Esempio n. 1
0
    def tst_conservation_of_counts(self):

        from scitbx import matrix
        from random import uniform
        from dials.algorithms.profile_model.gaussian_rs import CoordinateSystem
        from dials.algorithms.profile_model.gaussian_rs import transform
        from scitbx.array_family import flex

        assert (len(self.detector) == 1)

        s0 = self.beam.get_s0()
        m2 = self.gonio.get_rotation_axis()
        s0_length = matrix.col(self.beam.get_s0()).length()

        # Create an s1 map
        s1_map = transform.beam_vector_map(self.detector[0], self.beam, True)

        for i in range(100):

            # Get random x, y, z
            x = uniform(300, 1800)
            y = uniform(300, 1800)
            z = uniform(0, 9)

            # Get random s1, phi, panel
            s1 = matrix.col(self.detector[0].get_pixel_lab_coord(
                (x, y))).normalize() * s0_length
            phi = self.scan.get_angle_from_array_index(z, deg=False)
            panel = 0

            # Calculate the bounding box
            bbox = self.calculate_bbox(s1, z, panel)
            x0, x1, y0, y1, z0, z1 = bbox

            # Create the coordinate system
            cs = CoordinateSystem(m2, s0, s1, phi)

            # The grid index generator
            step_size = self.delta_divergence / self.grid_size
            grid_index = transform.GridIndexGenerator(cs, x0, y0,
                                                      (step_size, step_size),
                                                      self.grid_size, s1_map)

            # Create the image
            #image = flex.double(flex.grid(z1 - z0, y1 - y0, x1 - x0), 1)
            image = gaussian((z1 - z0, y1 - y0, x1 - x0), 10.0,
                             (z - z0, y - y0, x - x0), (2.0, 2.0, 2.0))
            mask = flex.bool(flex.grid(image.all()), False)
            for j in range(y1 - y0):
                for i in range(x1 - x0):
                    inside = False
                    gx00, gy00 = grid_index(j, i)
                    gx01, gy01 = grid_index(j, i + 1)
                    gx10, gy10 = grid_index(j + 1, i)
                    gx11, gy11 = grid_index(j + 1, i + 1)
                    mingx = min([gx00, gx01, gx10, gx11])
                    maxgx = max([gx00, gx01, gx10, gx11])
                    mingy = min([gy00, gy01, gy10, gy11])
                    maxgy = max([gy00, gy01, gy10, gy11])
                    if (mingx >= 0 and maxgx < 2 * self.grid_size + 1
                            and mingy >= 0 and maxgy < 2 * self.grid_size + 1):
                        inside = True
                    for k in range(1, z1 - z0 - 1):
                        mask[k, j, i] = inside

            # Transform the image to the grid
            transformed = transform.TransformForward(self.spec, cs, bbox, 0,
                                                     image.as_double(), mask)
            grid = transformed.profile()

            # Get the sums and ensure they're the same
            eps = 1e-7
            sum_grid = flex.sum(grid)
            sum_image = flex.sum(flex.double(flex.select(image, flags=mask)))
            assert (abs(sum_grid - sum_image) <= eps)

        # Test passed
        print 'OK'
Esempio n. 2
0
def test_forward_panel_edge(dials_data):
    expt = ExperimentList.from_file(
        dials_data("centroid_test_data").join(
            "imported_experiments.json").strpath)[0]

    # Get the models
    beam = expt.beam
    detector = expt.detector
    gonio = expt.goniometer
    scan = expt.scan

    # Set some parameters
    sigma_divergence = 0.00101229
    mosaicity = 0.157 * math.pi / 180
    n_sigma = 3
    grid_size = 7
    delta_divergence = n_sigma * sigma_divergence

    step_size = delta_divergence / grid_size
    delta_divergence2 = delta_divergence + step_size * 0.5
    delta_mosaicity = n_sigma * mosaicity

