nodmath.py
37.6 KB
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# -*- coding: utf-8 -*- """
#!/usr/bin/env python
import numpy as np
def nint(x):
if x > 0: return int(x+0.5000001)
else: return int(x-0.4999999)
def nanmean(a, axis=None):
if hasattr(np, 'nanmedian'):
return np.nanmean(a, axis)
else:
from scipy import stats
return stats.nanmean(np.array(a), axis)
def nanmedian(a, axis=None):
if hasattr(np, 'nanmedian'):
return np.nanmedian(a, axis)
else:
from scipy import stats
return stats.nanmedian(np.array(a), axis)
def nan_check(data, val, weight=False):
Data = 1*data
mask = np.isfinite(Data)
Data[~mask] = val
if weight:
return Data, np.array(mask, dtype=float)
else:
return Data
def nanmean_(datalist):
wsum = None
for d in datalist:
data, w = nan_check(d, 0.0, weight=True)
if wsum == None:
wsum = w.copy()
wdata = data.copy()
else:
wsum += w
wdata += data
mask = np.isfinite(wdata)
avg = np.where(mask, wdata/wsum, np.nan)
return avg
def erf(x):
a0 = -1.26551223
a1 = +1.00002368
a2 = +0.37409196
a3 = +0.09678418
a4 = -0.18628806
a5 = +0.27886807
a6 = -1.13520398
a7 = +1.48851578
a8 = -0.82215223
a9 = +0.17087227
t = 1.0/(1.0+0.5*abs(x))
p = ((((((((a9*t + a8)*t + a7)*t + a6)*t + a5*t) + a4)*t + a3)*t + a2)*t + a1)*t + a0
tau = t*np.exp(-x*x + p)
erfx = np.where(x >=0.0, 1-tau, tau-1)
return erfx
def erf0(x):
# constants
a1 = 0.254829592
a2 = -0.284496736
a3 = 1.421413741
a4 = -1.453152027
a5 = 1.061405429
p = 0.3275911
# Save the sign of x
sign = np.where(x < 0.0, -1, 1)
x = abs(x)
# A & S 7.1.26
t = 1.0/(1.0 + p*x)
y = 1.0 - (((((a5*t + a4)*t) + a3)*t + a2)*t + a1)*t*np.exp(-x*x)
return sign*y
def erfc(x):
return 1.0 - erf(x)
def padsin(vector, pad_width, iaxis, kwargs):
px = pad_width[0]
py = pad_width[1]
a = vector[px]
b = vector[-py-1]
vector[:px] = a*(np.sin(np.pi/(px-0)*np.arange(float(px))-np.pi/2.) + 1)/2.
vector[-py:] = b-b*(np.sin(np.pi/(py-0)*np.arange(float(py))-np.pi/2.) + 1)/2.
return vector
def deg2DMS(ra='', dec='', round=False):
RA, DEC, rs, ds = '', '', '', ''
if dec:
if str(dec)[0] == '-':
ds, dec = '-', abs(dec)
deg = int(dec)
decM = abs(int((dec-deg)*60))
if round:
decS = int((abs((dec-deg)*60)-decM)*60)
else:
decS = (abs((dec-deg)*60)-decM)*60
DEC = '{0}{1} {2} {3}'.format(ds, deg, decM, decS)
if ra:
if str(ra)[0] == '-':
rs, ra = '-', abs(ra)
raH = int(ra)
raM = int(((ra)-raH)*60)
if round:
raS = int(((((ra)-raH)*60)-raM)*60)
else:
raS = ((((ra)-raH)*60)-raM)*60
RA = '{0}{1} {2} {3}'.format(rs, raH, raM, raS)
if ra and dec:
return (RA, DEC)
else:
return RA or DEC
def deg2HMS(ra='', dec='', round=False):
RA, DEC, rs, ds = '', '', '', ''
if dec:
if str(dec)[0] == '-':
ds, dec = '-', abs(dec)
deg = int(dec)
decM = abs(int((dec-deg)*60))
if round:
decS = int((abs((dec-deg)*60)-decM)*60)
else:
decS = (abs((dec-deg)*60)-decM)*60
DEC = '{0}{1} {2} {3}'.format(ds, deg, decM, decS)
if ra:
if str(ra)[0] == '-':
rs, ra = '-', abs(ra)
raH = int(ra/15)
raM = int(((ra/15)-raH)*60)
if round:
raS = int(((((ra/15)-raH)*60)-raM)*60)
else:
raS = ((((ra/15)-raH)*60)-raM)*60
RA = '{0}{1} {2} {3}'.format(rs, raH, raM, raS)
if ra and dec:
return (RA, DEC)
else:
return RA or DEC
def extract(Z, shape, position, fill=np.NaN):
""" Extract a sub-array from Z using given shape and centered on
position.
If some part of the sub-array is out of Z bounds, result is
padded
with fill value.
**Parameters**
`Z` : array_like
Input array.
