Affine transformation for dask arrays: Wrapper around `ndimage.affine_transform`

affine_transform_dask.py

#!/usr/bin/env python

"""
Affine transformation for dask arrays: Wrapper around `ndimage.affine_transform`
"""

__author__ = "Marvin Albert"
__email__ = "[email protected]"


import numpy as np
import dask.array as da
from scipy import ndimage
def affine_transform_dask(
        input,
        matrix,
        offset=0.0,
        output_shape=None,
        output_chunks=None,
        **kwargs
):
    """
    Wraps `ndimage.affine_transformation` for dask arrays.
    For every output chunk, only the slice containing the
    relevant part of the input is passed on to
    `ndimage.affine_transformation`.

    To do:
      - optionally use cupyx.scipy.ndimage.affine_transform

    API wraps `ndimage.affine_transformation`, except for `output_chunks`.

    :param input: N-D numpy or dask array
    :param matrix:
    :param offset:
    :param output_shape:
    :param output_chunks:
    :param kwargs:
    :return: dask array
    """

    def resample_chunk(chunk, matrix, offset, kwargs, block_info=None):

        N = chunk.ndim
        input_shape = input.shape
        chunk_shape = chunk.shape

        chunk_offset = [i[0] for i in block_info[0]['array-location']]
        # print('chunk_offset', chunk_offset)

        chunk_edges = np.array([i for i in np.ndindex(tuple([2] * N))])\
                      * np.array(chunk_shape) + np.array(chunk_offset)
        rel_input_edges = np.dot(matrix, chunk_edges.T).T + offset

        # print('rel_input_edges', rel_input_edges) # ok
        # print('chunk_edges', chunk_edges) # ok

        rel_input_i = np.min(rel_input_edges, 0)
        rel_input_f = np.max(rel_input_edges, 0)

        # not sure yet how many additional pixels to include
        # (depends on interp order?)
        for dim, upper in zip(range(N), input_shape):
            rel_input_i[dim] = np.clip(rel_input_i[dim] - 2, 0, upper)
            rel_input_f[dim] = np.clip(rel_input_f[dim] + 2, 0, upper)

        rel_input_i = rel_input_i.astype(np.int64)
        rel_input_f = rel_input_f.astype(np.int64)

        # print('min max input', rel_input_i, rel_input_f)

        rel_input_slice = tuple([slice(int(rel_input_i[dim]),
                                       int(rel_input_f[dim]))
                                 for dim in range(N)])

        rel_input = input[rel_input_slice]

        # print('rel_input_slice', rel_input_slice)

        # modify offset to point into cropped input
        # y = Mx + o
        # coordinate substitution:
        # y' = y - y0(min_coord_px)
        # x' = x - x0(chunk_offset)
        # then
        # y' = Mx' + o + Mx0 - y0
        # M' = M
        # o' = o + Mx0 - y0

        offset_prime = offset + np.dot(matrix, chunk_offset) - rel_input_i

        chunk = ndimage.affine_transform(rel_input,
                                         matrix,
                                         offset_prime,
                                         output_shape=chunk_shape,
                                         **kwargs)

        return chunk

    if output_shape is None: output_shape = input.shape

    transformed = da.zeros(output_shape,
                           dtype=input.dtype,
                           chunks=output_chunks)

    transformed = transformed.map_blocks(resample_chunk,
                                         dtype=input.dtype,
                                         matrix=matrix,
                                         offset=offset,
                                         kwargs=kwargs,
                                         )

    return transformed


if __name__ == "__main__":

    from timeit import default_timer as timer
    from matplotlib import pyplot
    import tifffile

    # create test image
    N = 3
    a = 100

    np.random.seed(0)
    im = np.random.random([int(a / 20)] * N)
    im = ndimage.zoom(im, 20, order=1)
    im = im / im.max()
    im *= 1000
    im = im.astype(np.uint16)

    # transform into dask array
    chunksize = [32] * N
    dim = da.from_array(im, chunks=chunksize)

    # define (random) transformation
    matrix = np.eye(N) + (np.random.random((N, N)) - 0.5) / 5.
    offset = (np.random.random(N) - 0.5) / 5. * np.array(im.shape)

    print('matrix\n', matrix)
    print('offset\n', offset)

    # define resampling options
    # output_shape = im.shape
    output_shape = [int(a / 4)] * N
    output_chunks = [32] * N
    interp_order = 3

    # transform without dask
    ti = timer()
    im_t_nodask = ndimage.affine_transform(im, matrix, offset,
                                           output_shape=output_shape,
                                           order=interp_order)
    tf = timer()
    print('Timing without dask: %s seconds' %(tf-ti))

    # transform with function above using dask
    ti = timer()
    scheduler = 'single-threaded'
    # scheduler = 'threads'
    im_t_dask = affine_transform_dask(dim, matrix, offset,
                                           output_shape=output_shape,
                                           output_chunks=output_chunks,
                                           order=interp_order)
    im_t_dask_computed = im_t_dask.compute(scheduler=scheduler)
    tf = timer()
    print('Timing with dask: %s seconds' %(tf-ti))

    # write out dask graph to visualize chunk flow
    # python-graphviz needs to be installed, see:
    # https://docs.dask.org/en/latest/graphviz.html
    # im_t_dask.visualize(filename='affine_transformation_dask.png')

    # show and compare transformation results
    tifffile.imshow(np.array([im_t_nodask, im_t_dask_computed]), vmin=0, vmax=1000)
    pyplot.show()