    # Create the bounding box calculator
    calculate_bbox = BBoxCalculator3D(beam, detector, gonio, scan,
                                      delta_divergence2, delta_mosaicity)

    # Initialise the transform
    spec = transform.TransformSpec(beam, detector, gonio, scan,
                                   sigma_divergence, mosaicity, n_sigma + 1,
                                   grid_size)

    assert len(detector) == 1

    s0 = beam.get_s0()
    m2 = gonio.get_rotation_axis()
    s0_length = matrix.col(beam.get_s0()).length()

    image_size = detector[0].get_image_size()
    refl_xy = [
        (0, 0),
        (2, 3),
        (4, 1000),
        (1000, 5),
        (image_size[0] - 1, image_size[1] - 1),
        (image_size[0] - 2, 1),
        (1, image_size[1] - 5),
        (1000, image_size[1] - 4),
        (image_size[0] - 3, 1000),
    ]

    for x, y in refl_xy:
        z = random.uniform(0, 9)

        # Get random s1, phi, panel
        s1 = matrix.col(detector[0].get_pixel_lab_coord(
            (x, y))).normalize() * s0_length
        phi = scan.get_angle_from_array_index(z, deg=False)
        panel = 0

        # Calculate the bounding box
        bbox = calculate_bbox(s1, z, panel)
        x0, x1, y0, y1, z0, z1 = bbox

        # Create the coordinate system
        cs = CoordinateSystem(m2, s0, s1, phi)

        # Create the image
        image = gaussian((z1 - z0, y1 - y0, x1 - x0), 10.0,
                         (z - z0, y - y0, x - x0), (2.0, 2.0, 2.0))

        # Mask for the foreground pixels
        refl_mask = image > 1e-3
        bg = flex.double(image.accessor())

        # Shoebox mask, i.e. mask out pixels that are outside the panel bounds
        shoebox_mask = flex.bool(image.accessor(), False)
        for j in range(y1 - y0):
            for i in range(x1 - x0):
                if (j + y0 >= 0 and j + y0 < image_size[1] and i + x0 >= 0
                        and i + x0 < image_size[0]):
                    for k in range(z1 - z0):
                        shoebox_mask[k, j, i] = True

        mask = refl_mask & shoebox_mask

        # from matplotlib import pyplot as plt
        # fig, axes = plt.subplots(ncols=refl_mask.focus()[0], nrows=4)
        # for i in range(refl_mask.focus()[0]):
        # axes[0, i].imshow(image.as_numpy_array()[i])
        # axes[1, i].imshow(refl_mask.as_numpy_array()[i])
        # axes[2, i].imshow(shoebox_mask.as_numpy_array()[i])
        # axes[3, i].imshow(mask.as_numpy_array()[i])
        # plt.show()

        # Transform the image to the grid
        transformed = transform.TransformForward(spec, cs, bbox, 0,
                                                 image.as_double(), bg,
                                                 refl_mask)
        grid = transformed.profile()

        mask = refl_mask & shoebox_mask
        # assert only pixels within the panel were transformed
        assert flex.sum(grid) == pytest.approx(flex.sum(
            image.select(mask.as_1d())),
                                               rel=0.01)
        # The total transformed counts should be less than the (unmasked) image counts
        assert flex.sum(grid) < flex.sum(image)

        # Transform the image to the grid, this time without a background
        transformed = transform.TransformForward(spec, cs, bbox, 0,
                                                 image.as_double(), refl_mask)
        grid = transformed.profile()

        mask = refl_mask & shoebox_mask
        # assert only pixels within the panel were transformed
        assert flex.sum(grid) == pytest.approx(flex.sum(
            image.select(mask.as_1d())),
                                               rel=0.01)
        # The total transformed counts should be less than the (unmasked) image counts
        assert flex.sum(grid) < flex.sum(image)
Esempio n. 3
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def test_forward(dials_data):
    sequence = load.imageset(
        dials_data("centroid_test_data").join("sweep.json").strpath)

