/usr/lib/python2.7/dist-packages/photutils/morphology.py is in python-photutils 0.2.1-2.
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"""
Functions for centroiding sources and measuring their morphological
properties.
"""
from __future__ import (absolute_import, division, print_function,
unicode_literals)
import collections
import numpy as np
from astropy.modeling.models import Gaussian1D, Gaussian2D, Const1D, Const2D
from astropy.modeling.fitting import LevMarLSQFitter
from astropy.nddata.utils import overlap_slices
from .segmentation import SourceProperties
import warnings
from astropy.utils.exceptions import AstropyUserWarning
__all__ = ['GaussianConst2D', 'centroid_com', 'gaussian1d_moments',
'marginalize_data2d', 'centroid_1dg', 'centroid_2dg',
'fit_2dgaussian', 'data_properties', 'cutout_footprint']
class _GaussianConst1D(Const1D + Gaussian1D):
"""A 1D Gaussian plus a constant model."""
class GaussianConst2D(Const2D + Gaussian2D):
"""
A 2D Gaussian plus a constant model.
Parameters
----------
amplitude_0 : float
Value of the constant.
amplitude_1 : float
Amplitude of the Gaussian.
x_mean_1 : float
Mean of the Gaussian in x.
y_mean_1 : float
Mean of the Gaussian in y.
x_stddev_1 : float
Standard deviation of the Gaussian in x.
``x_stddev`` and ``y_stddev`` must be specified unless a covariance
matrix (``cov_matrix``) is input.
y_stddev_1 : float
Standard deviation of the Gaussian in y.
``x_stddev`` and ``y_stddev`` must be specified unless a covariance
matrix (``cov_matrix``) is input.
theta_1 : float, optional
Rotation angle in radians. The rotation angle increases
counterclockwise.
cov_matrix_1 : ndarray, optional
A 2x2 covariance matrix. If specified, overrides the ``x_stddev``,
``y_stddev``, and ``theta`` specification.
"""
def _convert_image(data, mask=None):
"""
Convert the input data to a float64 (double) `numpy.ndarray`,
required for input to `skimage.measure.moments` and
`skimage.measure.moments_central`.
The input ``data`` is copied unless it already has that
`numpy.dtype`.
If ``mask`` is input, then masked pixels are set to zero in the
output ``data``.
Parameters
----------
data : array_like
The 2D array of the image.
mask : array_like (bool), optional
A boolean mask, with the same shape as ``data``, where a `True`
value indicates the corresponding element of ``data`` is masked.
Masked pixels are set to zero in the output ``data``.
Returns
-------
image : `numpy.ndarray`, float64
The converted 2D array of the image, where masked pixels have
been set to zero.
"""
try:
if mask is None:
copy = False
else:
copy = True
image = np.asarray(data).astype(np.float, copy=copy)
except TypeError: # pragma: no cover
image = np.asarray(data).astype(np.float) # for numpy <= 1.6
if mask is not None:
mask = np.asanyarray(mask)
if data.shape != mask.shape:
raise ValueError('data and mask must have the same shape')
image[mask] = 0.0
return image
def centroid_com(data, mask=None):
"""
Calculate the centroid of a 2D array as its center of mass
determined from image moments.
Parameters
----------
data : array_like
The 2D array of the image.
mask : array_like (bool), optional
A boolean mask, with the same shape as ``data``, where a `True`
value indicates the corresponding element of ``data`` is masked.
Returns
-------
xcen, ycen : float
(x, y) coordinates of the centroid.
"""
from skimage.measure import moments
data = _convert_image(data, mask=mask)
m = moments(data, 1)
xcen = m[1, 0] / m[0, 0]
ycen = m[0, 1] / m[0, 0]
return xcen, ycen
def gaussian1d_moments(data, mask=None):
"""
Estimate 1D Gaussian parameters from the moments of 1D data.
This function can be useful for providing initial parameter values
when fitting a 1D Gaussian to the ``data``.
Parameters
----------
data : array_like (1D)
The 1D array.
mask : array_like (1D bool), optional
A boolean mask, with the same shape as ``data``, where a `True`
value indicates the corresponding element of ``data`` is masked.
Returns
-------
amplitude, mean, stddev : float
The estimated parameters of a 1D Gaussian.
"""
if mask is not None:
mask = np.asanyarray(mask)
data = data.copy()
data[mask] = 0.
x = np.arange(data.size)
x_mean = np.sum(x * data) / np.sum(data)
x_stddev = np.sqrt(abs(np.sum(data * (x - x_mean)**2) / np.sum(data)))
amplitude = np.nanmax(data) - np.nanmin(data)
return amplitude, x_mean, x_stddev
def marginalize_data2d(data, error=None, mask=None):
"""
Generate the marginal x and y distributions from a 2D data array.
