/usr/lib/python3/dist-packages/photutils/detection/findstars.py is in python3-photutils 0.3-3.
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"""
This module implements classes, called Finders, for detecting stars in
an astronomical image. The convention is that all Finders are subclasses
of an abstract class called ``StarFinderBase``. Each Finder class
should define a method called ``find_stars`` that finds stars in an
image.
"""
from __future__ import (absolute_import, division, print_function,
unicode_literals)
from collections import defaultdict
import warnings
import math
import abc
import numpy as np
from astropy.extern import six
from astropy.table import Column, Table
from astropy.utils.exceptions import AstropyUserWarning
from astropy.utils import deprecated
from astropy.utils.misc import InheritDocstrings
from astropy.stats import gaussian_fwhm_to_sigma
from .core import find_peaks
from ..utils.convolution import filter_data
__all__ = ['DAOStarFinder', 'IRAFStarFinder', 'StarFinderBase',
'daofind', 'irafstarfind']
class _ABCMetaAndInheritDocstrings(InheritDocstrings, abc.ABCMeta):
pass
@deprecated(0.3, alternative='DAOStarFinder')
def daofind(data, threshold, fwhm, ratio=1.0, theta=0.0, sigma_radius=1.5,
sharplo=0.2, sharphi=1.0, roundlo=-1.0, roundhi=1.0, sky=0.0,
exclude_border=False):
finder = DAOStarFinder(threshold, fwhm, ratio, theta, sigma_radius,
sharplo, sharphi, roundlo, roundhi, sky,
exclude_border)
return finder(data)
@deprecated(0.3, alternative='IRAFStarFinder')
def irafstarfind(data, threshold, fwhm, sigma_radius=1.5, minsep_fwhm=2.5,
sharplo=0.5, sharphi=2.0, roundlo=0.0, roundhi=0.2,
sky=None, exclude_border=False):
finder = IRAFStarFinder(threshold, fwhm, sigma_radius, minsep_fwhm,
sharplo, sharphi, roundlo, roundhi, sky,
exclude_border)
return finder(data)
@six.add_metaclass(_ABCMetaAndInheritDocstrings)
class StarFinderBase(object):
"""
Abstract base class for Star Finders.
"""
def __call__(self, data):
return self.find_stars(data)
@abc.abstractmethod
def find_stars(self, data):
"""
Find stars in an astronomical image.
Parameters
----------
data : array_like
The 2D image array.
Returns
-------
table : `~astropy.table.Table`
A table of found objects with the following parameters:
* ``id``: unique object identification number.
* ``xcentroid, ycentroid``: object centroid.
* ``sharpness``: object sharpness.
* ``roundness1``: object roundness based on symmetry.
* ``roundness2``: object roundness based on marginal Gaussian
fits.
* ``npix``: number of pixels in the Gaussian kernel.
* ``sky``: the input ``sky`` parameter.
* ``peak``: the peak, sky-subtracted, pixel value of the object.
* ``flux``: the object flux calculated as the peak density in
the convolved image divided by the detection threshold. This
derivation matches that of `DAOFIND`_ if ``sky`` is 0.0.
* ``mag``: the object instrumental magnitude calculated as
``-2.5 * log10(flux)``. The derivation matches that of
`DAOFIND`_ if ``sky`` is 0.0.
Notes
-----
For the convolution step, this routine sets pixels beyond the
image borders to 0.0. The equivalent parameters in IRAF's
`starfind`_ are ``boundary='constant'`` and ``constant=0.0``.
IRAF's `starfind`_ uses ``hwhmpsf``, ``fradius``, and ``sepmin``
as input parameters. The equivalent input values for
`~photutils.detection.IRAFStarFinder` are:
* ``fwhm = hwhmpsf * 2``
* ``sigma_radius = fradius * sqrt(2.0*log(2.0))``
* ``minsep_fwhm = 0.5 * sepmin``
The main differences between
`~photutils.detection.DAOStarFinder` and
`~photutils.detection.IRAFStarFinder` are:
* `~photutils.detection.IRAFStarFinder` always uses a 2D
circular Gaussian kernel, while
`~photutils.detection.DAOStarFinder` can use an elliptical
Gaussian kernel.
