imagewrapper.py 43.5 KB
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#!/usr/bin/env python
#
# imagewrapper.py - The ImageWrapper class.
#
# Author: Paul McCarthy <pauldmccarthy@gmail.com>
#
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"""This module provides the :class:`ImageWrapper` class, which can be used
to manage data access to ``nibabel`` NIFTI images.
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Terminology
-----------


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There are some confusing terms used in this module, so it may be useful to
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get their definitions straight:

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  - *Coverage*:    The portion of an image that has been covered in the data
                   range calculation. The ``ImageWrapper`` keeps track of
                   the coverage for individual volumes within a 4D image (or
                   slices in a 3D image).

  - *Slice*:       Portion of the image data which is being accessed. A slice
                   comprises either a tuple of ``slice`` objects (or integers),
                   or a sequence of ``(low, high)`` tuples, specifying the
                   index range into each image dimension that is covered by
                   the slice.

  - *Expansion*:   A sequence of ``(low, high)`` tuples, specifying an
                   index range into each image dimension, that is used to
                   *expand* the *coverage* of an image, based on a given set 
                   of *slices*.

  - *Fancy slice*: Any object which is used to slice an array, and is not
                   an ``int``, ``slice``, or ``Ellipsis``, or sequence of
                   these.
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"""


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import logging
import collections
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import itertools as it
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import numpy     as np
import nibabel   as nib
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import fsl.utils.notifier as notifier
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import fsl.utils.async    as async
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log = logging.getLogger(__name__)


class ImageWrapper(notifier.Notifier):
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    """The ``ImageWrapper`` class is a convenience class which manages data
    access to ``nibabel`` NIFTI images. The ``ImageWrapper`` class can be
    used to:
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      - Control whether the image is loaded into memory, or kept on disk
    
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      - Incrementally update the known image data range, as more image
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        data is read in.


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    *In memory or on disk?*

    The image data will be kept on disk, and accessed through the
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    ``nibabel.Nifti1Image.dataobj`` (or ``nibabel.Nifti2Image.dataobj``) array
    proxy, if:
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     - The ``loadData`` parameter to :meth:`__init__` is ``False``.
     - The :meth:`loadData` method never gets called.
     - The image data is not modified (via :meth:`__setitem__`.

    If any of these conditions do not hold, the image data will be loaded into
    memory and accessed directly, via the ``nibabel.Nifti1Image.get_data``
    method.


    *Image dimensionality*

    
    The ``ImageWrapper`` abstracts away trailing image dimensions of length 1.
    This means that if the header for a NIFTI image specifies that the image
    has four dimensions, but the fourth dimension is of length 1, you do not
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    need to worry about indexing that fourth dimension. However, all NIFTI
    images will be presented as having at least three dimensions, so if your
    image header specifies a third dimension of length 1, you will still
    need provide an index of 0 for that dimensions, for all data accesses.
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    *Data access*

    
    The ``ImageWrapper`` can be indexed in one of two ways:

       - With basic ``numpy``-like multi-dimensional array slicing (with step
         sizes of 1)
    
       - With boolean array indexing, where the boolean/mask array has the
         same shape as the image data.

    See https://docs.scipy.org/doc/numpy/reference/arrays.indexing.html for
    more details on numpy indexing.
 

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    *Data range*

    
    In order to avoid the computational overhead of calculating the image data
    range (its minimum/maximum values) when an image is first loaded in, an
    ``ImageWrapper`` incrementally updates the known image data range as data
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    is accessed. The ``ImageWrapper`` keeps track of the image data *coverage*,
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    the portion of the image which has already been considered in the data
    range calculation. When data from a region of the image not in the coverage
    is accessed, the coverage is expanded to include this region. The coverage
    is always expanded in a rectilinear manner, i.e. the coverage is always
    rectangular for a 2D image, or cuboid for a 3D image.

    
    For a 4D image, the ``ImageWrapper`` internally maintains a separate
    coverage and known data range for each 3D volume within the image. For a 3D
    image, separate coverages and data ranges are stored for each 2D slice.