`shape` : tuple
Shape of the output array
`position` : tuple
Position within Z
`fill` : scalar
Fill value
**Returns**
`out` : array_like
Z slice with given shape and center
**Examples**
>>> Z = np.arange(0,16).reshape((4,4))
>>> extract(Z, shape=(3,3), position=(0,0))
[[ NaN NaN NaN]
[ NaN 0. 1.]
[ NaN 4. 5.]]
Schema:
+-----------+
| 0 0 0 | = extract (Z, shape=(3,3), position=(0,0))
| +---------------+
| 0 | 0 1 | 2 3 | = Z
| | | |
| 0 | 4 5 | 6 7 |
+---|-------+ |
| 8 9 10 11 |
| |
| 12 13 14 15 |
+---------------+
>>> Z = np.arange(0,16).reshape((4,4))
>>> extract(Z, shape=(3,3), position=(3,3))
[[ 10. 11. NaN]
[ 14. 15. NaN]
[ NaN NaN NaN]]
Schema:
+---------------+
| 0 1 2 3 | = Z
| |
| 4 5 6 7 |
| +-----------+
| 8 9 |10 11 | 0 | = extract (Z, shape=(3,3),
position=(3,3))
| | | |
| 12 13 |14 15 | 0 |
+---------------+ |
| 0 0 0 |
+-----------+
"""
# assert(len(position) == len(Z.shape))
# if len(shape) < len(Z.shape):
# shape = shape + Z.shape[len(Z.shape)-len(shape):]
R = np.ones(shape, dtype=Z.dtype)*fill
P = np.array(list(position)).astype(int)
Rs = np.array(list(R.shape)).astype(int)
Zs = np.array(list(Z.shape)).astype(int)
R_start = np.zeros((len(shape),)).astype(int)
R_stop = np.array(list(shape)).astype(int)
Z_start = (P-Rs//2)
Z_stop = (P+Rs//2)+Rs%2
R_start = (R_start - np.minimum(Z_start,0)).tolist()
Z_start = (np.maximum(Z_start,0)).tolist()
R_stop = (R_stop - np.maximum(Z_stop-Zs,0)).tolist()
Z_stop = (np.minimum(Z_stop,Zs)).tolist()
r = [slice(start,stop) for start,stop in zip(R_start,R_stop)]
z = [slice(start,stop) for start,stop in zip(Z_start,Z_stop)]
R[r] = Z[z]
return R
def same_size(ms, ref=False, eps=1.e-2):
cx = ms[0].header['CRVAL1']
cy = ms[0].header['CRVAL2']
dx = ms[0].header['CDELT1']
dy = ms[0].header['CDELT2']
tx = ms[0].header['CTYPE1']
ty = ms[0].header['CTYPE2']
Rows = 0
Cols = 0
medge = None
edges = []
for m in ms:
rows, cols = m.data.shape
Rows = max(Rows, rows)
Cols = max(Cols, cols)
xl, xr = cx + (1-m.header['CRPIX1'])*dx, cx + (cols-m.header['CRPIX1'])*dx
yb, yt = cy + (1-m.header['CRPIX2'])*dy, cy + (rows-m.header['CRPIX2'])*dy
edges.append([yb, yt, xl, xr])
if medge == None:
medge = [yb, yt, xl, xr]
#b0 = cy
#l0 = cx
b0 = (yb+yt)/2.0
l0 = (xl+xr)/2.0
elif not ref:
medge[0] = min(medge[0], yb)
medge[1] = max(medge[1], yt)
medge[2] = max(medge[2], xl)
medge[3] = min(medge[3], xr)
b0 = (medge[1]+medge[0])/2.0
l0 = (medge[3]+medge[2])/2.0
Rows = nint((medge[1]-medge[0]) / dy) + 1
Cols = nint((medge[3]-medge[2]) / dx) + 1
out = 0
for m in ms:
if (m.header['CDELT1'] - dx)/dx > eps and (m.header['CDELT2'] - dy)/dy < eps:
out += 1
if m.header['CTYPE1'] != tx and m.header['CTYPE2'] != ty:
print tx, ty, m.header['CTYPE1'], m.header['CTYPE2']
out += 1
if out > 0:
return out, []
ms_new = []
n = 0
for m in ms:
rows, cols = m.data.shape
b = (edges[n][1]+edges[n][0])/2.0
l = (edges[n][3]+edges[n][2])/2.0
posx = cols/2.0 + (l0-l)/dx
posy = rows/2.0 + (b0-b)/dy
#print (Rows, Cols), (posx,posy)
m.data = extract(m.data, shape=(Rows, Cols), position=(nint(posy), nint(posx)))
m.header['CRPIX1'] = (Cols+1)/2.0 + (cx-l0)/dx
m.header['CRPIX2'] = (Rows+1)/2.0 + (cy-b0)/dy
#m.header['CRPIX1'] = (Cols+1)/2.0
#m.header['CRPIX2'] = (Rows+1)/2.0
#m.header['CRVAL1'] = l0
#m.header['CRVAL2'] = b0
m.header['CRVAL1'] = cx
m.header['CRVAL2'] = cy
m.header['NAXIS1'] = Cols
m.header['NAXIS2'] = Rows
ms_new.append(m)
n += 1
return out, ms_new
