BUG: Use manager to set title
effigies
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# emacs: -*- mode: python-mode; py-indent-offset: 4; indent-tabs-mode: nil -*-
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# vi: set ft=python sts=4 ts=4 sw=4 et:
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### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ##
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#
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# See COPYING file distributed along with the NiBabel package for the
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# copyright and license terms.
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#
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### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ##
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""" Utilities for calculating and applying affine orientations """
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import numpy as np |
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import numpy.linalg as npl |
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from .deprecated import deprecate_with_version |
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class OrientationError(Exception): |
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pass
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def io_orientation(affine, tol=None): |
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""" Orientation of input axes in terms of output axes for `affine`
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Valid for an affine transformation from ``p`` dimensions to ``q``
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dimensions (``affine.shape == (q + 1, p + 1)``).
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The calculated orientations can be used to transform associated
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arrays to best match the output orientations. If ``p`` > ``q``, then
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some of the output axes should be considered dropped in this
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orientation.
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Parameters
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----------
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affine : (q+1, p+1) ndarray-like
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Transformation affine from ``p`` inputs to ``q`` outputs. Usually this
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will be a shape (4,4) matrix, transforming 3 inputs to 3 outputs, but
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the code also handles the more general case
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tol : {None, float}, optional
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threshold below which SVD values of the affine are considered zero. If
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`tol` is None, and ``S`` is an array with singular values for `affine`,
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and ``eps`` is the epsilon value for datatype of ``S``, then `tol` set
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to ``S.max() * max((q, p)) * eps``
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Returns
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-------
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orientations : (p, 2) ndarray
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one row per input axis, where the first value in each row is the closest
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corresponding output axis. The second value in each row is 1 if the
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input axis is in the same direction as the corresponding output axis and
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-1 if it is in the opposite direction. If a row is [np.nan, np.nan],
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which can happen when p > q, then this row should be considered dropped.
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"""
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affine = np.asarray(affine) |
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q, p = affine.shape[0] - 1, affine.shape[1] - 1 |
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# extract the underlying rotation, zoom, shear matrix
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RZS = affine[:q, :p] |
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zooms = np.sqrt(np.sum(RZS * RZS, axis=0)) |
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# Zooms can be zero, in which case all elements in the column are zero, and
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# we can leave them as they are
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zooms[zooms == 0] = 1 |
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RS = RZS / zooms |
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# Transform below is polar decomposition, returning the closest
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# shearless matrix R to RS
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P, S, Qs = npl.svd(RS, full_matrices=False) |
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# Threshold the singular values to determine the rank.
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if tol is None: |
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tol = S.max() * max(RS.shape) * np.finfo(S.dtype).eps |
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keep = (S > tol) |
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R = np.dot(P[:, keep], Qs[keep]) |
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# the matrix R is such that np.dot(R,R.T) is projection onto the
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# columns of P[:,keep] and np.dot(R.T,R) is projection onto the rows
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# of Qs[keep]. R (== np.dot(R, np.eye(p))) gives rotation of the
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# unit input vectors to output coordinates. Therefore, the row
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# index of abs max R[:,N], is the output axis changing most as input
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# axis N changes. In case there are ties, we choose the axes
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# iteratively, removing used axes from consideration as we go
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ornt = np.ones((p, 2), dtype=np.int8) * np.nan |
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for in_ax in range(p): |
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col = R[:, in_ax] |
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if not np.allclose(col, 0): |
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out_ax = np.argmax(np.abs(col)) |
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ornt[in_ax, 0] = out_ax |
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assert col[out_ax] != 0 |
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if col[out_ax] < 0: |
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ornt[in_ax, 1] = -1 |
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else: |
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ornt[in_ax, 1] = 1 |
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# remove the identified axis from further consideration, by
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# zeroing out the corresponding row in R
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R[out_ax, :] = 0 |
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return ornt |
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def ornt_transform(start_ornt, end_ornt): |
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"""Return the orientation that transforms from `start_ornt` to `end_ornt`.
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Parameters
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----------
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start_ornt : (n,2) orientation array
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Initial orientation.
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end_ornt : (n,2) orientation array
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Final orientation.
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Returns
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-------
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orientations : (p, 2) ndarray
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The orientation that will transform the `start_ornt` to the `end_ornt`.