* `~photutils.detection.IRAFStarFinder` calculates the objects'
centroid, roundness, and sharpness using image moments.
.. _DAOFIND: http://stsdas.stsci.edu/cgi-bin/gethelp.cgi?daofind
.. _starfind: http://stsdas.stsci.edu/cgi-bin/gethelp.cgi?starfind
"""
raise NotImplementedError
class DAOStarFinder(StarFinderBase):
"""
Detect stars in an image using the DAOFIND (`Stetson 1987
<http://adsabs.harvard.edu/abs/1987PASP...99..191S>`_) algorithm.
DAOFIND (`Stetson 1987; PASP 99, 191
<http://adsabs.harvard.edu/abs/1987PASP...99..191S>`_) searches
images for local density maxima that have a peak amplitude greater
than ``threshold`` (approximately; ``threshold`` is applied to a
convolved image) and have a size and shape similar to the defined 2D
Gaussian kernel. The Gaussian kernel is defined by the ``fwhm``,
``ratio``, ``theta``, and ``sigma_radius`` input parameters.
``DAOStarFinder`` finds the object centroid by fitting the marginal x
and y 1D distributions of the Gaussian kernel to the marginal x and
y distributions of the input (unconvolved) ``data`` image.
``DAOStarFinder`` calculates the object roundness using two methods. The
``roundlo`` and ``roundhi`` bounds are applied to both measures of
roundness. The first method (``roundness1``; called ``SROUND`` in
`DAOFIND`_) is based on the source symmetry and is the ratio of a
measure of the object's bilateral (2-fold) to four-fold symmetry.
The second roundness statistic (``roundness2``; called ``GROUND`` in
`DAOFIND`_) measures the ratio of the difference in the height of
the best fitting Gaussian function in x minus the best fitting
Gaussian function in y, divided by the average of the best fitting
Gaussian functions in x and y. A circular source will have a zero
roundness. An source extended in x or y will have a negative or
positive roundness, respectively.
The sharpness statistic measures the ratio of the difference between
the height of the central pixel and the mean of the surrounding
non-bad pixels in the convolved image, to the height of the best
fitting Gaussian function at that point.
Parameters
----------
threshold : float
The absolute image value above which to select sources.
fwhm : float
The full-width half-maximum (FWHM) of the major axis of the
Gaussian kernel in units of pixels.
ratio : float, optional
The ratio of the minor to major axis standard deviations of the
Gaussian kernel. ``ratio`` must be strictly positive and less
than or equal to 1.0. The default is 1.0 (i.e., a circular
Gaussian kernel).
theta : float, optional
The position angle (in degrees) of the major axis of the
Gaussian kernel measured counter-clockwise from the positive x
axis.
sigma_radius : float, optional
The truncation radius of the Gaussian kernel in units of sigma
(standard deviation) [``1 sigma = FWHM /
(2.0*sqrt(2.0*log(2.0)))``].
sharplo : float, optional
The lower bound on sharpness for object detection.
sharphi : float, optional
The upper bound on sharpness for object detection.
roundlo : float, optional
The lower bound on roundess for object detection.
roundhi : float, optional
The upper bound on roundess for object detection.
sky : float, optional
The background sky level of the image. Setting ``sky`` affects
only the output values of the object ``peak``, ``flux``, and
``mag`` values. The default is 0.0, which should be used to
replicate the results from `DAOFIND`_.
exclude_border : bool, optional
Set to `True` to exclude sources found within half the size of
the convolution kernel from the image borders. The default is
`False`, which is the mode used by `DAOFIND`_.
See Also
--------
IRAFStarFinder
Notes
-----
For the convolution step, this routine sets pixels beyond the image
borders to 0.0. The equivalent parameters in `DAOFIND`_ are
``boundary='constant'`` and ``constant=0.0``.