def FixNaNs(x):
for row in range(x.shape[0]):
xrow = x[row]
idxs = np.nonzero(xrow == xrow)[0]
if len(idxs) > 0:
for i in range(0, idxs[0]):
xrow[i] = xrow[idxs[0]]
for i in range(idxs[-1]+1, xrow.size):
xrow[i] = xrow[idxs[-1]]
x[row] = xrow
return x
def nan_interpol(data):
mask = np.isnan(data)
mdata = data.copy()
mdata[mask] = np.interp(np.flatnonzero(mask), np.flatnonzero(~mask), data[~mask])
return mask, mdata
from scipy.ndimage import rotate
def map_rotate(data, p):
mask = np.isnan(data)
dmask = rotate(np.where(mask, 0, 1), p.angle, reshape=p.reshape, order=0, mode='nearest',
cval=0, prefilter=False)
data[mask] = np.interp(np.flatnonzero(mask), np.flatnonzero(~mask), data[~mask])
newdata = rotate(data, p.angle, reshape=p.reshape, order=p.order, mode=p.mode,
cval=np.nan, prefilter=p.prefilter)
return np.where(dmask == 0, np.nan, newdata)
from scipy.ndimage import map_coordinates
def map_interpolate(data, x, y):
mask = np.isnan(data)
dmask = map_coordinates(np.where(mask, 0, 1), (y, x), order=0, mode='nearest',
cval=0, prefilter=False, output=np.int32)
data[mask] = np.interp(np.flatnonzero(mask), np.flatnonzero(~mask), data[~mask])
newdata = map_coordinates(data, (y, x), order=4, mode='constant',
cval=np.nan, prefilter=True, output=np.float32)
return np.where(dmask == 0, np.nan, newdata)
return newdata
from scipy.ndimage import zoom
def map_zoom(data, rebin, order=4, prefilter=True):
mask = np.isnan(data)
dmask = zoom(np.where(mask, 0, 1), rebin, order=0, prefilter=False, output=np.int32)
data[mask] = np.interp(np.flatnonzero(mask), np.flatnonzero(~mask), data[~mask])
newdata = zoom(data, rebin, order=order, cval=np.nan, prefilter=True, output=np.float32)
return np.where(dmask == 0, np.nan, newdata)
def griddata(inp, points, outp, method='nearest'):
y_points, x_points = inp
grid_y, grid_x = outp
shape = grid_x.shape
grid_y = grid_y.ravel()
grid_x = grid_x.ravel()
store = np.zeros(len(grid_x))
for i in range(len(grid_x)):
distance2 = (y_points-grid_y[i])**2 + (x_points-grid_x[i])**2
j = np.where(distance2 == np.nanmin(distance2))
store[i] = points[j]
return store.reshape(shape)
def nan_interpolation(data):
mask = np.isnan(data)
data[mask] = np.interp(np.flatnonzero(mask), np.flatnonzero(~mask), data[~mask])
return data
def _polyfill(polygon):
return lambda x, y: point_in_polygon((x, y), polygon)
def polymask(data, polygon):
py, px = np.indices(data.shape)
mask = _polyfill(polygon)(*np.array([px, py]))
return mask.reshape(data.shape)
def sector_mask(shape,centre,radius,angle_range):
"""
Return a boolean mask for a circular sector. The start/stop angles in
`angle_range` should be given in clockwise order.
"""
x,y = np.ogrid[:shape[0],:shape[1]]
cx,cy = centre
tmin,tmax = np.deg2rad(angle_range)
# ensure stop angle > start angle
if tmax < tmin:
tmax += 2*np.pi
# convert cartesian --> polar coordinates
r2 = (x-cx)*(x-cx) + (y-cy)*(y-cy)
theta = np.arctan2(x-cx, y-cy) - tmin
# wrap angles between 0 and 2*pi
theta %= (2*np.pi)
# circular mask
rad1, rad2 = radius
circmask1 = r2 >= rad1*rad2
circmask2 = r2 <= rad2*rad2
circmask = circmask1*circmask2
# angular mask
anglemask = theta <= (tmax-tmin)
return circmask*anglemask
#From http://www.ariel.com.au/a/python-point-int-poly.html
# Modified by Nick ODell
from collections import namedtuple
def point_in_polygon(target, poly):
"""x,y is the point to test. poly is a list of tuples comprising the polygon."""