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    The ``ImageWrapper`` implements the :class:`.Notifier` interface.
    Listeners can register to be notified whenever the known image data range
    is updated. The data range can be accessed via the :attr:`dataRange`
    property.
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    The ``ImageWrapper`` class uses the following functions (also defined in 
    this module) to keep track of the portion of the image that has currently
    been included in the data range calculation:

    .. autosummary::
       :nosignatures:

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       naninfrange
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       isValidFancySliceObj
       canonicalSliceObj
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       sliceObjToSliceTuple
       sliceTupleToSliceObj
       sliceCovered
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       calcExpansion
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       adjustCoverage
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    """

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    def __init__(self,
                 image,
                 name=None,
                 loadData=False,
                 dataRange=None,
                 threaded=False):
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        """Create an ``ImageWrapper``.
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        :arg image:     A ``nibabel.Nifti1Image`` or ``nibabel.Nifti2Image``.
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        :arg name:      A name for this ``ImageWrapper``, solely used for 
                        debug log messages.
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        :arg loadData:  If ``True``, the image data is loaded into memory.
                        Otherwise it is kept on disk (and data access is
                        performed through the ``nibabel.Nifti1Image.dataobj``
                        array proxy).

        :arg dataRange: A tuple containing the initial ``(min, max)``  data
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                        range to use. See the :meth:`reset` method for
                        important information about this parameter.
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        :arg threaded:  If ``True``, the data range is updated on a
                        :class:`.TaskThread`. Otherwise (the default), the
                        data range is updated directly on reads/writes.
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        """
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        self.__image      = image
        self.__name       = name
        self.__taskThread = None
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        # Save the number of 'real' dimensions,
        # that is the number of dimensions minus
        # any trailing dimensions of length 1
        self.__numRealDims = len(image.shape)
        for d in reversed(image.shape):
            if d == 1: self.__numRealDims -= 1
            else:      break

        # And save the number of
        # 'padding' dimensions too.
        self.__numPadDims = len(image.shape) - self.__numRealDims

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        # Too many shapes! Figure out
        # what shape we should present
        # the data as (e.g. at least 3
        # dimensions). This is used in
        # __getitem__ to force the
        # result to have the correct
        # dimensionality.
        self.__canonicalShape = canonicalShape(image.shape)

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        # The internal state is stored
        # in these attributes - they're
        # initialised in the reset method.
        self.__range     = None
        self.__coverage  = None
        self.__volRanges = None
        self.__covered   = False

        self.reset(dataRange)

        if loadData:
            self.loadData()

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        if threaded:
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            self.__taskThread = async.TaskThread()
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            self.__taskThread.daemon = True
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            self.__taskThread.start()


    def __del__(self):
        """If this ``ImageWrapper`` was created with ``threaded=True``,
        the :class:`.TaskThread` is stopped.
        """
        self.__image = None
        if self.__taskThread is not None:
            self.__taskThread.stop()
            self.__taskThraed = None

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    def reset(self, dataRange=None):
        """Reset the internal state and known data range of this
        ``ImageWrapper``.

        
        :arg dataRange: A tuple containing the initial ``(min, max)``  data
                        range to use. See the :meth:`reset` method.


        .. note:: The ``dataRange`` parameter is intended for situations where
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                  the image data range is known in advance (e.g. it was
                  calculated earlier, and the image is being re-loaded). If a
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                  ``dataRange`` is passed in, it will *not* be overwritten by
                  any range calculated from the data, unless the calculated
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                  data range is wider than the provided ``dataRange``.
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        """
        
        if dataRange is None:
            dataRange = None, None

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        image =             self.__image
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        ndims =             self.__numRealDims - 1
        nvols = image.shape[self.__numRealDims - 1]

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        # The current known image data range. This
        # gets updated as more image data gets read.
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        self.__range = dataRange
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        # The coverage array is used to keep track of
        # the portions of the image which have been
        # considered in the data range calculation.
        # We use this coverage to avoid unnecessarily
        # re-calculating the data range on the same
        # part of the image.
        #
        # First of all, we're going to store a separate
        # 'coverage' for each 2D slice in the 3D image
        # (or 3D volume for 4D images). This effectively
        # means a seaprate coverage for each index in the
        # last 'real' image dimension (see above).
        # 
        # For each slice/volume, the the coverage is
        # stored as sequences of (low, high) indices, one
        # for each dimension in the slice/volume (e.g.
        # row/column for a slice, or row/column/depth
        # for a volume).
        #
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        # All of these indices are stored in a numpy array:
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        #   - first dimension:  low/high index
        #   - second dimension: image dimension
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        #   - third dimension:  slice/volume index 
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        self.__coverage = np.zeros((2, ndims, nvols), dtype=np.float32)
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        # Internally, we calculate and store the
        # data range for each volume/slice/vector
        self.__volRanges = np.zeros((nvols, 2), dtype=np.float32)

        self.__coverage[ :] = np.nan
        self.__volRanges[:] = np.nan
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        # This flag is set to true if/when the
        # full image data range becomes known
        # (i.e. when all data has been loaded in).
        self.__covered = False

