def centroid_similarity(self, inputs, targets, shape):
"""
Metric for similarity to centroid. Computes a similarity based on
inverse of normaised euclidian distance for every centroid neighbor.
Neighbors are determined by a structing element (cell-ish dims)
The output should be between 0-1 (therefore easily invertable)
MAKE SURE THIS IS TRUE!!!
Notes
-----
Currently uses a structing element to find centroid neighbors.
Hoping to add an option for using segmentation to get neighbors.
"""
offsets = _offsets_to_raveled_neighbors(shape, self.selem, self.centre)
euclid_dists = self.euclidian_distances()
weights = euclid_dists - 1
centroids = np.argwhere(np_targets == 1.)
score = 0
for c in centroids:
max_ind = np.inputs.shape[-1]
raveled_indices = c + offsets
in_bounds_indices = np.array([idx for idx in raveled_indices \
if idx >= 0 and idx < max_ind])
neighbors = np_inputs[in_bounds_indices]
weighted = neighbors * weights
score += weighted.mean()
return mean
def _indices_to_raveled_affinities(image_shape, selem, centre):
im_offsets = _offsets_to_raveled_neighbors(image_shape, selem, centre)
#im_offsets[-len(image_shape):] = 0
affs = np.concatenate(
[np.arange(len(image_shape)),
np.arange(len(image_shape))[::-1]])
indices = np.stack([affs, im_offsets], axis=1)
return indices
def test_offsets_to_raveled_neighbors_explicit_0():
"""Check reviewed example."""
image_shape = (100, 200, 3)
selem = np.ones((3, 3, 3), dtype=bool)
center = (1, 1, 1)
offsets = _util._offsets_to_raveled_neighbors(image_shape, selem, center)
desired = np.array([
3, -600, 1, -1, 600, -3, 4, 2, 603, -2, -4, -597, 601, -599, -601,
-603, 599, 597, 602, -604, 596, -596, -598, -602, 598, 604
])
assert_array_equal(offsets, desired)
def test_offsets_to_raveled_neighbors_highest_connectivity(image_shape, order):
"""
Check scenarios where footprint is always of the highest connectivity
and all dimensions are > 2.
"""
footprint = np.ones((3, ) * len(image_shape), dtype=bool)
center = (1, ) * len(image_shape)
offsets = _util._offsets_to_raveled_neighbors(image_shape, footprint,
center, order)
# Assert only neighbors are present, center was removed
assert len(offsets) == footprint.sum() - 1
assert 0 not in offsets
# Assert uniqueness
assert len(set(offsets)) == offsets.size
# offsets form pairs of with same value but different signs
# if footprint is symmetric around center
assert all(-x in offsets for x in offsets)
# Construct image whose values are the Manhattan distance to its center
image_center = tuple(s // 2 for s in image_shape)
coords = [
np.abs(np.arange(s, dtype=np.intp) - c)
for s, c in zip(image_shape, image_center)
]
grid = np.meshgrid(*coords, indexing="ij")
image = np.sum(grid, axis=0)
image_raveled = image.ravel(order)
image_center_raveled = np.ravel_multi_index(image_center,
image_shape,
order=order)
# Sample raveled image around its center
samples = []
for offset in offsets:
index = image_center_raveled + offset
samples.append(image_raveled[index])
# Assert that center with value 0 wasn't selected
assert np.min(samples) == 1
# Assert that only neighbors where selected
# (highest value == connectivity)
assert np.max(samples) == len(image_shape)
# Assert that nearest neighbors are selected first
assert list(sorted(samples)) == samples
def test_offsets_to_raveled_neighbors_explicit_1():
"""Check reviewed example where selem is larger in last dimension."""