point = namedtuple("Point", ("x", "y"))
line = namedtuple("Line", ("p1", "p2"))
target = point(*target)
inside = False
# Build list of coordinate pairs
# First, turn it into named tuples
poly = map(lambda p: point(*p), poly)
# Make two lists, with list2 shifted forward by one and wrapped around
list1 = poly
list2 = poly[1:] + [poly[0]]
poly = map(line, list1, list2)
for l in poly:
p1 = l.p1
p2 = l.p2
if p1.y == p2.y:
# This line is horizontal and thus not relevant.
continue
if max(p1.y, p2.y) < target.y <= min(p1.y, p2.y):
# This line is too high or low
continue
if target.x < max(p1.x, p2.x):
# Ignore this line because it's to the right of our point
continue
# Now, the line still might be to the right of our target point, but
# still to the right of one of the line endpoints.
rise = p1.y - p2.y
run = p1.x - p2.x
try:
slope = rise/float(run)
except ZeroDivisionError:
slope = float('inf')
# Find the x-intercept, that is, the place where the line we are
# testing equals the y value of our target point.
# Pick one of the line points, and figure out what the run between it
# and the target point is.
run_to_intercept = target.x - p1.x
x_intercept = p1.x + run_to_intercept / slope
if target.x < x_intercept:
# We almost crossed the line.
continue
inside = not inside
return inside
def toworld(header, pix):
""" converts pixel to world coordnates """
posx = header['CRVAL1'] + (pix[0] - header['CRPIX1']) * header['CDELT1']
posy = header['CRVAL2'] + (pix[1] - header['CRPIX2']) * header['CDELT2']
return (posx, posy)
def topixel(header, pos):
""" converts world coordinates ti pixel """
pix = (pos[0] - header['CRVAL1']) / header['CDELT1'] + header['CRPIX1']
piy = (pos[1] - header['CRVAL2']) / header['CDELT2'] + header['CRPIX2']
return (pix, piy)
def toworldn(header, pix):
""" converts pixel to world coordnates """
p = np.array(pix)
n,m,k = p.shape
p = p.reshape((n*k,m)).T
p[0] = header['CRVAL1'] + (p[0] - header['CRPIX1']) * header['CDELT1']
p[1] = header['CRVAL2'] + (p[1] - header['CRPIX2']) * header['CDELT2']
p = p.T
pos = p.reshape((n,m,k))
return pos
def topixeln(header, pos):
""" converts world coordinates ti pixel """
p = np.array(pos)
n,m,k = p.shape
p = p.reshape((n*k,m)).T
p[0] = (p[0] - header['CRVAL1']) / header['CDELT1'] + header['CRPIX1']
p[1] = (p[1] - header['CRVAL2']) / header['CDELT2'] + header['CRPIX2']
p = p.T
pix = p.reshape((n,m,k))
return pix
def smooth(x, window_len=11, window='hanning'):
"""smooth the data using a window with requested size.
This method is based on the convolution of a scaled window with the signal.
The signal is prepared by introducing reflected copies of the signal
(with the window size) in both ends so that transient parts are minimized
in the begining and end part of the output signal.
input:
x: the input signal
window_len: the dimension of the smoothing window; should be an odd integer
window: the type of window from 'flat', 'hanning', 'hamming', 'bartlett', 'blackman'
flat window will produce a moving average smoothing.
output:
the smoothed signal
example:
t=linspace(-2,2,0.1)
x=sin(t)+randn(len(t))*0.1
y=smooth(x)
see also:
numpy.hanning, numpy.hamming, numpy.bartlett, numpy.blackman, numpy.convolve
scipy.signal.lfilter
TODO: the window parameter could be the window itself if an array instead of a string
NOTE: length(output) != length(input), to correct this: return y[(window_len/2-1):-(window_len/2)] instead of just y.
"""
# nan interpolation
x = nan_interpolation(x)
# window_len must be odd
if 1-window_len%2: window_len += 1
if x.ndim != 1:
raise ValueError, "smooth only accepts 1 dimension arrays."
if x.size < window_len:
raise ValueError, "Input vector needs to be bigger than window size."
if window_len < 3:
return x
if not window in ['flat', 'hanning', 'hamming', 'bartlett', 'blackman']:
raise ValueError, "Window is on of 'flat', 'hanning', 'hamming', 'bartlett', 'blackman'"
s=np.r_[x[window_len-1:0:-1], x, x[-1:-window_len:-1]]
if window == 'flat': #moving average
w = np.ones(window_len, 'd')
else:
w = eval('np.'+window+'(window_len)')
y = np.convolve(w/w.sum(), s, mode='valid')
return y[(window_len/2):-(window_len/2)]
ly = (len(y)-len(x))/2
return y[ly:-ly]
"""
Port of Manuel Guizar's code from:
http://www.mathworks.com/matlabcentral/fileexchange/18401-efficient-subpixel-image-registration-by-cross-correlation
"""
import numpy as np
def _upsampled_dft(data, upsampled_region_size,
upsample_factor=1, axis_offsets=None):
"""
Upsampled DFT by matrix multiplication.
This code is intended to provide the same result as if the following
operations were performed:
- Embed the array "data" in an array that is ``upsample_factor`` times
larger in each dimension. ifftshift to bring the center of the
image to (1,1).
- Take the FFT of the larger array.
- Extract an ``[upsampled_region_size]`` region of the result, starting
with the ``[axis_offsets+1]`` element.