    # Get the models
    beam = sequence.get_beam()
    detector = sequence.get_detector()
    gonio = sequence.get_goniometer()
    scan = sequence.get_scan()

    # Set some parameters
    sigma_divergence = beam.get_sigma_divergence(deg=False)
    mosaicity = 0.157 * math.pi / 180
    n_sigma = 3
    grid_size = 7
    delta_divergence = n_sigma * sigma_divergence

    step_size = delta_divergence / grid_size
    delta_divergence2 = delta_divergence + step_size * 0.5
    delta_mosaicity = n_sigma * mosaicity

    # Create the bounding box calculator
    calculate_bbox = BBoxCalculator3D(beam, detector, gonio, scan,
                                      delta_divergence2, delta_mosaicity)

    # Initialise the transform
    spec = transform.TransformSpec(beam, detector, gonio, scan,
                                   sigma_divergence, mosaicity, n_sigma + 1,
                                   grid_size)

    # tst_conservation_of_counts(self):

    assert len(detector) == 1

    s0 = beam.get_s0()
    m2 = gonio.get_rotation_axis()
    s0_length = matrix.col(beam.get_s0()).length()

    # Create an s1 map
    s1_map = transform.beam_vector_map(detector[0], beam, True)

    for i in range(100):

        # Get random x, y, z
        x = random.uniform(300, 1800)
        y = random.uniform(300, 1800)
        z = random.uniform(0, 9)

        # Get random s1, phi, panel
        s1 = matrix.col(detector[0].get_pixel_lab_coord(
            (x, y))).normalize() * s0_length
        phi = scan.get_angle_from_array_index(z, deg=False)
        panel = 0

        # Calculate the bounding box
        bbox = calculate_bbox(s1, z, panel)
        x0, x1, y0, y1, z0, z1 = bbox

        # Create the coordinate system
        cs = CoordinateSystem(m2, s0, s1, phi)

        # The grid index generator
        step_size = delta_divergence / grid_size
        grid_index = transform.GridIndexGenerator(cs, x0, y0,
                                                  (step_size, step_size),
                                                  grid_size, s1_map)

        # Create the image
        # image = flex.double(flex.grid(z1 - z0, y1 - y0, x1 - x0), 1)
        image = gaussian((z1 - z0, y1 - y0, x1 - x0), 10.0,
                         (z - z0, y - y0, x - x0), (2.0, 2.0, 2.0))
        mask = flex.bool(flex.grid(image.all()), False)
        for j in range(y1 - y0):
            for i in range(x1 - x0):
                inside = False
                gx00, gy00 = grid_index(j, i)
                gx01, gy01 = grid_index(j, i + 1)
                gx10, gy10 = grid_index(j + 1, i)
                gx11, gy11 = grid_index(j + 1, i + 1)
                mingx = min([gx00, gx01, gx10, gx11])
                maxgx = max([gx00, gx01, gx10, gx11])
                mingy = min([gy00, gy01, gy10, gy11])
                maxgy = max([gy00, gy01, gy10, gy11])
                if (mingx >= 0 and maxgx < 2 * grid_size + 1 and mingy >= 0
                        and maxgy < 2 * grid_size + 1):
                    inside = True
                for k in range(1, z1 - z0 - 1):
                    mask[k, j, i] = inside

        # Transform the image to the grid
        transformed = transform.TransformForward(spec, cs, bbox, 0,
                                                 image.as_double(), mask)
        grid = transformed.profile()

        # Get the sums and ensure they're the same
        eps = 1e-7
        sum_grid = flex.sum(grid)
        sum_image = flex.sum(flex.double(flex.select(image, flags=mask)))
        assert abs(sum_grid - sum_image) <= eps

    # Test passed

    # tst_transform_with_background(self):

    assert len(detector) == 1
    s0 = beam.get_s0()
    m2 = gonio.get_rotation_axis()
    s0_length = matrix.col(beam.get_s0()).length()