image_shape = (10, 9, 8, 3)
selem = np.ones((3, 3, 3, 4), dtype=bool)
center = (1, 1, 1, 1)
offsets = _util._offsets_to_raveled_neighbors(image_shape, selem, center)
desired = np.array([
24, 3, 1, -1, -3, -24, -216, 216, -192, 215, -2, -21, -23, 2, -25, -27,
4, 217, 21, 219, -4, 23, 25, -240, 240, 192, 27, -213, -219, 213, -215,
-217, -243, 191, -241, 195, 189, 212, 26, 5, 20, 28, 22, 214, 243,
-237, -22, 241, -214, -212, 237, -218, -195, -20, 220, -193, -191, 218,
-189, -28, -26, 193, -239, -220, 239, 196, 221, 242, 236, 238, 194,
-244, -188, -238, -211, -196, -194, -190, -236, -19, 244, 29, 188,
-242, 190, -187, 197, -235, 245
])
assert_array_equal(offsets, desired)
def test_offsets_to_raveled_neighbors_selem_smaller_image(image_shape, order):
"""
Test if a dimension indicated by `image_shape` is smaller than in
`selem`.
"""
selem = np.ones((3, ) * len(image_shape), dtype=bool)
center = (1, ) * len(image_shape)
offsets = _util._offsets_to_raveled_neighbors(image_shape, selem, center,
order)
# Assert only neighbors are present, center and duplicates (possible
# for this scenario) where removed
assert len(offsets) <= selem.sum() - 1
assert 0 not in offsets
# Assert uniqueness
assert len(set(offsets)) == offsets.size
# offsets form pairs of with same value but different signs
# if selem is symmetric around center
assert all(-x in offsets for x in offsets)
def _prep_data(image, marker_coords, mask=None, affinities=False, output=None):
# INTENSITY VALUES
if affinities:
im_ndim = image.ndim - 1 # the first dim should represent affinities
image_shape = image.shape[1:]
image_strides = image[0].strides
image_itemsize = image[0].itemsize
raveled_image = np.zeros((image.shape[0], image[0].size),
dtype=image.dtype)
for i in range(image.shape[0]):
raveled_image[i] = image[i].ravel()
else:
im_ndim = image.ndim
image_shape = image.shape
image_strides = image.strides
image_itemsize = image.itemsize
raveled_image = image.ravel()
# NEIGHBORS
selem, centre = _validate_connectivity(im_ndim, 1, None)
if affinities:
# array of shape (ndim * 2, 2) giving the indicies of neighbor affinities
offsets = _indices_to_raveled_affinities(image_shape, selem, centre)
else:
offsets = _offsets_to_raveled_neighbors(image_shape, selem, centre)
raveled_markers = np.apply_along_axis(_raveled_coordinate, 1,
marker_coords,
**{'shape': image_shape})
if mask is None:
small_shape = [s - 2 for s in image_shape]
mask = np.ones(small_shape, dtype=bool)
mask = np.pad(mask, 1, constant_values=0)
assert image_shape == mask.shape
mask_raveled = mask.ravel()
if output is None:
output = np.zeros(mask_raveled.shape, dtype=raveled_image.dtype)
labels = np.arange(len(raveled_markers)) + 1
output[raveled_markers] = labels
strides = np.array(image_strides, dtype=np.intp) // image_itemsize
return raveled_image, raveled_markers, offsets, mask_raveled, output, strides
def watershed(image,
markers=None,
connectivity=1,
offset=None,
mask=None,
compactness=0,
watershed_line=False,
method=0):
"""Find watershed basins in `image` flooded from given `markers`.
Parameters
----------
image : ndarray (2-D, 3-D, ...) of integers
Data array where the lowest value points are labeled first.
markers : int, or ndarray of int, same shape as `image`, optional
The desired number of markers, or an array marking the basins with the
values to be assigned in the label matrix. Zero means not a marker. If
``None`` (no markers given), the local minima of the image are used as
markers.
connectivity : ndarray, optional
An array with the same number of dimensions as `image` whose
non-zero elements indicate neighbors for connection.
Following the scipy convention, default is a one-connected array of
the dimension of the image.
offset : array_like of shape image.ndim, optional
offset of the connectivity (one offset per dimension)
mask : ndarray of bools or 0s and 1s, optional
Array of same shape as `image`. Only points at which mask == True
will be labeled.
compactness : float, optional
Use compact watershed [3]_ with given compactness parameter.
Higher values result in more regularly-shaped watershed basins.
watershed_line : bool, optional
If watershed_line is True, a one-pixel wide line separates the regions
obtained by the watershed algorithm. The line has the label 0.
