File size: 23,091 Bytes
8f72b1f
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
"""
Copyright © 2025 Howard Hughes Medical Institute, Authored by Carsen Stringer , Michael Rariden and Marius Pachitariu.
"""
import logging
import os, tempfile, shutil, io
from tqdm import tqdm, trange
from urllib.request import urlopen
import cv2
from scipy.ndimage import find_objects, gaussian_filter, generate_binary_structure, label
from scipy.spatial import ConvexHull
import numpy as np
import colorsys
import fastremap
import fill_voids
from multiprocessing import Pool, cpu_count
# try:
#     from cellpose import metrics
# except:
#     import metrics as metrics
from models.seg_post_model.cellpose import metrics

try:
    from skimage.morphology import remove_small_holes
    SKIMAGE_ENABLED = True
except:
    SKIMAGE_ENABLED = False


class TqdmToLogger(io.StringIO):
    """
        Output stream for TQDM which will output to logger module instead of
        the StdOut.
    """
    logger = None
    level = None
    buf = ""

    def __init__(self, logger, level=None):
        super(TqdmToLogger, self).__init__()
        self.logger = logger
        self.level = level or logging.INFO

    def write(self, buf):
        self.buf = buf.strip("\r\n\t ")

    def flush(self):
        self.logger.log(self.level, self.buf)


def rgb_to_hsv(arr):
    rgb_to_hsv_channels = np.vectorize(colorsys.rgb_to_hsv)
    r, g, b = np.rollaxis(arr, axis=-1)
    h, s, v = rgb_to_hsv_channels(r, g, b)
    hsv = np.stack((h, s, v), axis=-1)
    return hsv


def hsv_to_rgb(arr):
    hsv_to_rgb_channels = np.vectorize(colorsys.hsv_to_rgb)
    h, s, v = np.rollaxis(arr, axis=-1)
    r, g, b = hsv_to_rgb_channels(h, s, v)
    rgb = np.stack((r, g, b), axis=-1)
    return rgb


def download_url_to_file(url, dst, progress=True):
    r"""Download object at the given URL to a local path.
            Thanks to torch, slightly modified
    Args:
        url (string): URL of the object to download
        dst (string): Full path where object will be saved, e.g. `/tmp/temporary_file`
        progress (bool, optional): whether or not to display a progress bar to stderr
            Default: True
    """
    file_size = None
    import ssl
    ssl._create_default_https_context = ssl._create_unverified_context
    u = urlopen(url)
    meta = u.info()
    if hasattr(meta, "getheaders"):
        content_length = meta.getheaders("Content-Length")
    else:
        content_length = meta.get_all("Content-Length")
    if content_length is not None and len(content_length) > 0:
        file_size = int(content_length[0])
    # We deliberately save it in a temp file and move it after
    dst = os.path.expanduser(dst)
    dst_dir = os.path.dirname(dst)
    f = tempfile.NamedTemporaryFile(delete=False, dir=dst_dir)
    try:
        with tqdm(total=file_size, disable=not progress, unit="B", unit_scale=True,
                  unit_divisor=1024) as pbar:
            while True:
                buffer = u.read(8192)
                if len(buffer) == 0:
                    break
                f.write(buffer)
                pbar.update(len(buffer))
        f.close()
        shutil.move(f.name, dst)
    finally:
        f.close()
        if os.path.exists(f.name):
            os.remove(f.name)


def distance_to_boundary(masks):
    """Get the distance to the boundary of mask pixels.

    Args:
        masks (int, 2D or 3D array): The masks array. Size [Ly x Lx] or [Lz x Ly x Lx], where 0 represents no mask and 1, 2, ... represent mask labels.

    Returns:
        dist_to_bound (2D or 3D array): The distance to the boundary. Size [Ly x Lx] or [Lz x Ly x Lx].

    Raises:
        ValueError: If the masks array is not 2D or 3D.