    # Create an s1 map
    s1_map = transform.beam_vector_map(detector[0], beam, True)

    for i in range(100):

        # Get random x, y, z
        x = random.uniform(300, 1800)
        y = random.uniform(300, 1800)
        z = random.uniform(0, 9)

        # Get random s1, phi, panel
        s1 = matrix.col(detector[0].get_pixel_lab_coord(
            (x, y))).normalize() * s0_length
        phi = scan.get_angle_from_array_index(z, deg=False)
        panel = 0

        # Calculate the bounding box
        bbox = calculate_bbox(s1, z, panel)
        x0, x1, y0, y1, z0, z1 = bbox

        # Create the coordinate system
        cs = CoordinateSystem(m2, s0, s1, phi)

        # The grid index generator
        step_size = delta_divergence / grid_size
        grid_index = transform.GridIndexGenerator(cs, x0, y0,
                                                  (step_size, step_size),
                                                  grid_size, s1_map)

        # Create the image
        # image = flex.double(flex.grid(z1 - z0, y1 - y0, x1 - x0), 1)
        image = gaussian((z1 - z0, y1 - y0, x1 - x0), 10.0,
                         (z - z0, y - y0, x - x0), (2.0, 2.0, 2.0))
        background = flex.random_double(len(image))
        background.resize(image.accessor())
        mask = flex.bool(flex.grid(image.all()), False)
        for j in range(y1 - y0):
            for i in range(x1 - x0):
                inside = False
                gx00, gy00 = grid_index(j, i)
                gx01, gy01 = grid_index(j, i + 1)
                gx10, gy10 = grid_index(j + 1, i)
                gx11, gy11 = grid_index(j + 1, i + 1)
                mingx = min([gx00, gx01, gx10, gx11])
                maxgx = max([gx00, gx01, gx10, gx11])
                mingy = min([gy00, gy01, gy10, gy11])
                maxgy = max([gy00, gy01, gy10, gy11])
                if (mingx >= 0 and maxgx <= 2 * grid_size + 1 and mingy >= 0
                        and maxgy <= 2 * grid_size + 1):
                    inside = True
                for k in range(1, z1 - z0 - 1):
                    mask[k, j, i] = inside

        # Transform the image to the grid
        transformed = transform.TransformForward(spec, cs, bbox, 0,
                                                 image.as_double(),
                                                 background.as_double(), mask)
        igrid = transformed.profile()
        bgrid = transformed.background()

        # Get the sums and ensure they're the same
        eps = 1e-7
        sum_igrid = flex.sum(igrid)
        sum_bgrid = flex.sum(bgrid)
        sum_image = flex.sum(flex.double(flex.select(image, flags=mask)))
        sum_bkgrd = flex.sum(flex.double(flex.select(background, flags=mask)))
        try:
            assert abs(sum_igrid - sum_image) <= eps
            assert abs(sum_bgrid - sum_bkgrd) <= eps
        except Exception:
            print("Failed for: ", (x, y, z))
            raise
Esempio n. 4
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def test_forward(dials_data):
    from dials.model.serialize import load
    from dials.algorithms.profile_model.gaussian_rs import transform
    from dials.algorithms.profile_model.gaussian_rs import BBoxCalculator3D

    sweep = load.sweep(
        dials_data("centroid_test_data").join("sweep.json").strpath)

    # Get the models
    beam = sweep.get_beam()
    detector = sweep.get_detector()
    gonio = sweep.get_goniometer()
    scan = sweep.get_scan()

    #        beam.set_direction((0.0, 0.0, 1.0))
    #        gonio.set_rotation_axis((1.0, 0.0, 0.0))
    #        detector.set_frame((1.0, 0.0, 0.0),
    #                                (0.0, 1.0, 0.0),
    #                                (-150, -150, -200))

