def average_filter(input, size=None, footprint=None, output=None, mode="reflect", cval=0.0, origin=0):
"""
Calculates a multi-dimensional average filter.
Parameters
----------
input : array-like
input array to filter
size : scalar or tuple, optional
See footprint, below
footprint : array, optional
Either `size` or `footprint` must be defined. `size` gives
the shape that is taken from the input array, at every element
position, to define the input to the filter function.
`footprint` is a boolean array that specifies (implicitly) a
shape, but also which of the elements within this shape will get
passed to the filter function. Thus ``size=(n,m)`` is equivalent
to ``footprint=np.ones((n,m))``. We adjust `size` to the number
of dimensions of the input array, so that, if the input array is
shape (10,10,10), and `size` is 2, then the actual size used is
(2,2,2).
output : array, optional
The ``output`` parameter passes an array in which to store the
filter output.
mode : {'reflect','constant','nearest','mirror', 'wrap'}, optional
The ``mode`` parameter determines how the array borders are
handled, where ``cval`` is the value when mode is equal to
'constant'. Default is 'reflect'
cval : scalar, optional
Value to fill past edges of input if ``mode`` is 'constant'. Default
is 0.0
origin : scalar, optional
The ``origin`` parameter controls the placement of the filter.
Default 0
Returns
-------
average_filter : ndarray
Returned array of same shape as `input`.
Notes
-----
Convenience implementation employing convolve.
See Also
--------
convolve : Convolve an image with a kernel.
"""
footprint = __make_footprint(input, size, footprint)
filter_size = footprint.sum()
output, return_value = _get_output(output, input)
sum_filter(input, footprint=footprint, output=output, mode=mode, cval=cval, origin=origin)
output /= filter_size
return return_value
def sls(minuend, subtrahend, metric = "ssd", noise = "global", signed = True,
sn_size = None, sn_footprint = None, sn_mode = "reflect", sn_cval = 0.0,
pn_size = None, pn_footprint = None, pn_mode = "reflect", pn_cval = 0.0):
"""
Computes the signed local similarity between two images.
Compares a patch around each voxel of the minuend array to a number of patches
centered at the points of a search neighbourhood in the subtrahend. Thus, creates
a multi-dimensional measure of patch similarity between the minuend and a
corresponding search area in the subtrahend.
This filter can also be used to compute local self-similarity, obtaining a
descriptor similar to the one described in [1].
minuend : array_like
Input array from which to subtract the subtrahend.
subtrahend : array_like
Input array to subtract from the minuend.
metric : {'ssd', 'mi', 'nmi', 'ncc'}, optional
The `metric` parameter determines the metric used to compute the
filter output. Default is 'ssd'.
noise : {'global', 'local'}, optional
The `noise` parameter determines how the noise is handled. If set
to 'global', the variance determining the noise is a scalar, if
set to 'local', it is a Gaussian smoothed field of estimated local
noise. Default is 'global'.
signed : bool, optional
Whether the filter output should be signed or not. If set to 'False',
only the absolute values will be returned. Default is 'True'.
sn_size : scalar or tuple, optional
See sn_footprint, below
sn_footprint : array, optional
The search neighbourhood.
Either `sn_size` or `sn_footprint` must be defined. `sn_size` gives
the shape that is taken from the input array, at every element
position, to define the input to the filter function.
`sn_footprint` is a boolean array that specifies (implicitly) a
shape, but also which of the elements within this shape will get
passed to the filter function. Thus ``sn_size=(n,m)`` is equivalent
to ``sn_footprint=np.ones((n,m))``. We adjust `sn_size` to the number
of dimensions of the input array, so that, if the input array is
shape (10,10,10), and `sn_size` is 2, then the actual size used is
(2,2,2).
sn_mode : {'reflect', 'constant', 'nearest', 'mirror', 'wrap'}, optional
The `sn_mode` parameter determines how the array borders are
handled, where `sn_cval` is the value when mode is equal to
'constant'. Default is 'reflect'
sn_cval : scalar, optional
Value to fill past edges of input if `sn_mode` is 'constant'. Default
is 0.0
pn_size : scalar or tuple, optional
See pn_footprint, below
pn_footprint : array, optional
The patch over which the distance measure is applied.