References
----------
.. [1] Stetson, P. 1987; PASP 99, 191 (http://adsabs.harvard.edu/abs/1987PASP...99..191S)
.. [2] http://stsdas.stsci.edu/cgi-bin/gethelp.cgi?daofind
.. _DAOFIND: http://stsdas.stsci.edu/cgi-bin/gethelp.cgi?daofind
"""
def __init__(self, threshold, fwhm, ratio=1.0, theta=0.0,
sigma_radius=1.5, sharplo=0.2, sharphi=1.0, roundlo=-1.0,
roundhi=1.0, sky=0.0, exclude_border=False):
self.threshold = threshold
self.fwhm = fwhm
self.ratio = ratio
self.theta = theta
self.sigma_radius = sigma_radius
self.sharplo = sharplo
self.sharphi = sharphi
self.roundlo = roundlo
self.roundhi = roundhi
self.sky = sky
self.exclude_border = exclude_border
def find_stars(self, data):
daofind_kernel = _FindObjKernel(self.fwhm, self.ratio, self.theta,
self.sigma_radius)
self.threshold *= daofind_kernel.relerr
objs = _findobjs(data, self.threshold, daofind_kernel,
exclude_border=self.exclude_border)
tbl = _daofind_properties(objs, self.threshold, daofind_kernel,
self.sky)
if len(objs) == 0:
warnings.warn('No sources were found.', AstropyUserWarning)
return tbl # empty table
table_mask = ((tbl['sharpness'] > self.sharplo) &
(tbl['sharpness'] < self.sharphi) &
(tbl['roundness1'] > self.roundlo) &
(tbl['roundness1'] < self.roundhi) &
(tbl['roundness2'] > self.roundlo) &
(tbl['roundness2'] < self.roundhi))
tbl = tbl[table_mask]
idcol = Column(name='id', data=np.arange(len(tbl)) + 1)
tbl.add_column(idcol, 0)
if len(tbl) == 0:
warnings.warn('Sources were found, but none pass the sharpness '
'and roundness criteria.', AstropyUserWarning)
return tbl
class IRAFStarFinder(StarFinderBase):
"""
Detect stars in an image using IRAF's "starfind" algorithm.
`starfind`_ searches images for local density maxima that have a
peak amplitude greater than ``threshold`` above the local background
and have a PSF full-width half-maximum similar to the input
``fwhm``. The objects' centroid, roundness (ellipticity), and
sharpness are calculated using image moments.
Parameters
----------
threshold : float
The absolute image value above which to select sources.
fwhm : float
The full-width half-maximum (FWHM) of the 2D circular Gaussian
kernel in units of pixels.
minsep_fwhm : float, optional
The minimum separation for detected objects in units of
``fwhm``.
sigma_radius : float, optional
The truncation radius of the Gaussian kernel in units of sigma
(standard deviation) [``1 sigma = FWHM /
2.0*sqrt(2.0*log(2.0))``].
sharplo : float, optional
The lower bound on sharpness for object detection.
sharphi : float, optional
The upper bound on sharpness for object detection.
roundlo : float, optional
The lower bound on roundess for object detection.
roundhi : float, optional
The upper bound on roundess for object detection.
sky : float, optional
The background sky level of the image. Inputing a ``sky`` value
will override the background sky estimate. Setting ``sky``
affects only the output values of the object ``peak``, ``flux``,
and ``mag`` values. The default is ``None``, which means the
sky value will be estimated using the `starfind`_ method.
exclude_border : bool, optional
Set to `True` to exclude sources found within half the size of
the convolution kernel from the image borders. The default is
`False`, which is the mode used by `starfind`_.