    # Set some parameters
    sigma_divergence = beam.get_sigma_divergence(deg=False)
    mosaicity = 0.157 * math.pi / 180
    n_sigma = 3
    grid_size = 7
    delta_divergence = n_sigma * sigma_divergence

    step_size = delta_divergence / grid_size
    delta_divergence2 = delta_divergence + step_size * 0.5
    delta_mosaicity = n_sigma * mosaicity

    # Create the bounding box calculator
    calculate_bbox = BBoxCalculator3D(beam, detector, gonio, scan,
                                      delta_divergence2, delta_mosaicity)

    # Initialise the transform
    spec = transform.TransformSpec(beam, detector, gonio, scan,
                                   sigma_divergence, mosaicity, n_sigma + 1,
                                   grid_size)

    # tst_conservation_of_counts(self):

    from scitbx import matrix
    from dials.algorithms.profile_model.gaussian_rs import CoordinateSystem
    from dials.algorithms.profile_model.gaussian_rs import transform
    from scitbx.array_family import flex

    assert len(detector) == 1

    s0 = beam.get_s0()
    m2 = gonio.get_rotation_axis()
    s0_length = matrix.col(beam.get_s0()).length()

    # Create an s1 map
    s1_map = transform.beam_vector_map(detector[0], beam, True)

    for i in range(100):

        # Get random x, y, z
        x = random.uniform(300, 1800)
        y = random.uniform(300, 1800)
        z = random.uniform(0, 9)

        # Get random s1, phi, panel
        s1 = matrix.col(detector[0].get_pixel_lab_coord(
            (x, y))).normalize() * s0_length
        phi = scan.get_angle_from_array_index(z, deg=False)
        panel = 0

        # Calculate the bounding box
        bbox = calculate_bbox(s1, z, panel)
        x0, x1, y0, y1, z0, z1 = bbox

        # Create the coordinate system
        cs = CoordinateSystem(m2, s0, s1, phi)

        # The grid index generator
        step_size = delta_divergence / grid_size
        grid_index = transform.GridIndexGenerator(cs, x0, y0,
                                                  (step_size, step_size),
                                                  grid_size, s1_map)

        # Create the image
        # image = flex.double(flex.grid(z1 - z0, y1 - y0, x1 - x0), 1)
        image = gaussian((z1 - z0, y1 - y0, x1 - x0), 10.0,
                         (z - z0, y - y0, x - x0), (2.0, 2.0, 2.0))
        mask = flex.bool(flex.grid(image.all()), False)
        for j in range(y1 - y0):
            for i in range(x1 - x0):
                inside = False
                gx00, gy00 = grid_index(j, i)
                gx01, gy01 = grid_index(j, i + 1)
                gx10, gy10 = grid_index(j + 1, i)
                gx11, gy11 = grid_index(j + 1, i + 1)
                mingx = min([gx00, gx01, gx10, gx11])
                maxgx = max([gx00, gx01, gx10, gx11])
                mingy = min([gy00, gy01, gy10, gy11])
                maxgy = max([gy00, gy01, gy10, gy11])
                if (mingx >= 0 and maxgx < 2 * grid_size + 1 and mingy >= 0
                        and maxgy < 2 * grid_size + 1):
                    inside = True
                for k in range(1, z1 - z0 - 1):
                    mask[k, j, i] = inside

        # Transform the image to the grid
        transformed = transform.TransformForward(spec, cs, bbox, 0,
                                                 image.as_double(), mask)
        grid = transformed.profile()

        # Get the sums and ensure they're the same
        eps = 1e-7
        sum_grid = flex.sum(grid)
        sum_image = flex.sum(flex.double(flex.select(image, flags=mask)))
        assert abs(sum_grid - sum_image) <= eps

    # Test passed

    #    def tst_transformed_centroid(self):

    #        from scitbx import matrix
    #        from random import uniform
    #        from dials.algorithms.profile_model.gaussian_rs import CoordinateSystem
    #        from dials.algorithms.profile_model.gaussian_rs import transform
    #        from scitbx.array_family import flex
    #        from time import time

