imagewrapper.py

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


Terminology
-----------


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

  - *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*.
"""


import logging
import collections
import itertools as it

import numpy     as np
import nibabel   as nib

import fsl.utils.notifier as notifier
import fsl.utils.async    as async


log = logging.getLogger(__name__)


class ImageWrapper(notifier.Notifier):
    """The ``ImageWrapper`` class is a convenience class which manages data
    access to ``nibabel`` NIFTI images. The ``ImageWrapper`` class can be
    used to:

    
      - Control whether the image is loaded into memory, or kept on disk
    
      - Incrementally update the known image data range, as more image
        data is read in.


    *In memory or on disk?*

    The image data will be kept on disk, and accessed through the
    ``nibabel.Nifti1Image.dataobj`` (or ``nibabel.Nifti2Image.dataobj``) array
    proxy, if:

     - 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
    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.


    *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
    is accessed. The ``ImageWrapper`` keeps track of the image data *coverage*,
    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.


    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.


    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:

       naninfrange
       isValidFancySliceObj
       canonicalSliceObj
       sliceObjToSliceTuple
       sliceTupleToSliceObj
       sliceCovered
       calcExpansion
       adjustCoverage
    """

    
    def __init__(self,
                 image,
                 name=None,
                 loadData=False,
                 dataRange=None,
                 threaded=False):
        """Create an ``ImageWrapper``.

        :arg image:     A ``nibabel.Nifti1Image`` or ``nibabel.Nifti2Image``.

        :arg name:      A name for this ``ImageWrapper``, solely used for 
                        debug log messages.

        :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
                        range to use. See the :meth:`reset` method for
                        important information about this parameter.

        :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.
        """

        self.__image      = image
        self.__name       = name
        self.__taskThread = None

        # 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

        # 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)

        # 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()

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


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

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

        # The current known image data range. This
        # gets updated as more image data gets read.
        self.__range = dataRange

        # 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).
        #
        # All of these indices are stored in a numpy array:
        #   - first dimension:  low/high index
        #   - second dimension: image dimension
        #   - third dimension:  slice/volume index 
        self.__coverage = np.zeros((2, ndims, nvols), dtype=np.float32)

        # 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

        # 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

        
    @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


    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.

        .. note:: If the specified volume is not covered, the returned array
                  will contain ``np.nan`` values.
        """
        return np.array(self.__coverage[..., vol])

    
    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()


    def __getData(self, sliceobj, isTuple=False):
        """Retrieves the image data at the location specified by ``sliceobj``.

        :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.
        """

        if isTuple:
            sliceobj = sliceTupleToSliceObj(sliceobj)

        # If the image has not been loaded
        # into memory, we can use the nibabel
        # 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.
        #
        # 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.
        if self.__image.in_memory: return self.__image.get_data()[sliceobj]
        else:                      return self.__image.dataobj[   sliceobj]


    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)
        return sliceCovered(slices, self.__coverage)


    def __expandCoverage(self, slices):
        """Expands the current image data range and coverage to encompass the
        given ``slices``.
        """

        _, expansions = calcExpansion(slices, self.__coverage)
        expansions    = collapseExpansions(expansions, self.__numRealDims - 1)

        log.debug('Updating image {} data range [slice: {}] '
                  '(current range: [{}, {}]; '
                  'number of expansions: {}; '
                  'current coverage: {})'.format(
                      self.__name,
                      slices,
                      self.__range[0],
                      self.__range[1],
                      len(expansions),
                      self.__coverage))

        # 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))
        
        # 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.
        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)):

                oldvlo, oldvhi = self.__volRanges[vol, :]
                voldata        = data[..., vi]

                newvlo, newvhi = naninfrange(voldata)

                if (not np.isnan(oldvlo)) and oldvlo < newvlo: newvlo = oldvlo
                if (not np.isnan(oldvhi)) and oldvhi > newvhi: newvhi = oldvhi

                # Update the stored range and
                # coverage for each volume 
                self.__volRanges[vol, :]  = newvlo, newvhi
                self.__coverage[..., vol] = adjustCoverage(
                    self.__coverage[..., vol], exp)

        # Calculate the new known data
        # range over the entire image
        # (i.e. over all volumes).
        newmin, newmax = naninfrange(self.__volRanges)

        oldmin, oldmax = self.__range
        self.__range   = (newmin, newmax)
        self.__covered = self.__imageIsCovered()

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


    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.

        if self.__taskThread is None:
            self.__expandCoverage(slices)
        else:
            name = '{}_read_{}'.format(id(self), slices)
            if not self.__taskThread.isQueued(name):
                self.__taskThread.enqueue(
                    self.__expandCoverage, slices, taskName=name)


    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.
        if overlap in (OVERLAP_SOME, OVERLAP_ALL):

            # 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.

            # 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]

            log.debug('Image {} data written - clearing known data '
                      'range on volumes {} - {} (write slice: {})'.format(
                          self.__name,
                          lowVol,
                          highVol,
                          slices))

            for vol in range(lowVol, highVol):
                self.__coverage[:, :, vol]    = np.nan
                self.__volRanges[     vol, :] = np.nan


        if self.__taskThread is None:
            self.__expandCoverage(slices)
        else:
            name = '{}_write_{}'.format(id(self), slices)
            if not self.__taskThread.isQueued(name):
                self.__taskThread.enqueue(
                    self.__expandCoverage, slices, taskName=name)

            
    def __getitem__(self, sliceobj):
        """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.
        """

        log.debug('Getting image data: {}'.format(sliceobj))
        
        image = self.__image
        shape = image.shape
        ndims = len(shape)

        fancy = isValidFancySliceObj(sliceobj, shape)

        if fancy:
            expNdims = ndims
        else:
            
            if not isinstance(sliceobj, tuple):
                sliceobj = (sliceobj,)