See Also
--------
DAOStarFinder
References
----------
.. [1] http://stsdas.stsci.edu/cgi-bin/gethelp.cgi?starfind
.. _starfind: http://stsdas.stsci.edu/cgi-bin/gethelp.cgi?starfind
"""
def __init__(self, threshold, fwhm, sigma_radius=1.5, minsep_fwhm=2.5,
sharplo=0.5, sharphi=2.0, roundlo=0.0, roundhi=0.2, sky=None,
exclude_border=False):
self.threshold = threshold
self.fwhm = fwhm
self.sigma_radius = sigma_radius
self.minsep_fwhm = minsep_fwhm
self.sharplo = sharplo
self.sharphi = sharphi
self.roundlo = roundlo
self.roundhi = roundhi
self.sky = sky
self.exclude_border = exclude_border
def find_stars(self, data):
starfind_kernel = _FindObjKernel(self.fwhm, ratio=1.0, theta=0.0,
sigma_radius=self.sigma_radius)
min_separation = max(2, int((self.fwhm * self.minsep_fwhm) + 0.5))
objs = _findobjs(data, self.threshold, starfind_kernel,
min_separation=min_separation,
exclude_border=self.exclude_border)
tbl = _irafstarfind_properties(objs, starfind_kernel, self.sky)
if len(objs) == 0:
warnings.warn('No sources were found.', AstropyUserWarning)
return tbl # empty table
table_mask = ((tbl['sharpness'] > self.sharplo) &
(tbl['sharpness'] < self.sharphi) &
(tbl['roundness'] > self.roundlo) &
(tbl['roundness'] < self.roundhi))
tbl = tbl[table_mask]
idcol = Column(name='id', data=np.arange(len(tbl)) + 1)
tbl.add_column(idcol, 0)
if len(tbl) == 0:
warnings.warn('Sources were found, but none pass the sharpness '
'and roundness criteria.', AstropyUserWarning)
return tbl
def _findobjs(data, threshold, kernel, min_separation=None,
exclude_border=False, local_peaks=True):
"""
Find sources in an image by convolving the image with the input
kernel and selecting connected pixels above a given threshold.
Parameters
----------
data : array_like
The 2D array of the image.
threshold : float
The absolute image value above which to select sources. Note
that this threshold is not the same threshold input to
``daofind`` or ``irafstarfind``. It should be multiplied by the
kernel relerr.
kernel : `_FindObjKernel`
The convolution kernel. The dimensions should match those of
the cutouts. The kernel should be normalized to zero sum.
exclude_border : bool, optional
Set to `True` to exclude sources found within half the size of
the convolution kernel from the image borders. The default is
`False`, which is the mode used by `DAOFIND`_ and `starfind`_.
local_peaks : bool, optional
Set to `True` to exactly match the `DAOFIND`_ method of finding
local peaks. If `False`, then only one peak per thresholded
segment will be used.
Returns
-------
objects : list of `_ImgCutout`
A list of `_ImgCutout` objects containing the image cutout for
each source.
.. _DAOFIND: http://stsdas.stsci.edu/cgi-bin/gethelp.cgi?daofind
.. _starfind: http://stsdas.stsci.edu/cgi-bin/gethelp.cgi?starfind
"""
from scipy import ndimage
x_kernradius = kernel.kern.shape[1] // 2
y_kernradius = kernel.kern.shape[0] // 2
if not exclude_border:
# create a larger image padded by zeros
ysize = int(data.shape[0] + (2. * y_kernradius))
xsize = int(data.shape[1] + (2. * x_kernradius))
data_padded = np.zeros((ysize, xsize))
data_padded[y_kernradius:y_kernradius + data.shape[0],
x_kernradius:x_kernradius + data.shape[1]] = data
data = data_padded
convolved_data = filter_data(data, kernel.kern, mode='constant',
fill_value=0.0, check_normalization=False)
if not exclude_border:
# keep border=0 in convolved data
convolved_data[:y_kernradius, :] = 0.
convolved_data[-y_kernradius:, :] = 0.
convolved_data[:, :x_kernradius] = 0.
convolved_data[:, -x_kernradius:] = 0.