    #        s0 = beam.get_s0()
    #        m2 = gonio.get_rotation_axis()
    #        s0_length = matrix.col(beam.get_s0()).length()

    #        # Create an s1 map
    #        s1_map = transform.beam_vector_map(detector, beam, True)

    #        # Get random x, y, z
    #        x = random.uniform(300, 1800)
    #        y = random.uniform(300, 1800)
    #        z = random.uniform(-10, 0)

    #        # Get random s1, phi, panel
    #        s1 = matrix.col(detector.get_pixel_lab_coord(
    #            (x, y))).normalize() * s0_length
    #        phi = scan.get_angle_from_array_index(z, deg=False)
    #        panel = 0

    #        # Calculate the bounding box
    #        bbox = calculate_bbox(s1, z, panel)
    #        x0, x1, y0, y1, z0, z1 = bbox

    #        # Create the coordinate system
    #        cs = CoordinateSystem(m2, s0, s1, phi)

    #        # The grid index generator
    #        step_size = delta_divergence / grid_size
    #        grid_index = transform.GridIndexGenerator(cs, x0, y0,
    #            (step_size, step_size), grid_size, s1_map)

    #        # Create the image
    #        image = gaussian((z1 - z0, y1 - y0, x1 - x0), 10.0,
    #            (z - z0, y - y0, x - x0), (2.0, 2.0, 2.0))

    #        print x, y, z, bbox
    #        print (z1 - z0, y1 - y0, x1 - x0), (z - z0, y - y0, x - x0)

    #        mask = flex.bool(flex.grid(image.all()), False)
    #        for j in range(y1 - y0):
    #            for i in range(x1 - x0):
    #                inside = False
    #                gx00, gy00 = grid_index(j, i)
    #                gx01, gy01 = grid_index(j, i+1)
    #                gx10, gy10 = grid_index(j+1, i)
    #                gx11, gy11 = grid_index(j+1, i+1)
    #                mingx = min([gx00, gx01, gx10, gx11])
    #                maxgx = max([gx00, gx01, gx10, gx11])
    #                mingy = min([gy00, gy01, gy10, gy11])
    #                maxgy = max([gy00, gy01, gy10, gy11])
    #                if (mingx >= 0 and maxgx <= 2 * grid_size + 1 and
    #                    mingy >= 0 and maxgy <= 2 * grid_size + 1):
    #                    inside = True
    #                for k in range(1, z1 - z0 - 1):
    #                    mask[k,j,i] = inside
    #                    #image[k,j,i] *= inside
    #        from matplotlib import pylab
    #        pylab.imshow(image.as_numpy_array()[(z1 - z0) / 2,:,:], interpolation='none')
    #        pylab.show()

    #        # Transform the image to the grid
    #        grid = transform(cs, bbox, image, mask)

    #        from matplotlib import pylab
    #        pylab.imshow(grid.as_numpy_array()[7,:,:], interpolation='none')
    #        pylab.show()

    #        # Get the sums and ensure they're the same
    #        eps = 1e-7
    #        sum_grid = flex.sum(grid)
    #        sum_image = flex.sum(flex.double(flex.select(image, flags=mask)))
    #        assert(abs(sum_grid - sum_image) <= eps)

    #        # Check the centroid
    #        sz = grid_size * 2 + 1
    #        grid_x = flex.double(flex.grid(sz, sz, sz))
    #        grid_y = flex.double(flex.grid(sz, sz, sz))
    #        grid_z = flex.double(flex.grid(sz, sz, sz))
    #        for k in range(sz):
    #            for j in range(sz):
    #                for i in range(sz):
    #                    grid_x[k,j,i] = i + 0.5
    #                    grid_y[k,j,i] = j + 0.5
    #                    grid_z[k,j,i] = k + 0.5
    #
    #        sum_grid_x = flex.sum(grid * grid_x)
    #        sum_grid_y = flex.sum(grid * grid_y)
    #        sum_grid_z = flex.sum(grid * grid_z)
    #        xc = sum_grid_x / sum_grid
    #        yc = sum_grid_y / sum_grid
    #        zc = sum_grid_z / sum_grid
    #        print xc, yc, zc
    #        assert(abs(xc - grid_size + 0.5) <= 0.5)
    #        assert(abs(yc - grid_size + 0.5) <= 0.5)
    #        assert(abs(zc - grid_size + 0.5) <= 0.5)