            # Figure out the number of dimensions
            # that the result should have, given
            # this slice object.
            expNdims = len(self.__canonicalShape) - \
                       len([s for s in sliceobj if isinstance(s, int)])

            # Truncate some dimensions from the
            # slice object if it has too many
            # (e.g. trailing dims of length 1).
            if len(sliceobj) > ndims:
                sliceobj = sliceobj[:ndims]
                
        # TODO Cache 3D images for large 4D volumes, 
        #      so you don't have to hit the disk?

        sliceobj = canonicalSliceObj(sliceobj, shape)
        data     = self.__getData(sliceobj)

        if not self.__covered:

            slices = sliceObjToSliceTuple(sliceobj, shape)

            if not sliceCovered(slices, self.__coverage):
                self.__updateDataRangeOnRead(slices, data)

        # Make sure that the result has the
        # shape that the caller is expecting.
        if not fancy and ndims != expNdims:
            data = data.reshape(list(data.shape) + [1] * (expNdims - ndims))

        return data


    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. 
        """

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

        # 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)


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


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
            sliceobj.shape == shape)


def canonicalSliceObj(sliceobj, shape):
    """Returns a canonical version of the given ``sliceobj``. See the
    ``nibabel.fileslice.canonical_slicers` function.
    """

    if not isValidFancySliceObj(sliceobj, shape):
        sliceobj = nib.fileslice.canonical_slicers(sliceobj, shape)

    return sliceobj
    

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


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

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

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

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

    indices = []

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

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

    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)


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

    :arg slices: A sequence of (low, high) index pairs.
    """

    sliceobj = []

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

    return tuple(sliceobj)


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

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

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

    newCoverage = np.zeros(oldCoverage.shape, dtype=np.uint32)

    for dim in range(oldCoverage.shape[1]):

        low,      high      = slices[        dim]
        lowCover, highCover = oldCoverage[:, dim]

        if np.isnan(lowCover)  or low  < lowCover:  lowCover  = low
        if np.isnan(highCover) or high > highCover: highCover = high

        newCoverage[:, dim] = lowCover, highCover

    return newCoverage


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:
    
              .. 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):
                state = OVERLAP_NONE
                break

            # The slice is contained within the
            # coverage on this dimension - check
            # the other dimensions.
            if lowSlice >= lowCover and highSlice <= highCover:
                continue

            # The slice does not overlap at all
            # with the coverage on this dimension
            # (or at all). No overlap - no need
            # to check the other dimensions.
            if lowSlice >= highCover or highSlice <= lowCover:
                state = OVERLAP_NONE
                break

            # There is some overlap between the
            # slice and coverage on this dimension
            # - check the other dimensions.
            state = OVERLAP_SOME
            
        overlapStates[i] = state

    if   np.any(overlapStates == OVERLAP_SOME): return OVERLAP_SOME
    elif np.all(overlapStates == OVERLAP_NONE): return OVERLAP_NONE
    elif np.all(overlapStates == OVERLAP_ALL):  return OVERLAP_ALL


def sliceCovered(slices, coverage):
    """Returns ``True`` if the portion of the image data calculated by
    the given ``slices` has already been calculated, ``False`` otherwise.

    :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.
    """

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

    for vol in range(lowVol, highVol):

        for dim in range(numDims):

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

            if np.isnan(lowCover) or np.isnan(highCover):
                return False

            if lowSlice  < lowCover:  return False
            if highSlice > highCover: return False

    return True


def calcExpansion(slices, coverage):
    """Calculates a series of *expansion* slices, which can be used to expand
    the given ``coverage`` so that it includes the given ``slices``.

    :arg slices:   Slices that the coverage needs to be expanded to cover.
    :arg coverage: Current image coverage.

    :returns: A list of volume indices, and a corresponding list of
              expansions.
    """

    numDims         = coverage.shape[1]
    padDims         = len(slices) - numDims - 1
    lowVol, highVol = slices[numDims] 

    expansions = []
    volumes    = []

    # Finish off an expansion by
    # adding indices for the vector/
    # slice/volume dimension, and for
    # 'padding' dimensions of size 1.
    def finishExpansion(exp, vol):
        exp.append((vol, vol + 1))
        for i in range(padDims):
            exp.append((0, 1))
        return exp
    
    for vol in range(lowVol, highVol):

        # No coverage of this volume - 
        # we need the whole slice.
        if np.any(np.isnan(coverage[:, :, vol])):
            exp = [(s[0], s[1]) for s in slices[:numDims]]
            exp = finishExpansion(exp, vol)
            volumes   .append(vol)
            expansions.append(exp)
            continue

        # First we'll figure out the index
        # range for each dimension that
        # needs to be added to the coverage.
        # We build a list of required ranges,
        # where each entry is a tuple
        # containing:
        #   (dimension, lowIndex, highIndex)
        reqRanges = []

        for dim in range(numDims):

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

            # The slice covers a region
            # below the current coverage
            if lowCover - lowSlice > 0:
                reqRanges.append((dim, int(lowSlice), int(lowCover)))
                
            # The slice covers a region
            # above the current coverage
            if highCover - highSlice < 0:
                reqRanges.append((dim, int(highCover), int(highSlice)))

        # Now we generate an expansion for
        # each of those ranges.
        volExpansions = []
        for dimx, xlo, xhi in reqRanges:

            expansion = [[np.nan, np.nan] for d in range(numDims)]

            # The expansion for each
            # dimension will span the range
            # for that dimension...
            expansion[dimx][0] = xlo
            expansion[dimx][1] = xhi
                
            # And will span the union of
            # the coverage, and calculated