selem = ndimage.generate_binary_structure(2, 2)
object_labels, nobjects = ndimage.label(convolved_data > threshold,
structure=selem)
objects = []
if nobjects == 0:
return objects
# find object peaks in the convolved data
if local_peaks:
# footprint overrides min_separation in find_peaks
if min_separation is None: # daofind
footprint = kernel.mask.astype(np.bool)
else:
from skimage.morphology import disk
footprint = disk(min_separation)
tbl = find_peaks(convolved_data, threshold, footprint=footprint)
coords = np.transpose([tbl['y_peak'], tbl['x_peak']])
else:
object_slices = ndimage.find_objects(object_labels)
coords = []
for object_slice in object_slices:
# thresholded_object is not the same size as the kernel
thresholded_object = convolved_data[object_slice]
ypeak, xpeak = np.unravel_index(thresholded_object.argmax(),
thresholded_object.shape)
xpeak += object_slice[1].start
ypeak += object_slice[0].start
coords.append((ypeak, xpeak))
for (ypeak, xpeak) in coords:
# now extract the object from the data, centered on the peak
# pixel in the convolved image, with the same size as the kernel
x0 = xpeak - x_kernradius
x1 = xpeak + x_kernradius + 1
y0 = ypeak - y_kernradius
y1 = ypeak + y_kernradius + 1
if x0 < 0 or x1 > data.shape[1]:
continue # pragma: no cover (isolated continue is never tested)
if y0 < 0 or y1 > data.shape[0]:
continue # pragma: no cover (isolated continue is never tested)
object_data = data[y0:y1, x0:x1]
object_convolved_data = convolved_data[y0:y1, x0:x1].copy()
if not exclude_border:
# correct for image padding
x0 -= x_kernradius
y0 -= y_kernradius
imgcutout = _ImgCutout(object_data, object_convolved_data, x0, y0)
objects.append(imgcutout)
return objects
def _irafstarfind_properties(imgcutouts, kernel, sky=None):
"""
Find the properties of each detected source, as defined by IRAF's
``starfind``.
Parameters
----------
imgcutouts : list of `_ImgCutout`
A list of `_ImgCutout` objects containing the image cutout for
each source.
kernel : `_FindObjKernel`
The convolution kernel. The dimensions should match those of
the cutouts. ``kernel.gkernel`` should have a peak pixel value
of 1.0 and not contain any masked pixels.
sky : float, optional
The absolute sky level. If sky is ``None``, then a local sky
level will be estimated (in a crude fashion).
Returns
-------
table : `~astropy.table.Table`
A table of the objects' properties.
"""
result = defaultdict(list)
for imgcutout in imgcutouts:
if sky is None:
skymask = ~kernel.mask.astype(np.bool) # 1=sky, 0=obj
nsky = np.count_nonzero(skymask)
if nsky == 0:
meansky = imgcutout.data.max() - imgcutout.convdata.max()
else:
meansky = (imgcutout.data * skymask).sum() / nsky
else:
meansky = sky
objvals = _irafstarfind_moments(imgcutout, kernel, meansky)
for key, val in objvals.items():
result[key].append(val)
names = ['xcentroid', 'ycentroid', 'fwhm', 'sharpness', 'roundness',
'pa', 'npix', 'sky', 'peak', 'flux', 'mag']
if len(result) == 0:
for name in names:
result[name] = []
table = Table(result, names=names)
return table
def _irafstarfind_moments(imgcutout, kernel, sky):
"""
Find the properties of each detected source, as defined by IRAF's
``starfind``.
Parameters
----------
imgcutout : `_ImgCutout`
The image cutout for a single detected source.
kernel : `_FindObjKernel`
The convolution kernel. The dimensions should match those of
``imgcutout``. ``kernel.gkernel`` should have a peak pixel
value of 1.0 and not contain any masked pixels.
sky : float
The local sky level around the source.
Returns
-------
result : dict
A dictionary of the object parameters.
"""
from skimage.measure import moments, moments_central
result = defaultdict(list)
img = np.array((imgcutout.data - sky) * kernel.mask)
img = np.where(img > 0, img, 0) # starfind discards negative pixels
if np.count_nonzero(img) <= 1:
return {}
m = moments(img, 1)
result['xcentroid'] = m[1, 0] / m[0, 0]
result['ycentroid'] = m[0, 1] / m[0, 0]
result['npix'] = float(np.count_nonzero(img)) # float for easier testing
result['sky'] = sky
result['peak'] = np.max(img)
flux = img.sum()
result['flux'] = flux
result['mag'] = -2.5 * np.log10(flux)
mu = moments_central(
img, result['ycentroid'], result['xcentroid'], 2) / m[0, 0]
musum = mu[2, 0] + mu[0, 2]
mudiff = mu[2, 0] - mu[0, 2]
result['fwhm'] = 2.0 * np.sqrt(np.log(2.0) * musum)
result['sharpness'] = result['fwhm'] / kernel.fwhm
result['roundness'] = np.sqrt(mudiff**2 + 4.0*mu[1, 1]**2) / musum
pa = 0.5 * np.arctan2(2.0 * mu[1, 1], mudiff) * (180.0 / np.pi)
if pa < 0.0:
pa += 180.0
result['pa'] = pa
result['xcentroid'] += imgcutout.x0
result['ycentroid'] += imgcutout.y0
return result
def _daofind_properties(imgcutouts, threshold, kernel, sky=0.0):
"""
Find the properties of each detected source, as defined by
`DAOFIND`_.