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"""
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start_ornt = np.asarray(start_ornt) |
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end_ornt = np.asarray(end_ornt) |
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if start_ornt.shape != end_ornt.shape: |
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raise ValueError("The orientations must have the same shape") |
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if start_ornt.shape[1] != 2: |
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raise ValueError(f"Invalid shape for an orientation: {start_ornt.shape}") |
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result = np.empty_like(start_ornt) |
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for end_in_idx, (end_out_idx, end_flip) in enumerate(end_ornt): |
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for start_in_idx, (start_out_idx, start_flip) in enumerate(start_ornt): |
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if end_out_idx == start_out_idx: |
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if start_flip == end_flip: |
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flip = 1 |
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else: |
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flip = -1 |
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result[start_in_idx, :] = [end_in_idx, flip] |
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break
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else: |
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raise ValueError("Unable to find out axis %d in start_ornt" % |
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end_out_idx) |
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return result |
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def apply_orientation(arr, ornt): |
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""" Apply transformations implied by `ornt` to the first
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n axes of the array `arr`
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Parameters
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----------
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arr : array-like of data with ndim >= n
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ornt : (n,2) orientation array
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orientation transform. ``ornt[N,1]` is flip of axis N of the
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array implied by `shape`, where 1 means no flip and -1 means
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flip. For example, if ``N==0`` and ``ornt[0,1] == -1``, and
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there's an array ``arr`` of shape `shape`, the flip would
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correspond to the effect of ``np.flipud(arr)``. ``ornt[:,0]`` is
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the transpose that needs to be done to the implied array, as in
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``arr.transpose(ornt[:,0])``
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Returns
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-------
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t_arr : ndarray
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data array `arr` transformed according to ornt
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"""
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t_arr = np.asarray(arr) |
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ornt = np.asarray(ornt) |
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n = ornt.shape[0] |
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if t_arr.ndim < n: |
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raise OrientationError('Data array has fewer dimensions than ' |
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'orientation') |
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# no coordinates can be dropped for applying the orientations
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if np.any(np.isnan(ornt[:, 0])): |
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raise OrientationError('Cannot drop coordinates when ' |
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'applying orientation to data') |
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# apply ornt transformations
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for ax, flip in enumerate(ornt[:, 1]): |
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if flip == -1: |
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t_arr = np.flip(t_arr, axis=ax) |
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full_transpose = np.arange(t_arr.ndim) |
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# ornt indicates the transpose that has occurred - we reverse it
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full_transpose[:n] = np.argsort(ornt[:, 0]) |
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t_arr = t_arr.transpose(full_transpose) |
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return t_arr |
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def inv_ornt_aff(ornt, shape): |
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""" Affine transform reversing transforms implied in `ornt`
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Imagine you have an array ``arr`` of shape `shape`, and you apply the
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transforms implied by `ornt` (more below), to get ``tarr``.
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``tarr`` may have a different shape ``shape_prime``. This routine
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returns the affine that will take a array coordinate for ``tarr``
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and give you the corresponding array coordinate in ``arr``.
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Parameters
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----------
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ornt : (p, 2) ndarray
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orientation transform. ``ornt[P, 1]` is flip of axis N of the array
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implied by `shape`, where 1 means no flip and -1 means flip. For
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example, if ``P==0`` and ``ornt[0, 1] == -1``, and there's an array
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``arr`` of shape `shape`, the flip would correspond to the effect of
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``np.flipud(arr)``. ``ornt[:,0]`` gives us the (reverse of the)
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transpose that has been done to ``arr``. If there are any NaNs in
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`ornt`, we raise an ``OrientationError`` (see notes)
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shape : length p sequence
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shape of array you may transform with `ornt`
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Returns
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-------
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transform_affine : (p + 1, p + 1) ndarray
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An array ``arr`` (shape `shape`) might be transformed according to
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`ornt`, resulting in a transformed array ``tarr``. `transformed_affine`
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is the transform that takes you from array coordinates in ``tarr`` to
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array coordinates in ``arr``.
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Notes
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-----
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If a row in `ornt` contains NaN, this means that the input row does not
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influence the output space, and is thus effectively dropped from the output
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space. In that case one ``tarr`` coordinate maps to many ``arr``
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coordinates, we can't invert the transform, and we raise an error
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"""
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ornt = np.asarray(ornt) |
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if np.any(np.isnan(ornt)): |
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raise OrientationError("We cannot invert orientation transform") |
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p = ornt.shape[0] |
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shape = np.array(shape)[:p] |
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# ornt implies a flip, followed by a transpose. We need the affine
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# that inverts these. Thus we need the affine that first undoes the
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# effect of the transpose, then undoes the effects of the flip.
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# ornt indicates the transpose that has occurred to get the current
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# ordering, relative to canonical, so we just use that.
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# undo_reorder is a row permutatation matrix
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axis_transpose = [int(v) for v in ornt[:, 0]] |
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undo_reorder = np.eye(p + 1)[axis_transpose + [p], :] |
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undo_flip = np.diag(list(ornt[:, 1]) + [1.0]) |
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center_trans = -(shape - 1) / 2.0 |
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undo_flip[:p, p] = (ornt[:, 1] * center_trans) - center_trans |
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return np.dot(undo_flip, undo_reorder) |
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@deprecate_with_version('orientation_affine deprecated. ' |
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'Please use inv_ornt_aff instead.', |
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'3.0', |
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'4.0') |
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def orientation_affine(ornt, shape): |
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return inv_ornt_aff(ornt, shape) |
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@deprecate_with_version('flip_axis is deprecated. ' |
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'Please use numpy.flip instead.', |
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'3.2', |
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'5.0') |
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def flip_axis(arr, axis=0): |
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""" Flip contents of `axis` in array `arr`
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Equivalent to ``np.flip(arr, axis)``.