    """
    if masks.ndim > 3 or masks.ndim < 2:
        raise ValueError("distance_to_boundary takes 2D or 3D array, not %dD array" %
                         masks.ndim)
    dist_to_bound = np.zeros(masks.shape, np.float64)

    if masks.ndim == 3:
        for i in range(masks.shape[0]):
            dist_to_bound[i] = distance_to_boundary(masks[i])
        return dist_to_bound
    else:
        slices = find_objects(masks)
        for i, si in enumerate(slices):
            if si is not None:
                sr, sc = si
                mask = (masks[sr, sc] == (i + 1)).astype(np.uint8)
                contours = cv2.findContours(mask, cv2.RETR_EXTERNAL,
                                            cv2.CHAIN_APPROX_NONE)
                pvc, pvr = np.concatenate(contours[-2], axis=0).squeeze().T
                ypix, xpix = np.nonzero(mask)
                min_dist = ((ypix[:, np.newaxis] - pvr)**2 +
                            (xpix[:, np.newaxis] - pvc)**2).min(axis=1)
                dist_to_bound[ypix + sr.start, xpix + sc.start] = min_dist
        return dist_to_bound


def masks_to_edges(masks, threshold=1.0):
    """Get edges of masks as a 0-1 array.

    Args:
        masks (int, 2D or 3D array): Size [Ly x Lx] or [Lz x Ly x Lx], where 0=NO masks and 1,2,...=mask labels.
        threshold (float, optional): Threshold value for distance to boundary. Defaults to 1.0.

    Returns:
        edges (2D or 3D array): Size [Ly x Lx] or [Lz x Ly x Lx], where True pixels are edge pixels.
    """
    dist_to_bound = distance_to_boundary(masks)
    edges = (dist_to_bound < threshold) * (masks > 0)
    return edges


def remove_edge_masks(masks, change_index=True):
    """Removes masks with pixels on the edge of the image.

    Args:
        masks (int, 2D or 3D array): The masks to be processed. Size [Ly x Lx] or [Lz x Ly x Lx], where 0 represents no mask and 1, 2, ... represent mask labels.
        change_index (bool, optional): If True, after removing masks, changes the indexing so that there are no missing label numbers. Defaults to True.

    Returns:
        outlines (2D or 3D array): The processed masks. Size [Ly x Lx] or [Lz x Ly x Lx], where 0 represents no mask and 1, 2, ... represent mask labels.
    """
    slices = find_objects(masks.astype(int))
    for i, si in enumerate(slices):
        remove = False
        if si is not None:
            for d, sid in enumerate(si):
                if sid.start == 0 or sid.stop == masks.shape[d]:
                    remove = True
                    break
            if remove:
                masks[si][masks[si] == i + 1] = 0
    shape = masks.shape
    if change_index:
        _, masks = np.unique(masks, return_inverse=True)
        masks = np.reshape(masks, shape).astype(np.int32)

    return masks


def masks_to_outlines(masks):
    """Get outlines of masks as a 0-1 array.

    Args:
        masks (int, 2D or 3D array): Size [Ly x Lx] or [Lz x Ly x Lx], where 0=NO masks and 1,2,...=mask labels.

    Returns:
        outlines (2D or 3D array): Size [Ly x Lx] or [Lz x Ly x Lx], where True pixels are outlines.
    """
    if masks.ndim > 3 or masks.ndim < 2:
        raise ValueError("masks_to_outlines takes 2D or 3D array, not %dD array" %
                         masks.ndim)
    outlines = np.zeros(masks.shape, bool)

    if masks.ndim == 3:
        for i in range(masks.shape[0]):
            outlines[i] = masks_to_outlines(masks[i])
        return outlines
    else:
        slices = find_objects(masks.astype(int))
        for i, si in enumerate(slices):
            if si is not None:
                sr, sc = si
                mask = (masks[sr, sc] == (i + 1)).astype(np.uint8)
                contours = cv2.findContours(mask, cv2.RETR_EXTERNAL,
                                            cv2.CHAIN_APPROX_NONE)
                pvc, pvr = np.concatenate(contours[-2], axis=0).squeeze().T
                vr, vc = pvr + sr.start, pvc + sc.start
                outlines[vr, vc] = 1
        return outlines


def outlines_list(masks, multiprocessing_threshold=1000, multiprocessing=None):
    """Get outlines of masks as a list to loop over for plotting.