Parameters
----------
imgcutouts : list of `_ImgCutout`
A list of `_ImgCutout` objects containing the image cutout for
each source.
threshold : float
The absolute image value above which to select sources.
kernel : `_FindObjKernel`
The convolution kernel. The dimensions should match those of
the objects in ``imgcutouts``. ``kernel.gkernel`` should have a
peak pixel value of 1.0 and not contain any masked pixels.
sky : float, optional
The local sky level around the source. ``sky`` is used only to
calculate the source peak value and flux. The default is 0.0.
Returns
-------
table : `~astropy.table.Table`
A table of the object parameters.
.. _DAOFIND: http://stsdas.stsci.edu/cgi-bin/gethelp.cgi?daofind
"""
result = defaultdict(list)
ykcen, xkcen = kernel.center
for imgcutout in imgcutouts:
convobj = imgcutout.convdata.copy()
convobj[ykcen, xkcen] = 0.0
q1 = convobj[0:ykcen+1, xkcen+1:]
q2 = convobj[0:ykcen, 0:xkcen+1]
q3 = convobj[ykcen:, 0:xkcen]
q4 = convobj[ykcen+1:, xkcen:]
sum2 = -q1.sum() + q2.sum() - q3.sum() + q4.sum()
sum4 = np.abs(convobj).sum()
result['roundness1'].append(2.0 * sum2 / sum4)
obj = imgcutout.data
objpeak = obj[ykcen, xkcen]
convpeak = imgcutout.convdata[ykcen, xkcen]
npts = kernel.mask.sum()
obj_masked = obj * kernel.mask
objmean = (obj_masked.sum() - objpeak) / (npts - 1) # exclude peak
sharp = (objpeak - objmean) / convpeak
result['sharpness'].append(sharp)
dx, dy, g_roundness = _daofind_centroid_roundness(obj, kernel)
yc, xc = imgcutout.center
result['xcentroid'].append(xc + dx)
result['ycentroid'].append(yc + dy)
result['roundness2'].append(g_roundness)
result['sky'].append(sky) # DAOFIND uses sky=0
result['npix'].append(float(obj.size))
result['peak'].append(objpeak - sky)
flux = (convpeak / threshold) - (sky * obj.size)
result['flux'].append(flux)
if flux <= 0:
mag = np.nan
else:
mag = -2.5 * np.log10(flux)
result['mag'].append(mag)
names = ['xcentroid', 'ycentroid', 'sharpness', 'roundness1', 'roundness2',
'npix', 'sky', 'peak', 'flux', 'mag']
if len(result) == 0:
for name in names:
result[name] = []
table = Table(result, names=names)
return table
def _daofind_centroid_roundness(obj, kernel):
"""
Calculate the source (x, y) centroid and `DAOFIND`_ "GROUND"
roundness statistic.
`DAOFIND`_ finds the centroid by fitting 1D Gaussians (marginal x/y
distributions of the kernel) to the marginal x/y distributions of
the original (unconvolved) image.
The roundness statistic measures the ratio of the difference in the
height of the best fitting Gaussian function in x minus the best
fitting Gaussian function in y, divided by the average of the best
fitting Gaussian functions in x and y. A circular source will have
a zero roundness. An source extended in x (y) will have a negative
(positive) roundness.
Parameters
----------
obj : array_like
The 2D array of the source cutout.
kernel : `_FindObjKernel`
The convolution kernel. The dimensions should match those of
``obj``. ``kernel.gkernel`` should have a peak pixel value of
1.0 and not contain any masked pixels.
Returns
-------
dx, dy : float
Fractional shift in x and y of the image centroid relative to
the maximum pixel.
g_roundness : float
`DAOFIND`_ roundness (GROUND) statistic.