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    @property
    def dataRange(self):
        """Returns the currently known data range as a tuple of ``(min, max)``
        values.
        """
        # If no image data has been accessed, we
        # default to whatever is stored in the
        # header (which may or may not contain
        # useful values).
        low, high = self.__range
        hdr       = self.__image.get_header()

        if low  is None: low  = float(hdr['cal_min'])
        if high is None: high = float(hdr['cal_max'])

        return low, high

    
    @property
    def covered(self):
        """Returns ``True`` if this ``ImageWrapper`` has read the entire
        image data, ``False`` otherwise.
        """
        return self.__covered


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    @property
    def shape(self):
        """Returns the shape that the image data is presented as. This is
        the same as the underlying image shape, but with trailing dimensions
        of length 1 removed, and at least three dimensions.
        """
        return self.__canonicalShape


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    def coverage(self, vol):
        """Returns the current image data coverage for the specified volume
        (for a 4D image, slice for a 3D image, or vector for a 2D images).

        :arg vol: Index of the volume/slice/vector to return the coverage
                  for.

        :returns: The coverage for the specified volume, as a ``numpy``
                  array of shape ``(nd, 2)``, where ``nd`` is the number
                  of dimensions in the volume.
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        .. note:: If the specified volume is not covered, the returned array
                  will contain ``np.nan`` values.
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        """
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        return np.array(self.__coverage[..., vol])
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    def loadData(self):
        """Forces all of the image data to be loaded into memory.

        .. note:: This method will be called by :meth:`__init__` if its
                  ``loadData`` parameter is ``True``.
        """

        # If the data is not already loaded, this will
        # cause nibabel to load it. By default, nibabel
        # will cache the numpy array that contains the
        # image data, so subsequent calls to this
        # method will not overwrite any changes that
        # have been made to the data array.
        self.__image.get_data()

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    def __getData(self, sliceobj, isTuple=False):
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        """Retrieves the image data at the location specified by ``sliceobj``.
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        :arg sliceobj: Something which can be used to slice an array, or
                       a sequence of (low, high) index pairs.

        :arg isTuple:  Set to ``True`` if ``sliceobj`` is a sequence of
                       (low, high) index pairs.
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        """

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        if isTuple:
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            sliceobj = sliceTupleToSliceObj(sliceobj)
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        # If the image has not been loaded
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        # into memory, we can use the nibabel
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        # ArrayProxy. Otheriwse if it is in
        # memory, we can access it directly.
        #
        # Furthermore, if it is in memory and
        # has been modified, the ArrayProxy
        # will give us out-of-date values (as
        # the ArrayProxy reads from disk). So
        # we have to read from the in-memory
        # array to get changed values.
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        #
        # Finally, note that if the caller has
        # given us a 'fancy' slice object (a
        # boolean numpy array), but the image
        # data is not in memory, we can't access
        # the data, as the nibabel ArrayProxy
        # (the dataobj attribute) cannot handle
        # fancy indexing. In this case an error
        # will be raised.
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        if self.__image.in_memory: return self.__image.get_data()[sliceobj]
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        else:                      return self.__image.dataobj[   sliceobj]
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    def __imageIsCovered(self):
        """Returns ``True`` if all portions of the image have been covered
        in the data range calculation, ``False`` otherwise.
        """
        
        shape  = self.__image.shape
        slices = zip([0] * len(shape), shape)
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        return sliceCovered(slices, self.__coverage)
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    def __expandCoverage(self, slices):
        """Expands the current image data range and coverage to encompass the
        given ``slices``.
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        """
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        _, expansions = calcExpansion(slices, self.__coverage)
        expansions    = collapseExpansions(expansions, self.__numRealDims - 1)
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        log.debug('Updating image {} data range [slice: {}] '
                  '(current range: [{}, {}]; '
                  'number of expansions: {}; '
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                  'current coverage: {}; '
                  'volume ranges: {})'.format(
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                      self.__name,
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                      slices,
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                      self.__range[0],
                      self.__range[1],
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                      len(expansions),
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                      self.__coverage,
                      self.__volRanges))
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        # As we access the data for each expansions,
        # we want it to have the same dimensionality
        # as the full image, so we can access data
        # for each volume in the image separately.
        # So we squeeze out the padding dimensions,
        # but not the volume dimension.
        squeezeDims = tuple(range(self.__numRealDims,
                                  self.__numRealDims + self.__numPadDims))
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        # The calcExpansion function splits up the
        # expansions on volumes - here we calculate
        # the min/max per volume/expansion, and
        # iteratively update the stored per-volume
        # coverage and data range.
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        for i, exp in enumerate(expansions):