Parameters
----------
data : array_like
The 2D data array.
error : array_like, optional
The 2D array of the 1-sigma errors of the input ``data``.
mask : array_like (bool), optional
A boolean mask, with the same shape as ``data``, where a `True`
value indicates the corresponding element of ``data`` is masked.
Returns
-------
marginal_data : list of `~numpy.ndarray`
The marginal x and y distributions of the input ``data``.
marginal_error : list of `~numpy.ndarray`
The marginal x and y distributions of the input ``error``.
marginal_mask : list of `~numpy.ndarray` (bool)
The marginal x and y distributions of the input ``mask``.
"""
if error is not None:
marginal_error = np.array(
[np.sqrt(np.sum(error**2, axis=i)) for i in [0, 1]])
else:
marginal_error = [None, None]
if mask is not None:
mask = np.asanyarray(mask)
marginal_mask = [np.sum(mask, axis=i).astype(np.bool) for i in [0, 1]]
else:
marginal_mask = [None, None]
marginal_data = [np.sum(data, axis=i) for i in [0, 1]]
return marginal_data, marginal_error, marginal_mask
def centroid_1dg(data, error=None, mask=None):
"""
Calculate the centroid of a 2D array by fitting 1D Gaussians to the
marginal x and y distributions of the array.
Parameters
----------
data : array_like
The 2D data array.
error : array_like, optional
The 2D array of the 1-sigma errors of the input ``data``.
mask : array_like (bool), optional
A boolean mask, with the same shape as ``data``, where a `True`
value indicates the corresponding element of ``data`` is masked.
Returns
-------
xcen, ycen : float
(x, y) coordinates of the centroid.
"""
mdata, merror, mmask = marginalize_data2d(data, error=error, mask=mask)
if merror[0] is None and mmask[0] is None:
mweights = [None, None]
else:
if merror[0] is not None:
mweights = [(1.0 / merror[i].clip(min=1.e-30)) for i in [0, 1]]
else:
mweights = np.array([np.ones(data.shape[1]),
np.ones(data.shape[0])])
# down-weight masked pixels
for i in [0, 1]:
mweights[i][mmask[i]] = 1.e-20
const_init = np.min(data)
centroid = []
for (mdata_i, mweights_i, mmask_i) in zip(mdata, mweights, mmask):
params_init = gaussian1d_moments(mdata_i, mask=mmask_i)
g_init = _GaussianConst1D(const_init, *params_init)
fitter = LevMarLSQFitter()
x = np.arange(mdata_i.size)
g_fit = fitter(g_init, x, mdata_i, weights=mweights_i)
centroid.append(g_fit.mean_1.value)
return tuple(centroid)
def centroid_2dg(data, error=None, mask=None):
"""
Calculate the centroid of a 2D array by fitting a 2D Gaussian (plus
a constant) to the array.
Parameters
----------
data : array_like
The 2D data array.
error : array_like, optional
The 2D array of the 1-sigma errors of the input ``data``.
mask : array_like (bool), optional
A boolean mask, with the same shape as ``data``, where a `True`
value indicates the corresponding element of ``data`` is masked.
Returns
-------
xcen, ycen : float
(x, y) coordinates of the centroid.
"""
gfit = fit_2dgaussian(data, error=error, mask=mask)
return gfit.x_mean_1.value, gfit.y_mean_1.value
def fit_2dgaussian(data, error=None, mask=None):
"""
Fit a 2D Gaussian plus a constant to a 2D image.
Parameters
----------
data : array_like
The 2D array of the image.
error : array_like, optional
The 2D array of the 1-sigma errors of the input ``data``.
mask : array_like (bool), optional
A boolean mask, with the same shape as ``data``, where a `True`
value indicates the corresponding element of ``data`` is masked.
Returns
-------
result : A `GaussianConst2D` model instance.
The best-fitting Gaussian 2D model.
