "nearest" or "average". If argument is not 'nearest', it'll use average by default.
"""
kernel_diam = radius * 2 + 1
if method == 'nearest':
kernel = np.zeros([kernel_diam + 1, kernel_diam + 1, 1])
kernel[kernel.shape[0] // 2, kernel.shape[1] // 2] = 1
else: # 'average'
kernel = np.outer(gaussian(kernel_diam + 1, radius),
gaussian(kernel_diam + 1, radius))
kernel = np.expand_dims(kernel, axis=-1)
return self.create(
fftconvolve(self.data, kernel, mode='valid', axes=[0, 1]),
self.labels)
def __call__(self, length, flagged=None):
self.length = length
self.flagged = flagged if not flagged is None else self.flagged
i = self.get_mask()
abs_residuals = np.interp(self.spectrum.wave, self.spectrum.wave[i],
self.abs_residuals[i])
window = gaussian(self.spectrum.N, length)
window /= np.sum(window)
error = convolve(abs_residuals, window, mode='same')
fmin = lambda a: np.power(
1. * np.sum(abs_residuals < a * error) / self.spectrum.N -
.682689492137, 2)
error *= minimize(fmin, 1, method='Nelder-Mead').x[0]
return error
def remove_stripe_based_filtering(sinogram, sigma, size, dim=1):
"""
Remove stripe artifacts in a sinogram using the filtering technique,
algorithm 2 in Ref. [1]. Angular direction is along the axis 0.
Parameters
----------
sinogram : array_like
2D array. Sinogram image
sigma : int
Sigma of the Gaussian window used to separate the low-pass and
high-pass components of the intensity profile of each column.
size : int
Window size of the median filter.
dim : {1, 2}, optional
Dimension of the window.
Returns
-------
array_like
2D array. Stripe-removed sinogram.
References
----------
.. [1] https://doi.org/10.1364/OE.26.028396
"""
pad = min(150, int(0.1 * sinogram.shape[0]))
sinogram = np.transpose(sinogram)
sino_pad = np.pad(sinogram, ((0, 0), (pad, pad)), mode='reflect')
(_, ncol) = sino_pad.shape
window = gaussian(ncol, std=sigma)
list_sign = np.power(-1.0, np.arange(ncol))
sino_smooth = np.copy(sinogram)
for i, sino_1d in enumerate(sino_pad):
sino_smooth[i] = np.real(
fft.ifft(fft.fft(sino_1d * list_sign) * window) *
list_sign)[pad:ncol - pad]
sino_sharp = sinogram - sino_smooth
if dim == 2:
sino_smooth_cor = median_filter(sino_smooth, (size, size))
else:
sino_smooth_cor = median_filter(sino_smooth, (size, 1))
return np.transpose(sino_smooth_cor + sino_sharp)
def create_kernel(dim0, dim1):
"""Create a two-dimensional LPF kernel, with a half-Hamming window along
the first dimension and a Gaussian along the second.
Parameters
----------
dim0 : int
Half-Hamming window length.
dim1 : int
Gaussian window length.
Returns
-------
kernel : np.ndarray
The 2d LPF kernel.
"""
dim0_weights = np.hamming(dim0 * 2 + 1)[:dim0]
dim1_weights = gaussian(dim1, dim1 * 0.25, True)
kernel = dim0_weights[:, np.newaxis] * dim1_weights[np.newaxis, :]
return kernel / kernel.sum()
def create_kernel(dim0, dim1):
"""Create a two-dimensional LPF kernel, with a half-Hamming window along
the first dimension and a Gaussian along the second.
Parameters
----------
dim0 : int
Half-Hamming window length.
dim1 : int
Gaussian window length.
Returns
-------
kernel : np.ndarray
The 2d LPF kernel.
"""
dim0_weights = np.hamming(dim0 * 2 + 1)[:dim0]
dim1_weights = gaussian(dim1, dim1 * 0.25, True)
kernel = dim0_weights[:, np.newaxis] * dim1_weights[np.newaxis, :]
return kernel / kernel.sum()
def test_decon(self):
"""
Convolution with subsequent deconvolution.