Returns
-------
out : ndarray
A labeled matrix of the same type and shape as markers
See also
--------
skimage.segmentation.random_walker: random walker segmentation
A segmentation algorithm based on anisotropic diffusion, usually
slower than the watershed but with good results on noisy data and
boundaries with holes.
Notes
-----
This function implements a watershed algorithm [1]_ [2]_ that apportions
pixels into marked basins. The algorithm uses a priority queue to hold
the pixels with the metric for the priority queue being pixel value, then
the time of entry into the queue - this settles ties in favor of the
closest marker.
Some ideas taken from
Soille, "Automated Basin Delineation from Digital Elevation Models Using
Mathematical Morphology", Signal Processing 20 (1990) 171-182
The most important insight in the paper is that entry time onto the queue
solves two problems: a pixel should be assigned to the neighbor with the
largest gradient or, if there is no gradient, pixels on a plateau should
be split between markers on opposite sides.
This implementation converts all arguments to specific, lowest common
denominator types, then passes these to a C algorithm.
Markers can be determined manually, or automatically using for example
the local minima of the gradient of the image, or the local maxima of the
distance function to the background for separating overlapping objects
(see example).
References
----------
.. [1] https://en.wikipedia.org/wiki/Watershed_%28image_processing%29
.. [2] http://cmm.ensmp.fr/~beucher/wtshed.html
.. [3] Peer Neubert & Peter Protzel (2014). Compact Watershed and
Preemptive SLIC: On Improving Trade-offs of Superpixel Segmentation
Algorithms. ICPR 2014, pp 996-1001. :DOI:`10.1109/ICPR.2014.181`
https://www.tu-chemnitz.de/etit/proaut/forschung/rsrc/cws_pSLIC_ICPR.pdf
Examples
--------
The watershed algorithm is useful to separate overlapping objects.
We first generate an initial image with two overlapping circles:
>>> x, y = np.indices((80, 80))
>>> x1, y1, x2, y2 = 28, 28, 44, 52
>>> r1, r2 = 16, 20
>>> mask_circle1 = (x - x1)**2 + (y - y1)**2 < r1**2
>>> mask_circle2 = (x - x2)**2 + (y - y2)**2 < r2**2
>>> image = np.logical_or(mask_circle1, mask_circle2)
Next, we want to separate the two circles. We generate markers at the
maxima of the distance to the background:
>>> from scipy import ndimage as ndi
>>> distance = ndi.distance_transform_edt(image)
>>> from skimage.feature import peak_local_max
>>> local_maxi = peak_local_max(distance, labels=image,
... footprint=np.ones((3, 3)),
... indices=False)
>>> markers = ndi.label(local_maxi)[0]
Finally, we run the watershed on the image and markers:
>>> labels = watershed(-distance, markers, mask=image)
The algorithm works also for 3-D images, and can be used for example to
separate overlapping spheres.
"""
image, markers, mask = _validate_inputs(image, markers, mask, connectivity)
connectivity, offset = _validate_connectivity(image.ndim - 1, connectivity,
offset)
# pad the image, markers, and mask so that we can use the mask to
# keep from running off the edges
pad_width = [(p, p) for p in offset]
image0 = np.pad(image[..., 0], pad_width, mode='constant')
image1 = np.pad(image[..., 1], pad_width, mode='constant')
image2 = np.pad(image[..., 2], pad_width, mode='constant')
mask = np.pad(mask, pad_width, mode='constant').ravel()
output = np.pad(markers, pad_width, mode='constant')
distance = np.zeros_like(output, dtype=float)
#distance = distance.astype(float)
flat_neighborhood = _offsets_to_raveled_neighbors(image0.shape,
connectivity,
center=offset)
marker_locations = np.flatnonzero(output)
image_strides = np.array(image0.strides, dtype=np.intp) // image.itemsize
_watershed_cy.watershed_raveled(image0.ravel(), image1.ravel(),
image2.ravel(), marker_locations,
flat_neighborhood, mask, image_strides,
compactness, output.ravel(),
distance.ravel(), watershed_line, method)
output = crop(output, pad_width, copy=True)
distance = crop(distance, pad_width, copy=True)
#print('Using method {}'.format(method))
return output, distance