            data = self.__getData(exp, isTuple=True)
            data = data.squeeze(squeezeDims)

            vlo, vhi = exp[self.__numRealDims - 1]

            for vi, vol in enumerate(range(vlo, vhi)):
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                oldvlo, oldvhi = self.__volRanges[vol, :]
                voldata        = data[..., vi]
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                newvlo, newvhi = naninfrange(voldata)
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                if (not np.isnan(oldvlo)) and oldvlo < newvlo: newvlo = oldvlo
                if (not np.isnan(oldvhi)) and oldvhi > newvhi: newvhi = oldvhi
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                # Update the stored range and
                # coverage for each volume 
                self.__volRanges[vol, :]  = newvlo, newvhi
                self.__coverage[..., vol] = adjustCoverage(
                    self.__coverage[..., vol], exp)
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        # Calculate the new known data
        # range over the entire image
        # (i.e. over all volumes).
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        newmin, newmax = naninfrange(self.__volRanges)
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        oldmin, oldmax = self.__range
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        self.__range   = (newmin, newmax)
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        self.__covered = self.__imageIsCovered()

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        if any((oldmin is None, oldmax is None)) or \
           not np.all(np.isclose([oldmin, oldmax], [newmin, newmax])):
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            log.debug('Image {} range changed: [{}, {}] -> [{}, {}]'.format(
                self.__name,
                oldmin,
                oldmax,
                newmin,
                newmax))
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            self.notify()

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    def __updateDataRangeOnRead(self, slices, data):
        """Called by :meth:`__getitem__`. Calculates the minimum/maximum
        values of the given data (which has been extracted from the portion of
        the image specified by ``slices``), and updates the known data range
        of the image.

        :arg slices: A tuple of tuples, each tuple being a ``(low, high)``
                     index pair, one for each dimension in the image. 
        
        :arg data:   The image data at the given ``slices`` (as a ``numpy``
                     array).
        """

        # TODO You could do something with
        #      the provided data to avoid
        #      reading it in again.

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        if self.__taskThread is None:
            self.__expandCoverage(slices)
        else:
            name = '{}_read_{}'.format(id(self), slices)
            if not self.__taskThread.isQueued(name):
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                self.__taskThread.enqueue(
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                    self.__expandCoverage, slices, taskName=name)
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    def __updateDataRangeOnWrite(self, slices, data):
        """Called by :meth:`__setitem__`. Assumes that the image data has
        been changed (the data at ``slices`` has been replaced with ``data``.
        Updates the image data coverage, and known data range accordingly.

        :arg slices: A tuple of tuples, each tuple being a ``(low, high)``
                     index pair, one for each dimension in the image. 
        
        :arg data:   The image data at the given ``slices`` (as a ``numpy``
                     array). 
        """

        overlap = sliceOverlap(slices, self.__coverage)

        # If there's no overlap between the written
        # area and the current coverage, then it's
        # easy - we just expand the coverage to
        # include the newly written area.
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        # 
        # But if there is overlap between the written
        # area and the current coverage, things are
        # more complicated, because the portion of
        # the image that has been written over may
        # have contained the currently known data
        # minimum/maximum. We have no way of knowing
        # this, so we have to reset the coverage (on
        # the affected volumes), and recalculate the
        # data range.
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        if overlap in (OVERLAP_SOME, OVERLAP_ALL):

            # TODO Could you store the location of the
            #      data minimum/maximum (in each volume),
            #      so you know whether resetting the
            #      coverage is necessary?
            lowVol, highVol = slices[self.__numRealDims - 1]

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            # We create a single slice which
            # encompasses the given slice, and
            # all existing coverages for each
            # volume in the given slice. The
            # data range for this slice will
            # be recalculated.
            slices = adjustCoverage(self.__coverage[:, :, lowVol], slices)
            for vol in range(lowVol + 1, highVol):
                slices = adjustCoverage(slices, self.__coverage[:, :, vol].T)

            slices = np.array(slices.T, dtype=np.uint32)
            slices = tuple(it.chain(map(tuple, slices), [(lowVol, highVol)]))