It achieves this result by computing the DFT in the output array without
the need to zeropad. Much faster and memory efficient than the zero-padded
FFT approach if ``upsampled_region_size`` is much smaller than
``data.size * upsample_factor``.
Parameters
----------
data : 2D ndarray
The input data array (DFT of original data) to upsample.
upsampled_region_size : integer or tuple of integers, optional
The size of the region to be sampled. If one integer is provided, it
is duplicated up to the dimensionality of ``data``.
upsample_factor : integer, optional
The upsampling factor. Defaults to 1.
axis_offsets : tuple of integers, optional
The offsets of the region to be sampled. Defaults to None (uses
image center)
Returns
-------
output : 2D ndarray
The upsampled DFT of the specified region.
"""
# if people pass in an integer, expand it to a list of equal-sized sections
if not hasattr(upsampled_region_size, "__iter__"):
upsampled_region_size = [upsampled_region_size, ] * data.ndim
else:
if len(upsampled_region_size) != data.ndim:
raise ValueError("shape of upsampled region sizes must be equal "
"to input data's number of dimensions.")
if axis_offsets is None:
axis_offsets = [0, ] * data.ndim
else:
if len(axis_offsets) != data.ndim:
raise ValueError("number of axis offsets must be equal to input "
"data's number of dimensions.")
col_kernel = np.exp(
(-1j * 2 * np.pi / (data.shape[1] * upsample_factor)) *
(np.fft.ifftshift(np.arange(data.shape[1]))[:, None] -
np.floor(data.shape[1] / 2)).dot(
np.arange(upsampled_region_size[1])[None, :] - axis_offsets[1])
)
row_kernel = np.exp(
(-1j * 2 * np.pi / (data.shape[0] * upsample_factor)) *
(np.arange(upsampled_region_size[0])[:, None] - axis_offsets[0]).dot(
np.fft.ifftshift(np.arange(data.shape[0]))[None, :] -
np.floor(data.shape[0] / 2))
)
return row_kernel.dot(data).dot(col_kernel)
def _compute_phasediff(cross_correlation_max):
"""
Compute global phase difference between the two images (should be
zero if images are non-negative).
Parameters
----------
cross_correlation_max : complex
The complex value of the cross correlation at its maximum point.
"""
return np.arctan2(cross_correlation_max.imag, cross_correlation_max.real)
def _compute_error(cross_correlation_max, src_amp, target_amp):
"""
Compute RMS error metric between ``src_image`` and ``target_image``.
Parameters
----------
cross_correlation_max : complex
The complex value of the cross correlation at its maximum point.
src_amp : float
The normalized average image intensity of the source image
target_amp : float
The normalized average image intensity of the target image
"""
error = 1.0 - cross_correlation_max * cross_correlation_max.conj() /\
(src_amp * target_amp)
return np.sqrt(np.abs(error))
#[1] Manuel Guizar-Sicairos, Samuel T. Thurman, and James R. Fienup,
# "Efficient subpixel image registration algorithms," Optics Letters 33,
# 156-158 (2008).
#======================================
# Cross-Correlation (Phase Correlation)
#======================================
def register_translation(src_image, target_image, upsample_factor=1,
space="real"):
"""
Efficient subpixel image translation registration by cross-correlation.
This code gives the same precision as the FFT upsampled cross-correlation
in a fraction of the computation time and with reduced memory requirements.
It obtains an initial estimate of the cross-correlation peak by an FFT and
then refines the shift estimation by upsampling the DFT only in a small
neighborhood of that estimate by means of a matrix-multiply DFT.
Parameters
----------
src_image : ndarray
Reference image.
target_image : ndarray
Image to register. Must be same dimensionality as ``src_image``.
upsample_factor : int, optional
Upsampling factor. Images will be registered to within
``1 / upsample_factor`` of a pixel. For example
``upsample_factor == 20`` means the images will be registered
within 1/20th of a pixel. Default is 1 (no upsampling)
space : string, one of "real" or "fourier"
Defines how the algorithm interprets input data. "real" means data
will be FFT'd to compute the correlation, while "fourier" data will
bypass FFT of input data. Case insensitive.
Returns
-------
shifts : ndarray
Shift vector (in pixels) required to register ``target_image`` with
``src_image``. Axis ordering is consistent with numpy (e.g. Z, Y, X)
error : float
Translation invariant normalized RMS error between ``src_image`` and
``target_image``.
phasediff : float
Global phase difference between the two images (should be
zero if images are non-negative).
References
----------
.. [1] Manuel Guizar-Sicairos, Samuel T. Thurman, and James R. Fienup,
"Efficient subpixel image registration algorithms,"
Optics Letters 33, 156-158 (2008).