    #        # Test passed
    #        print 'OK'

    # tst_transform_with_background(self):

    from scitbx import matrix
    from dials.algorithms.profile_model.gaussian_rs import CoordinateSystem
    from dials.algorithms.profile_model.gaussian_rs import transform
    from scitbx.array_family import flex

    assert len(detector) == 1
    s0 = beam.get_s0()
    m2 = gonio.get_rotation_axis()
    s0_length = matrix.col(beam.get_s0()).length()

    # Create an s1 map
    s1_map = transform.beam_vector_map(detector[0], beam, True)

    for i in range(100):

        # Get random x, y, z
        x = random.uniform(300, 1800)
        y = random.uniform(300, 1800)
        z = random.uniform(0, 9)

        # Get random s1, phi, panel
        s1 = matrix.col(detector[0].get_pixel_lab_coord(
            (x, y))).normalize() * s0_length
        phi = scan.get_angle_from_array_index(z, deg=False)
        panel = 0

        # Calculate the bounding box
        bbox = calculate_bbox(s1, z, panel)
        x0, x1, y0, y1, z0, z1 = bbox

        # Create the coordinate system
        cs = CoordinateSystem(m2, s0, s1, phi)

        # The grid index generator
        step_size = delta_divergence / grid_size
        grid_index = transform.GridIndexGenerator(cs, x0, y0,
                                                  (step_size, step_size),
                                                  grid_size, s1_map)

        # Create the image
        # image = flex.double(flex.grid(z1 - z0, y1 - y0, x1 - x0), 1)
        image = gaussian((z1 - z0, y1 - y0, x1 - x0), 10.0,
                         (z - z0, y - y0, x - x0), (2.0, 2.0, 2.0))
        background = flex.random_double(len(image))
        background.resize(image.accessor())
        mask = flex.bool(flex.grid(image.all()), False)
        for j in range(y1 - y0):
            for i in range(x1 - x0):
                inside = False
                gx00, gy00 = grid_index(j, i)
                gx01, gy01 = grid_index(j, i + 1)
                gx10, gy10 = grid_index(j + 1, i)
                gx11, gy11 = grid_index(j + 1, i + 1)
                mingx = min([gx00, gx01, gx10, gx11])
                maxgx = max([gx00, gx01, gx10, gx11])
                mingy = min([gy00, gy01, gy10, gy11])
                maxgy = max([gy00, gy01, gy10, gy11])
                if (mingx >= 0 and maxgx <= 2 * grid_size + 1 and mingy >= 0
                        and maxgy <= 2 * grid_size + 1):
                    inside = True
                for k in range(1, z1 - z0 - 1):
                    mask[k, j, i] = inside

        # Transform the image to the grid
        transformed = transform.TransformForward(spec, cs, bbox, 0,
                                                 image.as_double(),
                                                 background.as_double(), mask)
        igrid = transformed.profile()
        bgrid = transformed.background()

        # Get the sums and ensure they're the same
        eps = 1e-7
        sum_igrid = flex.sum(igrid)
        sum_bgrid = flex.sum(bgrid)
        sum_image = flex.sum(flex.double(flex.select(image, flags=mask)))
        sum_bkgrd = flex.sum(flex.double(flex.select(background, flags=mask)))
        try:
            assert abs(sum_igrid - sum_image) <= eps
            assert abs(sum_bgrid - sum_bkgrd) <= eps
        except Exception:
            print("Failed for: ", (x, y, z))
            raise