"""
# The incoming wavelet
g = gaussian(51, 2.5)
# Impulse response
r = np.zeros_like(g)
r[0] = 1
r[15] = .25
# convolve the two to a signal
s = np.convolve(g, r)[:len(g)]
# Deconvolve
_, _, r2 = it(g, s, 1, omega_min=0.5)
# test result
self.assertTrue(np.allclose(r, r2[0:len(r)], atol=0.0001))
def gaussian(t, std=1, plotflag=False):
r"""Ricker wavelet
Create a Gaussian wavelet given time axis ``t`` and standard deviation ``std``
using :py:func:`scipy.signal.gaussian`.
Parameters
----------
t : :obj:`numpy.ndarray`
Time axis (positive part including zero sample)
std : :obj:`float`, optional
Standard deviation of gaussian
plotflag : :obj:`bool`, optional
Quickplot
Returns
-------
w : :obj:`numpy.ndarray`
Wavelet
t : :obj:`numpy.ndarray`
Symmetric time axis
wcenter : :obj:`int`
Index of center of wavelet
"""
if len(t)%2 == 0:
t = t[:-1]
warnings.warn('one sample removed from time axis...')
w = gaussian(len(t)*2-1, std=std)
t = np.concatenate((np.flipud(-t[1:]), t), axis=0)
wcenter = np.argmax(np.abs(w))
if plotflag:
plt.figure(figsize=(7, 2))
plt.plot(t, w, 'k', lw=2)
plt.title('Gaussian wavelet')
plt.xlabel('t')
return w, t, wcenter
def smooth1d(array, window_size=None, kernel='gaussian'):
"""Apply a centered window smoothing to a 1D array.
Parameters
----------
array : ndarray
the array to apply the smoothing to
window_size : int
the size of the smoothing window
kernel : str
the type of smoothing (`gaussian`, `mean`)
Returns
-------
the smoothed array (same dim as input)
"""
# some defaults
if window_size is None:
if len(array) >= 9:
window_size = 9
elif len(array) >= 7:
window_size = 7
elif len(array) >= 5:
window_size = 5
elif len(array) >= 3:
window_size = 3
if window_size % 2 == 0:
raise ValueError('Window should be an odd number.')
if isinstance(kernel, str):
if kernel == 'gaussian':
kernel = gaussian(window_size, 1)
elif kernel == 'mean':
kernel = np.ones(window_size)
else:
raise NotImplementedError('Kernel: ' + kernel)
kernel = kernel / np.asarray(kernel).sum()
return convolve1d(array, kernel, mode='mirror')
def remove_stripe_based_filtering_sorting(sinogram, sigma, size, dim=1):
"""
Combination of algorithm 2 and algorithm 3 in [1].
Removing stripes using the filtering and sorting technique.
Angular direction is along the axis 0.
Parameters
----------
sinogram : float
2D array.
sigma : int
Sigma of the Gaussian window used to separate the low-pass and
high-pass components of the intensity profile of each column.
size : int
Window size of the median filter.
dim : {1, 2}, optional
Dimension of the window.
Returns
-------
float
2D array. Stripe-removed sinogram.
"""
pad = 150 # To reduce artifacts caused by FFT
sinogram = np.transpose(sinogram)
sinopad = np.pad(sinogram, ((0, 0), (pad, pad)), mode='reflect')
(_, ncol) = sinopad.shape
window = gaussian(ncol, std=sigma)
listsign = np.power(-1.0, np.arange(ncol))
sinosmooth = np.copy(sinogram)
for i, sinolist in enumerate(sinopad):
# sinosmooth[i] = np.real(ifft(fft(
# sinolist * listsign) * window) * listsign)[pad:ncol-pad]
sinosmooth[i] = np.real(
fft.ifft(fft.fft(sinolist * listsign) * window) *
listsign)[pad:ncol - pad]
sinosharp = sinogram - sinosmooth
sinosmooth_cor = np.transpose(
remove_stripe_based_sorting(np.transpose(sinosmooth), size, dim))
return np.transpose(sinosmooth_cor + sinosharp)
def test_it_max(self):
"""
Convolution with subsequent deconvolution. One Iteration should
only recover the largest peak.