"""
# images must be the same shape
if src_image.shape != target_image.shape:
raise ValueError("Error: images must be same size for "
"register_translation")
# only 2D data makes sense right now
if src_image.ndim != 2 and upsample_factor > 1:
raise NotImplementedError("Error: register_translation only supports "
"subpixel registration for 2D images")
# assume complex data is already in Fourier space
if space.lower() == 'fourier':
src_freq = src_image
target_freq = target_image
# real data needs to be fft'd.
elif space.lower() == 'real':
src_image = np.array(src_image, dtype=np.complex128, copy=False)
target_image = np.array(target_image, dtype=np.complex128, copy=False)
src_freq = np.fft.fftn(src_image)
target_freq = np.fft.fftn(target_image)
else:
raise ValueError("Error: register_translation only knows the \"real\" "
"and \"fourier\" values for the ``space`` argument.")
# Whole-pixel shift - Compute cross-correlation by an IFFT
shape = src_freq.shape
image_product = src_freq * target_freq.conj()
cross_correlation = np.fft.ifftn(image_product)
# Locate maximum
maxima = np.unravel_index(np.argmax(np.abs(cross_correlation)),
cross_correlation.shape)
midpoints = np.array([np.fix(axis_size / 2) for axis_size in shape])
shifts = np.array(maxima, dtype=np.float64)
shifts[shifts > midpoints] -= np.array(shape)[shifts > midpoints]
if upsample_factor == 1:
src_amp = np.sum(np.abs(src_freq) ** 2) / src_freq.size
target_amp = np.sum(np.abs(target_freq) ** 2) / target_freq.size
CCmax = cross_correlation.max()
# If upsampling > 1, then refine estimate with matrix multiply DFT
else:
# Initial shift estimate in upsampled grid
shifts = np.round(shifts * upsample_factor) / upsample_factor
upsampled_region_size = np.ceil(upsample_factor * 1.5)
# Center of output array at dftshift + 1
dftshift = np.fix(upsampled_region_size / 2.0)
upsample_factor = np.array(upsample_factor, dtype=np.float64)
normalization = (src_freq.size * upsample_factor ** 2)
# Matrix multiply DFT around the current shift estimate
sample_region_offset = dftshift - shifts*upsample_factor
cross_correlation = _upsampled_dft(image_product.conj(),
upsampled_region_size,
upsample_factor,
sample_region_offset).conj()
cross_correlation /= normalization
# Locate maximum and map back to original pixel grid
maxima = np.array(np.unravel_index(
np.argmax(np.abs(cross_correlation)),
cross_correlation.shape),
dtype=np.float64)
maxima -= dftshift
shifts = shifts + maxima / upsample_factor
CCmax = cross_correlation.max()
src_amp = _upsampled_dft(src_freq * src_freq.conj(),
1, upsample_factor)[0, 0]
src_amp /= normalization
target_amp = _upsampled_dft(target_freq * target_freq.conj(),
1, upsample_factor)[0, 0]
target_amp /= normalization
# If its only one row or column the shift along that dimension has no
# effect. We set to zero.
for dim in range(src_freq.ndim):
if shape[dim] == 1:
shifts[dim] = 0
return shifts, _compute_error(CCmax, src_amp, target_amp),\
_compute_phasediff(CCmax)
def center_of_gravity(data1, data2, clip=None):
import scipy.ndimage as nd
mask1 = data1 > clip*np.nanmax(data1)
mask2 = data2 > clip*np.nanmax(data2)
d1 = np.where(mask1*mask2, data1, np.nan)
d2 = np.where(mask1*mask2, data2, np.nan)
b1x, b1y = nd.measurements.center_of_mass(d1, ~np.isnan(d1))
b2x, b2y = nd.measurements.center_of_mass(d2, ~np.isnan(d2))
return b1x-b2x, b1y-b2y
from scipy.ndimage import fourier_shift
def subpixel_shift(data1, data2, clip=0.1):
dx, dy = center_of_gravity(data1, data2, clip=clip)
nanz = 0
dxs, dys = dx, dy
d2 = data2.copy()
while (abs(dx) > 0.1 or abs(dy) > 0.1) and nanz < 100:
data2 = np.fft.ifft2(fourier_shift(np.fft.fft2(data2), (dx, dy))).real
dx, dy = center_of_gravity(data1, data2, clip=0.1)
dxs += dx
dys += dy
nanz += 1
data2 = np.fft.ifft2(fourier_shift(np.fft.fft2(d2), (dxs, dys))).real
return dxs, dys, data2
def rebin1(a, size):
sh = 1,1,size,a.shape[0]//size
return a.reshape(sh).mean(-1)
def rebin(a, shape):
sh = shape[0],a.shape[0]//shape[0],shape[1],a.shape[1]//shape[1]
return a.reshape(sh).mean(-1).mean(1)
def hist_range_threshold(hist, bin_edges, percent):
hist = np.concatenate((hist, [0]))
threshold = .5*percent/100*hist.sum()
i_bin_min = np.cumsum(hist).searchsorted(threshold)