"""
if data.size < 7:
warnings.warn('data array must have a least 7 values to fit a 2D '
'Gaussian plus a constant', AstropyUserWarning)
return None
if error is not None:
weights = 1.0 / error
else:
weights = None
if mask is not None:
mask = np.asanyarray(mask)
if weights is None:
weights = np.ones_like(data)
# down-weight masked pixels
weights[mask] = 1.e-30
# Subtract the minimum of the data as a crude background estimate.
# This will also make the data values positive, preventing issues with
# the moment estimation in data_properties (moments from negative data
# values can yield undefined Gaussian parameters, e.g. x/y_stddev).
shift = np.min(data)
data = np.copy(data) - shift
props = data_properties(data, mask=mask)
init_values = np.array([props.xcentroid.value, props.ycentroid.value,
props.semimajor_axis_sigma.value,
props.semiminor_axis_sigma.value,
props.orientation.value])
init_const = 0. # subtracted data minimum above
init_amplitude = np.nanmax(data) - np.nanmin(data)
g_init = GaussianConst2D(init_const, init_amplitude, *init_values)
fitter = LevMarLSQFitter()
y, x = np.indices(data.shape)
gfit = fitter(g_init, x, y, data, weights=weights)
gfit.amplitude_0 = gfit.amplitude_0 + shift
return gfit
def data_properties(data, mask=None, background=None):
"""
Calculate the centroid and morphological properties of a 2D array,
e.g., an image cutout of an object.
Parameters
----------
data : array_like or `~astropy.units.Quantity`
The 2D array of the image.
mask : array_like (bool), optional
A boolean mask, with the same shape as ``data``, where a `True`
value indicates the corresponding element of ``data`` is masked.
Masked data are excluded from all calculations.
background : float, array_like, or `~astropy.units.Quantity`, optional
The background level that was previously present in the input
``data``. ``background`` may either be a scalar value or a 2D
image with the same shape as the input ``data``. Inputting the
``background`` merely allows for its properties to be measured
within each source segment. The input ``background`` does *not*
get subtracted from the input ``data``, which should already be
background-subtracted.
Returns
-------
result : `~photutils.segmentation.SourceProperties` instance
A `~photutils.segmentation.SourceProperties` object.
"""
segment_image = np.ones(data.shape, dtype=np.int)
return SourceProperties(data, segment_image, label=1, mask=mask,
background=background)
def cutout_footprint(data, position, box_size=3, footprint=None, mask=None,
error=None):
"""
Cut out a region from data (and optional mask and error) centered at
specified (x, y) position.
The size of the region is specified via the ``box_size`` or
``footprint`` keywords. The output mask for the cutout region
represents the combination of the input mask and footprint mask.
Parameters
----------
data : array_like
The 2D array of the image.
position : 2 tuple
The ``(x, y)`` pixel coordinate of the center of the region.
box_size : scalar or tuple, optional
The size of the region to cutout from ``data``. If ``box_size``
is a scalar, then the region shape will be ``(box_size,
box_size)``. Either ``box_size`` or ``footprint`` must be
defined. If they are both defined, then ``footprint`` overrides
``box_size``.
footprint : `~numpy.ndarray` of bools, optional
A boolean array where `True` values describe the local footprint
region. ``box_size=(n, m)`` is equivalent to
``footprint=np.ones((n, m))``. Either ``box_size`` or
``footprint`` must be defined. If they are both defined, then
``footprint`` overrides ``box_size``.
mask : array_like, bool, optional
A boolean mask with the same shape as ``data``, where a `True`
value indicates the corresponding element of ``data`` is masked.
error : array_like, optional
The 2D array of the 1-sigma errors of the input ``data``.
Returns
-------
region_data : `~numpy.ndarray`
The ``data`` cutout.
region_mask : `~numpy.ndarray`
The ``mask`` cutout.
region_error : `~numpy.ndarray`
The ``error`` cutout.
slices : tuple of slices
Slices in each dimension of the ``data`` array used to define
the cutout region.
"""
if len(position) != 2:
raise ValueError('position must have a length of 2')
if footprint is None:
if box_size is None:
raise ValueError('box_size or footprint must be defined.')
if not isinstance(box_size, collections.Iterable):
shape = (box_size, box_size)
else:
if len(box_size) != 2:
raise ValueError('box_size must have a length of 2')
shape = box_size
footprint = np.ones(shape, dtype=bool)
else:
footprint = np.asanyarray(footprint, dtype=bool)
slices_large, slices_small = overlap_slices(data.shape, footprint.shape,
position[::-1])
region_data = data[slices_large]
if error is not None:
region_error = error[slices_large]
else:
region_error = None
if mask is not None:
region_mask = mask[slices_large]
else:
region_mask = np.zeros_like(region_data, dtype=bool)
footprint_mask = ~footprint
footprint_mask = footprint_mask[slices_small] # trim if necessary
region_mask = np.logical_or(region_mask, footprint_mask)
return region_data, region_mask, region_error, slices_large
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