def yGaussianND(param, inds, sidx):
"""
param: (mean, max - mean, z, y, x, sigmaz, sigmay, sigmax)
ind: coordinate as N.indices (float32)
sidx: idx of param where sigma starts (2 + ndim)
"""
s = 2. * param[sidx:] * param[sidx:] # sigma
zyx = param[2:sidx] #- 0.5 # use pixel center
DST = N.zeros(inds[0].shape, inds[0].dtype.type)
for i in range(sidx - 2):
IND = zyx[i] - inds[i]
DST -= (IND * IND) / s[i]
return param[0] + param[1] * N.exp(DST)
def yGaussianND(param, inds, sidx):
"""
param: (mean, max - mean, z, y, x, sigmaz, sigmay, sigmax)
ind: coordinate as N.indices (float32)
sidx: idx of param where sigma starts (2 + ndim)
"""
s = 2. * param[sidx:] * param[sidx:] # sigma
zyx = param[2:sidx] #- 0.5 # use pixel center
DST = N.zeros(inds[0].shape, inds[0].dtype.type)
for i in range(sidx - 2):
IND = zyx[i] - inds[i]
DST -= (IND * IND) / s[i]
return param[0] + param[1] * N.exp(DST)
def logpolar(image, center=None, angles=None, radii=None):
"""Return log-polar transformed image and log base."""
shape = image.shape
if center is None:
center = shape[0] / 2, shape[1] / 2
if angles is None:
angles = shape[0]
if radii is None:
radii = shape[1]
theta = N.zeros((angles, radii), dtype=N.float64)
theta.T[:] = -N.linspace(0, N.pi, angles, endpoint=False)
#d = radii
d = N.hypot(shape[0] - center[0], shape[1] - center[1])
log_base = 10.0**(N.log10(d) / (radii))
radius = N.empty_like(theta)
radius[:] = N.power(log_base, N.arange(radii, dtype=N.float64)) - 1.0
x = radius * N.sin(theta) + center[0]
y = radius * N.cos(theta) + center[1]
output = N.zeros_like(x)
ndii.map_coordinates(image, [x, y], output=output)
return output, log_base
def radialaverage(data, center=None, useMaxShape=False):
"""
data: ND array
center: coordinate of center of radii
useMinShape: the output uses the maximum shape available
return 1D array
"""
if center is None:
center = N.array(data.shape) // 2
if len(center) != data.ndim:
raise ValueError(
'dimension of center (%i) does not match the dimension of data (%i)'
% (len(center), data.ndim))
zyx = N.indices((data.shape))
r = N.zeros(data.shape, N.float32)
for i, t in enumerate(zyx):
r += (t - center[i])**2
r = N.sqrt(r)
#y, x = N.indices((data.shape))
#r = N.sqrt((x - center[0])**2 + (y - center[1])**2) # distance from the center
r = r.astype(N.int)
if data.dtype.type in (N.complex64, N.complex128):
rbin = N.bincount(r.ravel(), data.real.ravel())
ibin = N.bincount(r.ravel(), data.imag.ravel())
tbin = N.empty(rbin.shape, data.dtype.type)
tbin.real = rbin
tbin.imag = ibin
else:
tbin = N.bincount(r.ravel(), data.ravel())
nr = N.bincount(r.ravel())
radialprofile = tbin / nr.astype(N.float32)
if not useMaxShape:
minShape = min(list(N.array(data.shape) - center) + list(center))
radialprofile = radialprofile[:minShape]
return radialprofile
def logpolar(image, center=None, angles=None, radii=None):
"""Return log-polar transformed image and log base."""
shape = image.shape
if center is None:
center = shape[0] / 2, shape[1] / 2
if angles is None:
angles = shape[0]
if radii is None:
radii = shape[1]
theta = N.zeros((angles, radii), dtype=N.float64)
theta.T[:] = -N.linspace(0, N.pi, angles, endpoint=False)
#d = radii
d = N.hypot(shape[0]-center[0], shape[1]-center[1])
log_base = 10.0 ** (N.log10(d) / (radii))
radius = N.empty_like(theta)
radius[:] = N.power(log_base, N.arange(radii,
dtype=N.float64)) - 1.0
x = radius * N.sin(theta) + center[0]
y = radius * N.cos(theta) + center[1]
output = N.zeros_like(x)
ndii.map_coordinates(image, [x, y], output=output)
return output, log_base
def radialaverage(data, center=None, useMaxShape=False):
"""
data: ND array
center: coordinate of center of radii
useMinShape: the output uses the maximum shape available
return 1D array
"""
if center is None:
center = N.array(data.shape) // 2
if len(center) != data.ndim:
raise ValueError('dimension of center (%i) does not match the dimension of data (%i)' % (len(center), data.ndim))
zyx = N.indices((data.shape))
r = N.zeros(data.shape, N.float32)
for i, t in enumerate(zyx):
r += (t - center[i])**2
r = N.sqrt(r)
#y, x = N.indices((data.shape))
#r = N.sqrt((x - center[0])**2 + (y - center[1])**2) # distance from the center
r = r.astype(N.int)
if data.dtype.type in (N.complex64, N.complex128):
rbin = N.bincount(r.ravel(), data.real.ravel())
ibin = N.bincount(r.ravel(), data.imag.ravel())
tbin = N.empty(rbin.shape, data.dtype.type)
tbin.real = rbin
tbin.imag = ibin
else:
tbin = N.bincount(r.ravel(), data.ravel())
nr = N.bincount(r.ravel())
radialprofile = tbin / nr.astype(N.float32)
if not useMaxShape:
minShape = min(list(N.array(data.shape) - center) + list(center))
radialprofile = radialprofile[:minShape]
return radialprofile
def keepShape(a, shape, difmod=None):
canvas = N.zeros(shape, a.dtype.type)
if difmod is None:
dif = (shape - N.array(a.shape, N.float32)) / 2.
mod = N.ceil(N.mod(dif, 1))
else:
dif, mod = difmod
dif = N.where(dif > 0, N.ceil(dif), N.floor(dif))
# smaller
aoff = N.where(dif < 0, 0, dif)
aslc = [slice(dp, shape[i] - dp + mod[i]) for i, dp in enumerate(aoff)]
# larger
coff = N.where(dif > 0, 0, -dif)
cslc = [slice(dp, a.shape[i] - dp + mod[i]) for i, dp in enumerate(coff)]
canvas[aslc] = a[cslc]
if difmod is None:
return canvas, mod
else:
return canvas
def keepShape(a, shape, difmod=None):
canvas = N.zeros(shape, a.dtype.type)
if difmod is None:
dif = (shape - N.array(a.shape, N.float32)) / 2.
mod = N.ceil(N.mod(dif, 1))
else:
dif, mod = difmod
dif = N.where(dif > 0, N.ceil(dif), N.floor(dif))
# smaller
aoff = N.where(dif < 0, 0, dif)
aslc = [slice(dp, shape[i]-dp+mod[i]) for i, dp in enumerate(aoff)]
# larger
coff = N.where(dif > 0, 0, -dif)
cslc = [slice(dp, a.shape[i]-dp+mod[i]) for i, dp in enumerate(coff)]
canvas[aslc] = a[cslc]
if difmod is None:
return canvas, mod
else:
return canvas