i_bin_max = -1-np.cumsum(np.flipud(hist)).searchsorted(threshold)
return bin_edges[i_bin_min], bin_edges[i_bin_max]
def color_get_histogram(data, nbins):
from guiqwt._scaler import _histogram
if data is None:
return [0,], [0,1]
_min = np.nanmin(data)
_max = np.nanmax(data)
bins = np.unique(np.array(np.linspace(_min, _max, nbins+1), dtype=data.dtype))
res2 = np.zeros((bins.size+1,), np.uint32)
_histogram(data.flatten(), bins, res2)
res = res2[1:-1], bins
return res
def lut_range_threshold(data, nbins, percent):
hist, bin_edges = color_get_histogram(data, nbins)
return hist_range_threshold(hist, bin_edges, percent)
def plotPDF(data, cmap, percent, rebin=1):
from matplotlib import pylab as plt
import matplotlib
import Image
from nodmath import nan_interpolation, map_zoom, hist_range_threshold, color_get_histogram,\
lut_range_threshold
xmin, xmax = lut_range_threshold(data, 256, percent)
data = np.clip(data[3:-3, 3:-3], xmin, xmax)
rows, cols = data.shape
if rebin > 1:
data = map_zoom(data, rebin, order=3, prefilter=True)
m = matplotlib.cm.ScalarMappable(norm=None, cmap=cmap)
colormapped = m.to_rgba(data)*255
outputImage = Image.fromarray(np.uint8(colormapped))
outputImage.save("pixmap.png")
#outputImage.show()
#fig = plt.figure()
#ax = fig.add_axes((0,0,1,1))
#ax.set_axis_off()
#ax.matshow(data, cmap=cmap)
#plt.show()
import scipy, scipy.signal
def savitzky_golay( y, window_size, order, deriv = 0 ):
r"""Smooth (and optionally differentiate) data with a Savitzky-Golay filter.
The Savitzky-Golay filter removes high frequency noise from data.
It has the advantage of preserving the original shape and
features of the signal better than other types of filtering
approaches, such as moving averages techhniques.
Parameters
----------
y : array_like, shape (N,)
the values of the time history of the signal.
window_size : int
the length of the window. Must be an odd integer number.
order : int
the order of the polynomial used in the filtering.
Must be less then `window_size` - 1.
deriv: int
the order of the derivative to compute (default = 0 means only smoothing)
Returns
-------
ys : ndarray, shape (N)
the smoothed signal (or it's n-th derivative).
Notes
-----
The Savitzky-Golay is a type of low-pass filter, particularly
suited for smoothing noisy data. The main idea behind this
approach is to make for each point a least-square fit with a
polynomial of high order over a odd-sized window centered at
the point.
Examples
--------
t = np.linspace(-4, 4, 500)
y = np.exp( -t**2 ) + np.random.normal(0, 0.05, t.shape)
ysg = savitzky_golay(y, window_size=31, order=4)
import matplotlib.pyplot as plt
plt.plot(t, y, label='Noisy signal')
plt.plot(t, np.exp(-t**2), 'k', lw=1.5, label='Original signal')
plt.plot(t, ysg, 'r', label='Filtered signal')
plt.legend()
plt.show()
References
----------
.. [1] A. Savitzky, M. J. E. Golay, Smoothing and Differentiation of
Data by Simplified Least Squares Procedures. Analytical
Chemistry, 1964, 36 (8), pp 1627-1639.
.. [2] Numerical Recipes 3rd Edition: The Art of Scientific Computing
W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery
Cambridge University Press ISBN-13: 9780521880688
"""
try:
window_size = np.abs( np.int( window_size ) )
order = np.abs( np.int( order ) )
except ValueError, msg:
raise ValueError( "window_size and order have to be of type int" )
if window_size % 2 != 1 or window_size < 1:
raise TypeError( "window_size size must be a positive odd number" )
if window_size < order + 2:
raise TypeError( "window_size is too small for the polynomials order" )
order_range = range( order + 1 )
half_window = ( window_size - 1 ) // 2
# precompute coefficients
b = np.mat( [[k ** i for i in order_range] for k in range( -half_window, half_window + 1 )] )
m = np.linalg.pinv( b ).A[deriv]
# pad the signal at the extremes with
# values taken from the signal itself
firstvals = y[0] - np.abs( y[1:half_window + 1][::-1] - y[0] )
lastvals = y[-1] + np.abs( y[-half_window - 1:-1][::-1] - y[-1] )
y = np.concatenate( ( firstvals, y, lastvals ) )
return np.convolve( m, y, mode = 'valid' )
def savitzky_golay_piecewise( xvals, data, kernel = 11, order = 4 ):
turnpoint = 0
last = len( xvals )
if xvals[1] > xvals[0] : #x is increasing?