.. _DAOFIND: http://stsdas.stsci.edu/cgi-bin/gethelp.cgi?daofind
"""
dx, hx = _daofind_centroidfit(obj, kernel, axis=0)
dy, hy = _daofind_centroidfit(obj, kernel, axis=1)
g_roundness = 2.0 * (hx - hy) / (hx + hy)
return dx, dy, g_roundness
def _daofind_centroidfit(obj, kernel, axis):
"""
Find the source centroid along one axis by fitting a 1D Gaussian to
the marginal x or y distribution of the unconvolved source data.
Parameters
----------
obj : array_like
The 2D array of the source cutout.
kernel : `_FindObjKernel`
The convolution kernel. The dimensions should match those of
``obj``. ``kernel.gkernel`` should have a peak pixel value of
1.0 and not contain any masked pixels.
axis : {0, 1}
The axis for which the centroid is computed:
* 0: for the x axis
* 1: for the y axis
Returns
-------
dx : float
Fractional shift in x or y (depending on ``axis`` value) of the
image centroid relative to the maximum pixel.
hx : float
Height of the best-fitting Gaussian to the marginal x or y
(depending on ``axis`` value) distribution of the unconvolved
source data.
"""
# define a triangular weighting function, peaked in the middle
# and equal to one at the edge
nyk, nxk = kernel.shape
ykrad, xkrad = kernel.center
ywtd, xwtd = np.mgrid[0:nyk, 0:nxk]
xwt = xkrad - abs(xwtd - xkrad) + 1.0
ywt = ykrad - abs(ywtd - ykrad) + 1.0
if axis == 0:
wt = xwt[0]
wts = ywt
ksize = nxk
kernel_sigma = kernel.xsigma
krad = ksize // 2
sumdx_vec = krad - np.arange(ksize)
elif axis == 1:
wt = ywt.T[0]
wts = xwt
ksize = nyk
kernel_sigma = kernel.ysigma
krad = ksize // 2
sumdx_vec = np.arange(ksize) - krad
n = wt.sum()
sg = (kernel.gkernel * wts).sum(axis)
sumg = (wt * sg).sum()
sumg2 = (wt * sg**2).sum()
vec = krad - np.arange(ksize)
dgdx = sg * vec
sdgdx = (wt * dgdx).sum()
sdgdx2 = (wt * dgdx**2).sum()
sgdgdx = (wt * sg * dgdx).sum()
sd = (obj * wts).sum(axis)
sumd = (wt * sd).sum()
sumgd = (wt * sg * sd).sum()
sddgdx = (wt * sd * dgdx).sum()
sumdx = (wt * sd * sumdx_vec).sum()
# linear least-squares fit (data = sky + hx*gkernel) to find amplitudes
denom = (n*sumg2 - sumg**2)
hx = (n*sumgd - sumg*sumd) / denom
# sky = (sumg2*sumd - sumg*sumgd) / denom
dx = (sgdgdx - (sddgdx - sdgdx*sumd)) / (hx * sdgdx2 / kernel_sigma**2)
hsize = (ksize / 2.)
if abs(dx) > hsize:
dx = 0
if sumd == 0:
dx = 0.0
else:
dx = float(sumdx / sumd)
if abs(dx) > hsize:
dx = 0.0
return dx, hx
class _ImgCutout(object):
"""Class to hold image cutouts."""
def __init__(self, data, convdata, x0, y0):
"""
Parameters
----------
data : array_like
The cutout 2D image from the input unconvolved 2D image.
convdata : array_like
The cutout 2D image from the convolved 2D image.
x0, y0 : float
Image coordinates of the lower left pixel of the cutout region.
The pixel origin is (0, 0).
"""
self.data = data
self.convdata = convdata
self.x0 = x0
self.y0 = y0
@property
def radius(self):
return [size // 2 for size in self.data.shape]
@property
def center(self):
yr, xr = self.radius
return yr + self.y0, xr + self.x0
class _FindObjKernel(object):
"""
Calculate a 2D Gaussian density enhancement kernel. This kernel has
negative wings and sums to zero. It is used by both `DAOStarFinder`
and `IRAFStarFinder`.