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            log.debug('Image {} data written - clearing known data '
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                      'range on volumes {} - {} (write slice: {}; '
                      'coverage: {}; volRanges: {})'.format(
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                          self.__name,
                          lowVol,
                          highVol,
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                          slices,
                          self.__coverage[:, :, lowVol:highVol],
                          self.__volRanges[lowVol:highVol, :]))
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            for vol in range(lowVol, highVol):
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                self.__coverage[:, :, vol]    = np.nan
                self.__volRanges[     vol, :] = np.nan
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        if self.__taskThread is None:
            self.__expandCoverage(slices)
        else:
            name = '{}_write_{}'.format(id(self), slices)
            if not self.__taskThread.isQueued(name):
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                self.__taskThread.enqueue(
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                    self.__expandCoverage, slices, taskName=name)
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    def __getitem__(self, sliceobj):
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        """Returns the image data for the given ``sliceobj``, and updates
        the known image data range if necessary.

        :arg sliceobj: Something which can slice the image data.
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        """
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        log.debug('Getting image data: {}'.format(sliceobj))
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        shape              = self.__canonicalShape
        realShape          = self.__image.shape
        sliceobj           = canonicalSliceObj(   sliceobj, shape)
        fancy              = isValidFancySliceObj(sliceobj, shape)
        expNdims, expShape = expectedShape(       sliceobj, shape)
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        # TODO Cache 3D images for large 4D volumes, 
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        #      so you don't have to hit the disk?
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        # Make the slice object compatible with the
        # actual image shape, and retrieve the data.
        sliceobj = canonicalSliceObj(sliceobj, realShape)
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        data     = self.__getData(sliceobj)
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        # Update data range for the 
        # data that we just read in
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        if not self.__covered:
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            slices = sliceObjToSliceTuple(sliceobj, realShape)
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            if not sliceCovered(slices, self.__coverage):
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                self.__updateDataRangeOnRead(slices, data)
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        # Make sure that the result has the
        # shape that the caller is expecting.
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        if fancy: data = data.reshape((data.size, ))
        else:     data = data.reshape(expShape)

        # If expNdims == 0, we should
        # return a scalar. If expNdims
        # == 0, but data.size != 1,
        # something is wrong somewhere
        # (and is not being handled
        # here).
        if expNdims == 0 and data.size == 1:

            # Funny behaviour with numpy scalar arrays.
            # data[()] returns a numpy scalar (which is
            # what we want). But data.item() returns a
            # python scalar. And if the data is a
            # ndarray with 0 dims, data[0] will raise
            # an error!
            data = data[()]
                
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        return data
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    def __setitem__(self, sliceobj, values):
        """Writes the given ``values`` to the image at the given ``sliceobj``.

        
        :arg sliceobj: Something which can be used to slice the array.
        :arg values:   Data to write to the image.

        
        .. note:: Modifying image data will cause the entire image to be
                  loaded into memory. 
        """

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        realShape = self.__image.shape
        sliceobj  = canonicalSliceObj(   sliceobj, realShape)
        slices    = sliceObjToSliceTuple(sliceobj, realShape)

        # If the image shape does not match its
        # 'display' shape (either less three
        # dims, or  has trailing dims of length
        # 1), we might need to re-shape the
        # values to prevent numpy from raising
        # an error in the assignment below.
        if realShape != self.__canonicalShape:
            
            expNdims, expShape = expectedShape(sliceobj, realShape)

            # If we are slicing a scalar, the
            # assigned value has to be scalar.
            if expNdims == 0 and isinstance(values, collections.Sequence):

                if len(values) > 1:
                    raise IndexError('Invalid assignment: [{}] = {}'.format(
                        sliceobj, len(values)))
        
                values = values[0]

            # Make sure that the values 
            # have a compatible shape.
            else:
                
                values = np.array(values)
                if values.shape != expShape:
                    values = values.reshape(expShape)
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        # The image data has to be in memory
        # for the data to be changed. If it's
        # already in memory, this call won't
        # have any effect.
        self.loadData()

        self.__image.get_data()[sliceobj] = values
        self.__updateDataRangeOnWrite(slices, values)


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def naninfrange(data):
    """Returns the minimum and maximum values in the given ``numpy`` array,
    ignoring ``nan`` and ``inf`` values.