for i in range( 1, last ) : #yes
if xvals[i] < xvals[i - 1] : #search where x starts to fall
turnpoint = i
break
else: #no, x is decreasing
for i in range( 1, last ) : #search where it starts to rise
if xvals[i] > xvals[i - 1] :
turnpoint = i
break
if turnpoint == 0 : #no change in direction of x
return savitzky_golay( data, kernel, order )
else:
#smooth the first piece
firstpart = savitzky_golay( data[0:turnpoint], kernel, order )
#recursively smooth the rest
rest = savitzky_golay_piecewise( xvals[turnpoint:], data[turnpoint:], kernel, order )
return numpy.concatenate( ( firstpart, rest ) )
def sgolay2d ( z, window_size, order, derivative = None ):
"""
"""
# number of terms in the polynomial expression
n_terms = ( order + 1 ) * ( order + 2 ) / 2.0
if window_size % 2 == 0:
raise ValueError( 'window_size must be odd' )
if window_size ** 2 < n_terms:
raise ValueError( 'order is too high for the window size' )
half_size = window_size // 2
# exponents of the polynomial.
# p(x,y) = a0 + a1*x + a2*y + a3*x^2 + a4*y^2 + a5*x*y + ...
# this line gives a list of two item tuple. Each tuple contains
# the exponents of the k-th term. First element of tuple is for x
# second element for y.
# Ex. exps = [(0,0), (1,0), (0,1), (2,0), (1,1), (0,2), ...]
exps = [ ( k - n, n ) for k in range( order + 1 ) for n in range( k + 1 ) ]
# coordinates of points
ind = np.arange( -half_size, half_size + 1, dtype = np.float64 )
dx = np.repeat( ind, window_size )
dy = np.tile( ind, [window_size, 1] ).reshape( window_size ** 2, )
# build matrix of system of equation
A = np.empty( ( window_size ** 2, len( exps ) ) )
for i, exp in enumerate( exps ):
A[:, i] = ( dx ** exp[0] ) * ( dy ** exp[1] )
# pad input array with appropriate values at the four borders
new_shape = z.shape[0] + 2 * half_size, z.shape[1] + 2 * half_size
Z = np.zeros( ( new_shape ) )
# top band
band = z[0, :]
Z[:half_size, half_size:-half_size] = band - np.abs( np.flipud( z[1:half_size + 1, :] ) - band )
# bottom band
band = z[-1, :]
Z[-half_size:, half_size:-half_size] = band + np.abs( np.flipud( z[-half_size - 1:-1, :] ) - band )
# left band
band = np.tile( z[:, 0].reshape( -1, 1 ), [1, half_size] )
Z[half_size:-half_size, :half_size] = band - np.abs( np.fliplr( z[:, 1:half_size + 1] ) - band )
# right band
band = np.tile( z[:, -1].reshape( -1, 1 ), [1, half_size] )
Z[half_size:-half_size, -half_size:] = band + np.abs( np.fliplr( z[:, -half_size - 1:-1] ) - band )
# central band
Z[half_size:-half_size, half_size:-half_size] = z
# top left corner
band = z[0, 0]
Z[:half_size, :half_size] = band - np.abs( np.flipud( np.fliplr( z[1:half_size + 1, 1:half_size + 1] ) ) - band )
# bottom right corner
band = z[-1, -1]
Z[-half_size:, -half_size:] = band + np.abs( np.flipud( np.fliplr( z[-half_size - 1:-1, -half_size - 1:-1] ) ) - band )
# top right corner
band = Z[half_size, -half_size:]
Z[:half_size, -half_size:] = band - np.abs( np.flipud( Z[half_size + 1:2 * half_size + 1, -half_size:] ) - band )
# bottom left corner
band = Z[-half_size:, half_size].reshape( -1, 1 )
Z[-half_size:, :half_size] = band - np.abs( np.fliplr( Z[-half_size:, half_size + 1:2 * half_size + 1] ) - band )
# solve system and convolve
if derivative == None:
m = np.linalg.pinv( A )[0].reshape( ( window_size, -1 ) )
return scipy.signal.fftconvolve( Z, m, mode = 'valid' )
elif derivative == 'col':
c = np.linalg.pinv( A )[1].reshape( ( window_size, -1 ) )
return scipy.signal.fftconvolve( Z, -c, mode = 'valid' )
elif derivative == 'row':
r = np.linalg.pinv( A )[2].reshape( ( window_size, -1 ) )
return scipy.signal.fftconvolve( Z, -r, mode = 'valid' )
elif derivative == 'both':
c = np.linalg.pinv( A )[1].reshape( ( window_size, -1 ) )
r = np.linalg.pinv( A )[2].reshape( ( window_size, -1 ) )
return scipy.signal.fftconvolve( Z, -r, mode = 'valid' ), scipy.signal.fftconvolve( Z, -c, mode = 'valid' )
def main():
Z = np.arange(0,36).reshape((6,6))
print Z
print
print "extract(Z, shape=(3,3), position=(0,0))"
print extract(Z, shape=(3,3), position=(0,0))
print
print "extract(Z, shape=(3,3), position=(3,3))"
print extract(Z, shape=(3,3), position=(3,3))
print
print "extract(Z, shape=(10,10), position=(3,3))"
print extract(Z, shape=(10,10), position=(3,3))
if __name__ == '__main__':
main()