"""
# The incoming wavelet
g = gaussian(51, 2.5)
# Impulse response
r = np.zeros_like(g)
r[0] = 1
r[15] = .25
# convolve the two to a signal
s = np.convolve(g, r)[:len(g)]
# Deconvolve
_, _, r2 = it(g, s, 1, it_max=1, omega_min=0.5)
# test result
self.assertFalse(np.allclose(r, r2[0:len(r)], atol=0.1))
self.assertAlmostEqual(r[0], r2[0], places=4)
def ACR_model(latency, width, weights, latency_pad, fs):
full_mod = np.array([])
stds = width / 4 #SD of the sources in seconds
source_mods = []
for source in range(stds.size):
gauss_source = gaussian(np.round(width[source] * fs),
np.round(stds[source] * fs))
source_mods.append(gauss_source - np.min(gauss_source))
for source in range(len(source_mods)):
if source == 2:
continue
if (source == 1): # do mixed source
s2 = np.concatenate((np.zeros(
int(
np.round((np.sum(width[:2]) + width[2] / 2 - latency[2]) *
fs))), source_mods[2]))
s1 = np.concatenate(
(source_mods[1], np.zeros(s2.size - source_mods[1].size)))
mixed_source = weights[1] * s1 + weights[2] * s2
full_mod = np.append(full_mod, mixed_source)
else:
full_mod = np.append(
full_mod,
np.min(source_mods[source]) *
np.ones(int(np.round(latency_pad[source] * fs))))
full_mod = np.append(full_mod,
weights[source] * source_mods[source])
return full_mod
def angle_variance_using_mean_vector(_edge_magnitude, _edge_angle):
"""
平均ベクトルに基づくエッジ角度分散の計算
*REF:*\ `[PDF]角度統計 <http://q-bio.jp/images/5/53/角度統計配布_qbio4th.pdf>`__
- :math:`N` : 計算対象の角度の個数
- まず、:math:`\\cos`、:math:`\\sin` の平均値を計算する
- それぞれを :math:`M_{\\cos}`、:math:`M_{\\sin}` とすると
.. math::
M_{\\cos} = \\frac{1}{N} \\sum^{N} \\cos{\\theta} ;, ;; M_{\\sin} = \\frac{1}{N} \\sum^{N} \\sin{\\theta}
- ここで、平均ベクトルを考える
- 平均ベクトル :math:`(R\\cos{\\Theta}, R\\sin{\\Theta})` は次のように定義される
.. math::
(R\\cos{\\Theta}, R\\sin{\\Theta}) = (M_{\\cos}, M_{\\sin})
- このとき、エッジ角度分散 :math:`V` は平均ベクトルの長さ :math:`R`
を用いて次のように定義される
- :math:`V = 1 - R`
- :math:`R` は以下の計算で算出する
- :math:`R = \\sqrt{ {M_{\\cos}}^2 + {M_{\\sin}}^2 }`
Parameters
----------
_edge_magnitude : numpy.ndarray
エッジ強度
_edge_angle : numpy.ndarray
エッジ角度
Returns
-------
float
エッジ角度の分散値 [0, 1]
"""
radians = _edge_angle
weights = _edge_magnitude
gaussian_kernel = np.outer(
gaussian(_edge_magnitude.shape[0],
std=_edge_magnitude.shape[0] / 3),
gaussian(_edge_magnitude.shape[1],
std=_edge_magnitude.shape[1] / 3))
weights = weights * gaussian_kernel
if np.isclose(np.sum(weights), 0):
return 0
# weights /= weights.max()
M_cos = np.average(np.cos(radians), weights=weights)
M_sin = np.average(np.sin(radians), weights=weights)
R = np.hypot(M_cos, M_sin)
variance = 1 - R
# return variance
return variance * np.mean(weights)
