import numpy as np
from ..util._map_array import map_array, ArrayMap
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def join_segmentations(s1, s2, return_mapping: bool = False):
"""Return the join of the two input segmentations.
The join J of S1 and S2 is defined as the segmentation in which two
voxels are in the same segment if and only if they are in the same
segment in *both* S1 and S2.
Parameters
----------
s1, s2 : numpy arrays
s1 and s2 are label fields of the same shape.
return_mapping : bool, optional
If true, return mappings for joined segmentation labels to the original labels.
Returns
-------
j : numpy array
The join segmentation of s1 and s2.
map_j_to_s1 : ArrayMap, optional
Mapping from labels of the joined segmentation j to labels of s1.
map_j_to_s2 : ArrayMap, optional
Mapping from labels of the joined segmentation j to labels of s2.
Examples
--------
>>> from skimage.segmentation import join_segmentations
>>> s1 = np.array([[0, 0, 1, 1],
... [0, 2, 1, 1],
... [2, 2, 2, 1]])
>>> s2 = np.array([[0, 1, 1, 0],
... [0, 1, 1, 0],
... [0, 1, 1, 1]])
>>> join_segmentations(s1, s2)
array([[0, 1, 3, 2],
[0, 5, 3, 2],
[4, 5, 5, 3]])
>>> j, m1, m2 = join_segmentations(s1, s2, return_mapping=True)
>>> m1
ArrayMap(array([0, 1, 2, 3, 4, 5]), array([0, 0, 1, 1, 2, 2]))
>>> np.all(m1[j] == s1)
True
>>> np.all(m2[j] == s2)
True
"""
if s1.shape != s2.shape:
raise ValueError(
"Cannot join segmentations of different shape. "
f"s1.shape: {s1.shape}, s2.shape: {s2.shape}"
)
# Reindex input label images
s1_relabeled, _, backward_map1 = relabel_sequential(s1)
s2_relabeled, _, backward_map2 = relabel_sequential(s2)
# Create joined label image
factor = s2.max() + 1
j_initial = factor * s1_relabeled + s2_relabeled
j, _, map_j_to_j_initial = relabel_sequential(j_initial)
if not return_mapping:
return j
# Determine label mapping
labels_j = np.unique(j_initial)
labels_s1_relabeled, labels_s2_relabeled = np.divmod(labels_j, factor)
map_j_to_s1 = ArrayMap(
map_j_to_j_initial.in_values, backward_map1[labels_s1_relabeled]
)
map_j_to_s2 = ArrayMap(
map_j_to_j_initial.in_values, backward_map2[labels_s2_relabeled]
)
return j, map_j_to_s1, map_j_to_s2
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def relabel_sequential(label_field, offset=1):
"""Relabel arbitrary labels to {`offset`, ... `offset` + number_of_labels}.
This function also returns the forward map (mapping the original labels to
the reduced labels) and the inverse map (mapping the reduced labels back
to the original ones).
Parameters
----------
label_field : numpy array of int, arbitrary shape
An array of labels, which must be non-negative integers.
offset : int, optional
The return labels will start at `offset`, which should be
strictly positive.
Returns
-------
relabeled : numpy array of int, same shape as `label_field`
The input label field with labels mapped to
{offset, ..., number_of_labels + offset - 1}.
The data type will be the same as `label_field`, except when
offset + number_of_labels causes overflow of the current data type.
forward_map : ArrayMap
The map from the original label space to the returned label
space. Can be used to re-apply the same mapping. See examples
for usage. The output data type will be the same as `relabeled`.
inverse_map : ArrayMap
The map from the new label space to the original space. This
can be used to reconstruct the original label field from the
relabeled one. The output data type will be the same as `label_field`.
Notes
-----
The label 0 is assumed to denote the background and is never remapped.
The forward map can be extremely big for some inputs, since its
length is given by the maximum of the label field. However, in most
situations, ``label_field.max()`` is much smaller than
``label_field.size``, and in these cases the forward map is
guaranteed to be smaller than either the input or output images.
Examples
--------
>>> from skimage.segmentation import relabel_sequential
>>> label_field = np.array([1, 1, 5, 5, 8, 99, 42])
>>> relab, fw, inv = relabel_sequential(label_field)
>>> relab
array([1, 1, 2, 2, 3, 5, 4])
>>> print(fw)
ArrayMap:
1 → 1
5 → 2
8 → 3
42 → 4
99 → 5
>>> np.array(fw)
array([0, 1, 0, 0, 0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5])
>>> np.array(inv)
array([ 0, 1, 5, 8, 42, 99])
>>> (fw[label_field] == relab).all()
True
>>> (inv[relab] == label_field).all()
True
>>> relab, fw, inv = relabel_sequential(label_field, offset=5)
>>> relab
array([5, 5, 6, 6, 7, 9, 8])
"""
if offset <= 0:
raise ValueError("Offset must be strictly positive.")
if np.min(label_field) < 0:
raise ValueError("Cannot relabel array that contains negative values.")
offset = int(offset)
in_vals = np.unique(label_field)
if in_vals[0] == 0:
# always map 0 to 0
out_vals = np.concatenate([[0], np.arange(offset, offset + len(in_vals) - 1)])
else:
out_vals = np.arange(offset, offset + len(in_vals))
input_type = label_field.dtype
if input_type.kind not in "iu":
raise TypeError("label_field must have an integer dtype")
# Some logic to determine the output type:
# - we don't want to return a smaller output type than the input type,
# ie if we get uint32 as labels input, don't return a uint8 array.
# - but, in some cases, using the input type could result in overflow. The
# input type could be a signed integer (e.g. int32) but
# `np.min_scalar_type` will always return an unsigned type. We check for
# that by casting the largest output value to the input type. If it is
# unchanged, we use the input type, else we use the unsigned minimum
# required type
required_type = np.min_scalar_type(out_vals[-1])
if input_type.itemsize < required_type.itemsize:
output_type = required_type
else:
if out_vals[-1] < np.iinfo(input_type).max:
output_type = input_type
else:
output_type = required_type
out_array = np.empty(label_field.shape, dtype=output_type)
out_vals = out_vals.astype(output_type)
map_array(label_field, in_vals, out_vals, out=out_array)
fw_map = ArrayMap(in_vals, out_vals)
inv_map = ArrayMap(out_vals, in_vals)
return out_array, fw_map, inv_map