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Parameters
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----------
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arr : array-like
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axis : int, optional
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axis to flip. Default `axis` == 0
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Returns
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-------
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farr : array
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Array with axis `axis` flipped
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"""
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return np.flip(arr, axis) |
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def ornt2axcodes(ornt, labels=None): |
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""" Convert orientation `ornt` to labels for axis directions
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Parameters
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----------
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ornt : (N,2) array-like
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orientation array - see io_orientation docstring
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labels : optional, None or sequence of (2,) sequences
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(2,) sequences are labels for (beginning, end) of output axis. That
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is, if the first row in `ornt` is ``[1, 1]``, and the second (2,)
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sequence in `labels` is ('back', 'front') then the first returned axis
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code will be ``'front'``. If the first row in `ornt` had been
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``[1, -1]`` then the first returned value would have been ``'back'``.
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If None, equivalent to ``(('L','R'),('P','A'),('I','S'))`` - that is -
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RAS axes.
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Returns
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-------
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axcodes : (N,) tuple
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labels for positive end of voxel axes. Dropped axes get a label of
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None.
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Examples
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--------
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>>> ornt2axcodes([[1, 1],[0,-1],[2,1]], (('L','R'),('B','F'),('D','U')))
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('F', 'L', 'U')
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"""
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if labels is None: |
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labels = list(zip('LPI', 'RAS')) |
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axcodes = [] |
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for axno, direction in np.asarray(ornt): |
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if np.isnan(axno): |
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axcodes.append(None) |
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continue
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axint = int(np.round(axno)) |
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if axint != axno: |
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raise ValueError(f'Non integer axis number {axno:f}') |
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elif direction == 1: |
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axcode = labels[axint][1] |
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elif direction == -1: |
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axcode = labels[axint][0] |
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else: |
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raise ValueError('Direction should be -1 or 1') |
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axcodes.append(axcode) |
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return tuple(axcodes) |
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def axcodes2ornt(axcodes, labels=None): |
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""" Convert axis codes `axcodes` to an orientation
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Parameters
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----------
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axcodes : (N,) tuple
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axis codes - see ornt2axcodes docstring
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labels : optional, None or sequence of (2,) sequences
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(2,) sequences are labels for (beginning, end) of output axis. That
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is, if the first element in `axcodes` is ``front``, and the second
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(2,) sequence in `labels` is ('back', 'front') then the first
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row of `ornt` will be ``[1, 1]``. If None, equivalent to
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``(('L','R'),('P','A'),('I','S'))`` - that is - RAS axes.
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Returns
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-------
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ornt : (N,2) array-like
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orientation array - see io_orientation docstring
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Examples
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--------
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>>> axcodes2ornt(('F', 'L', 'U'), (('L','R'),('B','F'),('D','U')))
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array([[ 1., 1.],
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[ 0., -1.],
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[ 2., 1.]])
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"""
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labels = list(zip('LPI', 'RAS')) if labels is None else labels |
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allowed_labels = sum([list(L) for L in labels], []) + [None] |
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if len(allowed_labels) != len(set(allowed_labels)): |
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raise ValueError(f'Duplicate labels in {allowed_labels}') |
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if not set(axcodes).issubset(allowed_labels): |
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raise ValueError(f'Not all axis codes {list(axcodes)} in label set {allowed_labels}') |
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n_axes = len(axcodes) |
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ornt = np.ones((n_axes, 2), dtype=np.int8) * np.nan |
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for code_idx, code in enumerate(axcodes): |
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for label_idx, codes in enumerate(labels): |
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if code is None: |
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continue
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if code in codes: |
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if code == codes[0]: |
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ornt[code_idx, :] = [label_idx, -1] |
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else: |
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ornt[code_idx, :] = [label_idx, 1] |
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break
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return ornt |
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def aff2axcodes(aff, labels=None, tol=None): |
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""" axis direction codes for affine `aff`
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Parameters
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----------
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aff : (N,M) array-like
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affine transformation matrix
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labels : optional, None or sequence of (2,) sequences
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Labels for negative and positive ends of output axes of `aff`. See
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docstring for ``ornt2axcodes`` for more detail
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tol : None or float
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Tolerance for SVD of affine - see ``io_orientation`` for more detail.
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Returns
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-------
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axcodes : (N,) tuple
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labels for positive end of voxel axes. Dropped axes get a label of
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None.
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Examples
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--------
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>>> aff = [[0,1,0,10],[-1,0,0,20],[0,0,1,30],[0,0,0,1]]
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| 378 |
>>> aff2axcodes(aff, (('L','R'),('B','F'),('D','U')))
|
|
| 379 |
('B', 'R', 'U')
|
|
| 380 |
"""
|
|
| 381 | 33 |
ornt = io_orientation(aff, tol) |
| 382 | 33 |
return ornt2axcodes(ornt, labels) |
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