    The ``numpy.nanmin``/``numpy.nanmax`` functions do not handle
    positive/negative infinity, so if such values are in the data, we need to
    use an alternate approach to calculating the minimum/maximum.
    """

    if not np.issubdtype(data.dtype, np.float):
        return data.min(), data.max()

    # But np.nanmin/nanmax are substantially
    # faster than the alternate, so we try it
    # first.
    dmin = np.nanmin(data)
    dmax = np.nanmax(data)

    # If there are no nans/infs in the data,
    # we can just use nanmin/nanmax
    if np.isfinite(dmin) and np.isfinite(dmax):
        return dmin, dmax

    # The entire array contains nans
    if np.isnan(dmin):
        return dmin, dmin

    # Otherwise we need to calculate min/max
    # only on finite values. This is the slow
    # option.

    # Find all finite values
    finite = np.isfinite(data)

    # Try to calculate min/max on those values.
    # An error will be raised if there are no
    # finite values in the array
    try:
        return data[finite].min(), data[finite].max()
    except:
        return np.nan, np.nan


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def isValidFancySliceObj(sliceobj, shape):
    """Returns ``True`` if the given ``sliceobj`` is a valid and fancy slice
    object.

    ``nibabel`` refers to slice objects as "fancy" if they comprise anything
    but tuples of simple ``slice`` objects. The ``ImageWrapper`` class
    supports one type of "fancy" slicing, where the ``sliceobj`` is a boolean
    ``numpy`` array of the same shape as the image.

    This function returns ``True`` if the given ``sliceobj`` adheres to these
    requirements, ``False`` otherwise.
    """

    # We only support boolean numpy arrays
    # which have the same shape as the image
    return (isinstance(sliceobj, np.ndarray) and
            sliceobj.dtype == np.bool        and
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            np.prod(sliceobj.shape) == np.prod(shape))
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def canonicalSliceObj(sliceobj, shape):
    """Returns a canonical version of the given ``sliceobj``. See the
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    ``nibabel.fileslice.canonical_slicers`` function.
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    """

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    # Fancy slice objects must have 
    # the same shape as the data
    if isValidFancySliceObj(sliceobj, shape):
        return sliceobj.reshape(shape)

    else:

        if not isinstance(sliceobj, tuple):
            sliceobj = (sliceobj,)
        
        if len(sliceobj) > len(shape):
            sliceobj = sliceobj[:len(shape)]
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        return nib.fileslice.canonical_slicers(sliceobj, shape)
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def canonicalShape(shape):
    """Calculates a *canonical* shape, how the given ``shape`` should
    be presented. The shape is forced to be at least three dimensions,
    with any other trailing dimensions of length 1 ignored.
    """

    shape = list(shape)

    # Squeeze out empty dimensions, as
    # 3D image can sometimes be listed
    # as having 4 or more dimensions 
    for i in reversed(range(len(shape))):
        if shape[i] == 1: shape = shape[:i]
        else:             break

    # But make sure the shape 
    # has at 3 least dimensions
    if len(shape) < 3:
        shape = shape + [1] * (3 - len(shape))

    return shape


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def expectedShape(sliceobj, shape):
    """Given a slice object, and the shape of an array to which
    that slice object is going to be applied, returns the expected
    shape of the result.

    .. note:: It is assumed that the ``sliceobj`` has been passed through
              the :func:`canonicalSliceObj` function.

    :arg sliceobj: Something which can be used to slice an array
                   of shape ``shape``.

    :arg shape:    Shape of the array being sliced.

    :returns:      A tuple containing:
    
                     - Expected number of dimensions of the result
    
                     - Expected shape of the result (or ``None`` if
                       ``sliceobj`` is fancy).
    """
    
    if isValidFancySliceObj(sliceobj, shape):
        return 1, None

    # Truncate some dimensions from the
    # slice object if it has too many
    # (e.g. trailing dims of length 1).
    elif len(sliceobj) > len(shape):
        sliceobj = sliceobj[:len(shape)]

    # Figure out the number of dimensions
    # that the result should have, given
    # this slice object. 
    expShape = []

    for i in range(len(sliceobj)):

        # Each dimension which has an 
        # int slice will be collapsed
        if isinstance(sliceobj[i], int):
            continue

        start = sliceobj[i].start
        stop  = sliceobj[i].stop
        
        if start is None: start = 0
        if stop  is None: stop  = shape[i]

        expShape.append(stop - start)

    return len(expShape), expShape


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def sliceObjToSliceTuple(sliceobj, shape):
    """Turns an array slice object into a tuple of (low, high) index
    pairs, one pair for each dimension in the given shape
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    :arg sliceobj: Something which can be used to slice an array of shape
                   ``shape``.