Either `pn_size` or `pn_footprint` must be defined. `pn_size` gives
the shape that is taken from the input array, at every element
position, to define the input to the filter function.
`pn_footprint` is a boolean array that specifies (implicitly) a
shape, but also which of the elements within this shape will get
passed to the filter function. Thus ``pn_size=(n,m)`` is equivalent
of dimensions of the input array, so that, if the input array is
shape (10,10,10), and `pn_size` is 2, then the actual size used is
(2,2,2).
pn_mode : {'reflect', 'constant', 'nearest', 'mirror', 'wrap'}, optional
The `pn_mode` parameter determines how the array borders are
handled, where `pn_cval` is the value when mode is equal to
'constant'. Default is 'reflect'
pn_cval : scalar, optional
Value to fill past edges of input if `pn_mode` is 'constant'. Default
is 0.0
[1] Mattias P. Heinrich, Mark Jenkinson, Manav Bhushan, Tahreema Matin, Fergus V. Gleeson, Sir Michael Brady, Julia A. Schnabel
MIND: Modality independent neighbourhood descriptor for multi-modal deformable registration
Medical Image Analysis, Volume 16, Issue 7, October 2012, Pages 1423-1435, ISSN 1361-8415
http://dx.doi.org/10.1016/j.media.2012.05.008
"""
minuend = numpy.asarray(minuend)
subtrahend = numpy.asarray(subtrahend)
if numpy.iscomplexobj(minuend):
raise TypeError('complex type not supported')
if numpy.iscomplexobj(subtrahend):
raise TypeError('complex type not supported')
mshape = [ii for ii in minuend.shape if ii > 0]
sshape = [ii for ii in subtrahend.shape if ii > 0]
if not len(mshape) == len(sshape):
raise RuntimeError("minuend and subtrahend must be of same shape")
if not numpy.all([sm == ss for sm, ss in zip(mshape, sshape)]):
raise RuntimeError("minuend and subtrahend must be of same shape")
sn_footprint = __make_footprint(minuend, sn_size, sn_footprint)
sn_fshape = [ii for ii in sn_footprint.shape if ii > 0]
if len(sn_fshape) != minuend.ndim:
raise RuntimeError('search neighbourhood footprint array has incorrect shape.')
#!TODO: Is this required?
if not sn_footprint.flags.contiguous:
sn_footprint = sn_footprint.copy()
# created a padded copy of the subtrahend, whereas the padding mode is always 'reflect'
subtrahend = pad(subtrahend, footprint=sn_footprint, mode=sn_mode, cval=sn_cval)
# compute slicers for position where the search neighbourhood sn_footprint is TRUE
slicers = [[slice(x, (x + 1) - d if 0 != (x + 1) - d else None) for x in range(d)] for d in sn_fshape]
slicers = [sl for sl, tv in zip(itertools.product(*slicers), sn_footprint.flat) if tv]
# compute difference images and sign images for search neighbourhood elements
ssds = [ssd(minuend, subtrahend[slicer], normalized=True, signed=signed, size=pn_size, footprint=pn_footprint, mode=pn_mode, cval=pn_cval) for slicer in slicers]
distance = [x[0] for x in ssds]
distance_sign = [x[1] for x in ssds]
# compute local variance, which constitutes an approximation of local noise, out of patch-distances over the neighbourhood structure
variance = numpy.average(distance, 0)
variance = gaussian_filter(variance, sigma=3) #!TODO: Figure out if a fixed sigma is desirable here... I think that yes
if 'global' == noise:
variance = variance.sum() / float(numpy.product(variance.shape))
# variance[variance < variance_global / 10.] = variance_global / 10. #!TODO: Should I keep this i.e. regularizing the variance to be at least 10% of the global one?
# compute sls
sls = [dist_sign * numpy.exp(-1 * (dist / variance)) for dist_sign, dist in zip(distance_sign, distance)]
# convert into sls image, swapping dimensions to have varying patches in the last dimension
return numpy.rollaxis(numpy.asarray(sls), 0, minuend.ndim + 1)