Parameters
----------
fwhm : float
The full-width half-maximum (FWHM) of the major axis of the
Gaussian kernel in units of pixels.
ratio : float, optional
The ratio of the minor to major axis standard deviations of the
Gaussian kernel. ``ratio`` must be strictly positive and less
than or equal to 1.0. The default is 1.0 (i.e., a circular
Gaussian kernel).
theta : float, optional
The position angle (in degrees) of the major axis of the
Gaussian kernel measured counter-clockwise from the positive x
axis.
sigma_radius : float, optional
The truncation radius of the Gaussian kernel in units of sigma
(standard deviation) [``1 sigma = FWHM /
2.0*sqrt(2.0*log(2.0))``]. The default is 1.5.
Notes
-----
The object attributes include the dimensions of the elliptical
kernel and the coefficients of a 2D elliptical Gaussian function
expressed as:
``f(x,y) = A * exp(-g(x,y))``
where
``g(x,y) = a*(x-x0)**2 + 2*b*(x-x0)*(y-y0) + c*(y-y0)**2``
References
----------
.. [1] http://en.wikipedia.org/wiki/Gaussian_function
"""
def __init__(self, fwhm, ratio=1.0, theta=0.0, sigma_radius=1.5):
if fwhm < 0:
raise ValueError('fwhm must be positive, '
'got fwhm={0}'.format(fwhm))
if ratio <= 0 or ratio > 1:
raise ValueError('ratio must be positive and less or equal '
'than 1, got ratio={0}'.format(ratio))
if sigma_radius <= 0:
raise ValueError('sigma_radius must be positive, got '
'sigma_radius={0}'.format(sigma_radius))
self.fwhm = fwhm
self.sigma_radius = sigma_radius
self.ratio = ratio
self.theta = theta
self.theta_radians = np.deg2rad(self.theta)
self.xsigma = self.fwhm * gaussian_fwhm_to_sigma
self.ysigma = self.xsigma * self.ratio
self.a = None
self.b = None
self.c = None
self.f = None
self.nx = None
self.ny = None
self.xc = None
self.yc = None
self.circrad = None
self.ellrad = None
self.gkernel = None
self.mask = None
self.npts = None
self.kern = None
self.relerr = None
self.set_gausspars()
self.mk_kern()
@property
def shape(self):
return self.kern.shape
@property
def center(self):
"""Index of the kernel center."""
return [size // 2 for size in self.kern.shape]
def set_gausspars(self):
xsigma2 = self.xsigma**2
ysigma2 = self.ysigma**2
cost = np.cos(self.theta_radians)
sint = np.sin(self.theta_radians)
self.a = (cost**2 / (2.0 * xsigma2)) + (sint**2 / (2.0 * ysigma2))
self.b = 0.5 * cost * sint * (1.0/xsigma2 - 1.0/ysigma2) # CCW
self.c = (sint**2 / (2.0 * xsigma2)) + (cost**2 / (2.0 * ysigma2))
# find the extent of an ellipse with radius = sigma_radius*sigma;
# solve for the horizontal and vertical tangents of an ellipse
# defined by g(x,y) = f
self.f = self.sigma_radius**2 / 2.0
denom = self.a*self.c - self.b**2
self.nx = 2 * int(max(2, math.sqrt(self.c*self.f / denom))) + 1
self.ny = 2 * int(max(2, math.sqrt(self.a*self.f / denom))) + 1
return
def mk_kern(self):
yy, xx = np.mgrid[0:self.ny, 0:self.nx]
self.xc = self.nx // 2
self.yc = self.ny // 2
self.circrad = np.sqrt((xx-self.xc)**2 + (yy-self.yc)**2)
self.ellrad = (self.a*(xx-self.xc)**2 +
2.0*self.b*(xx-self.xc)*(yy-self.yc) +
self.c*(yy-self.yc)**2)
self.gkernel = np.exp(-self.ellrad)
self.mask = np.where((self.ellrad <= self.f) |
(self.circrad <= 2.0), 1, 0).astype(np.int16)
self.npts = self.mask.sum()
self.kern = self.gkernel * self.mask
# normalize the kernel to zero sum (denom = variance * npts)
denom = ((self.kern**2).sum() - (self.kern.sum()**2 / self.npts))
self.relerr = 1.0 / np.sqrt(denom)
self.kern = (((self.kern - (self.kern.sum() / self.npts)) / denom) *
self.mask)
return
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