    :arg shape:    Shape of the array being sliced.
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    """

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    if isValidFancySliceObj(sliceobj, shape):
        return tuple((0, s) for s in shape)

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    indices = []

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    # The sliceobj could be a single sliceobj
    # or integer, instead of a tuple
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    if not isinstance(sliceobj, collections.Sequence):
        sliceobj = [sliceobj]

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    # Turn e.g. array[6] into array[6, :, :]
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    if len(sliceobj) != len(shape):
        missing  = len(shape) - len(sliceobj)
        sliceobj = list(sliceobj) + [slice(None) for i in range(missing)]

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    for dim, s in enumerate(sliceobj):

        # each element in the slices tuple should 
        # be a slice object or an integer
        if isinstance(s, slice): i = [s.start, s.stop]
        else:                    i = [s,       s + 1]

        if i[0] is None: i[0] = 0
        if i[1] is None: i[1] = shape[dim]

        indices.append(tuple(i))

    return tuple(indices)


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def sliceTupleToSliceObj(slices):
    """Turns a sequence of (low, high) index pairs into a tuple of array
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    ``slice`` objects.
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    :arg slices: A sequence of (low, high) index pairs.
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    """

    sliceobj = []

    for lo, hi in slices:
        sliceobj.append(slice(lo, hi, 1))

    return tuple(sliceobj)


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def adjustCoverage(oldCoverage, slices): 
    """Adjusts/expands the given ``oldCoverage`` so that it covers the
    given set of ``slices``.

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    :arg oldCoverage: A ``numpy`` array of shape ``(2, n)`` containing
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                      the (low, high) index pairs for ``n`` dimensions of
                      a single slice/volume in the image.
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    :arg slices:      A sequence of (low, high) index pairs. If ``slices``
                      contains more dimensions than are specified in
                      ``oldCoverage``, the trailing dimensions are ignored.

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    :return: A ``numpy`` array containing the adjusted/expanded coverage.
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    """

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    newCoverage = np.zeros(oldCoverage.shape, dtype=oldCoverage.dtype)
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    for dim in range(oldCoverage.shape[1]):
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        low,      high      = slices[        dim]
        lowCover, highCover = oldCoverage[:, dim]
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        if np.isnan(lowCover)  or low  < lowCover:  lowCover  = low
        if np.isnan(highCover) or high > highCover: highCover = high
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        newCoverage[:, dim] = lowCover, highCover
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    return newCoverage

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OVERLAP_ALL = 0
"""Indicates that the slice is wholly contained within the coverage.  This is
a return code for the :func:`sliceOverlap` function.
"""


OVERLAP_SOME = 1
"""Indicates that the slice partially overlaps with the coverage. This is a
return code for the :func:`sliceOverlap` function.
"""


OVERLAP_NONE = 2
"""Indicates that the slice does not overlap with the coverage. This is a
return code for the :func:`sliceOverlap` function.
"""


def sliceOverlap(slices, coverage):
    """Determines whether the given ``slices`` overlap with the given
    ``coverage``.

    :arg slices:    A sequence of (low, high) index pairs, assumed to cover
                    all image dimensions.
    :arg coverage:  A ``numpy`` array of shape ``(2, nd, nv)`` (where ``nd``
                    is the number of dimensions being covered, and ``nv`` is
                    the number of volumes (or vectors/slices) in the image,
                    which contains the (low, high) index pairs describing
                    the current image coverage.

    :returns: One of the following codes:
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              .. autosummary::

              OVERLAP_ALL
              OVERLAP_SOME
              OVERLAP_NONE
    """

    numDims         = coverage.shape[1]
    lowVol, highVol = slices[numDims]

    # Overlap state is calculated for each volume
    overlapStates = np.zeros(highVol - lowVol)

    for i, vol in enumerate(range(lowVol, highVol)):

        state = OVERLAP_ALL

        for dim in range(numDims):

            lowCover, highCover = coverage[:, dim, vol]
            lowSlice, highSlice = slices[     dim] 

            # No coverage
            if np.isnan(lowCover) or np.isnan(highCover):
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