    Args:
        masks (ndarray): Array of masks.
        multiprocessing_threshold (int, optional): Threshold for enabling multiprocessing. Defaults to 1000.
        multiprocessing (bool, optional): Flag to enable multiprocessing. Defaults to None.

    Returns:
        list: List of outlines.

    Raises:
        None

    Notes:
        - This function is a wrapper for outlines_list_single and outlines_list_multi.
        - Multiprocessing is disabled for Windows.
    """
    # default to use multiprocessing if not few_masks, but allow user to override
    if multiprocessing is None:
        few_masks = np.max(masks) < multiprocessing_threshold
        multiprocessing = not few_masks

    # disable multiprocessing for Windows
    if os.name == "nt":
        if multiprocessing:
            logging.getLogger(__name__).warning(
                "Multiprocessing is disabled for Windows")
        multiprocessing = False

    if multiprocessing:
        return outlines_list_multi(masks)
    else:
        return outlines_list_single(masks)


def outlines_list_single(masks):
    """Get outlines of masks as a list to loop over for plotting.

    Args:
        masks (ndarray): masks (0=no cells, 1=first cell, 2=second cell,...)

    Returns:
        list: List of outlines as pixel coordinates.

    """
    outpix = []
    for n in np.unique(masks)[1:]:
        mn = masks == n
        if mn.sum() > 0:
            contours = cv2.findContours(mn.astype(np.uint8), mode=cv2.RETR_EXTERNAL,
                                        method=cv2.CHAIN_APPROX_NONE)
            contours = contours[-2]
            cmax = np.argmax([c.shape[0] for c in contours])
            pix = contours[cmax].astype(int).squeeze()
            if len(pix) > 4:
                outpix.append(pix)
            else:
                outpix.append(np.zeros((0, 2)))
    return outpix


def outlines_list_multi(masks, num_processes=None):
    """
    Get outlines of masks as a list to loop over for plotting.

    Args:
        masks (ndarray): masks (0=no cells, 1=first cell, 2=second cell,...)

    Returns:
        list: List of outlines as pixel coordinates.
    """
    if num_processes is None:
        num_processes = cpu_count()

    unique_masks = np.unique(masks)[1:]
    with Pool(processes=num_processes) as pool:
        outpix = pool.map(get_outline_multi, [(masks, n) for n in unique_masks])
    return outpix


def get_outline_multi(args):
    """Get the outline of a specific mask in a multi-mask image.

    Args:
        args (tuple): A tuple containing the masks and the mask number.

    Returns:
        numpy.ndarray: The outline of the specified mask as an array of coordinates.

    """
    masks, n = args
    mn = masks == n
    if mn.sum() > 0:
        contours = cv2.findContours(mn.astype(np.uint8), mode=cv2.RETR_EXTERNAL,
                                    method=cv2.CHAIN_APPROX_NONE)
        contours = contours[-2]
        cmax = np.argmax([c.shape[0] for c in contours])
        pix = contours[cmax].astype(int).squeeze()
        return pix if len(pix) > 4 else np.zeros((0, 2))
    return np.zeros((0, 2))


def dilate_masks(masks, n_iter=5):
    """Dilate masks by n_iter pixels.

    Args:
        masks (ndarray): Array of masks.
        n_iter (int, optional): Number of pixels to dilate the masks. Defaults to 5.

    Returns:
        ndarray: Dilated masks.
    """
    dilated_masks = masks.copy()
    for n in range(n_iter):
        # define the structuring element to use for dilation
        kernel = np.ones((3, 3), "uint8")
        # find the distance to each mask (distances are zero within masks)
        dist_transform = cv2.distanceTransform((dilated_masks == 0).astype("uint8"),
                                               cv2.DIST_L2, 5)
        # dilate each mask and assign to it the pixels along the border of the mask
        # (does not allow dilation into other masks since dist_transform is zero there)
        for i in range(1, np.max(masks) + 1):
            mask = (dilated_masks == i).astype("uint8")
            dilated_mask = cv2.dilate(mask, kernel, iterations=1)
            dilated_mask = np.logical_and(dist_transform < 2, dilated_mask)
            dilated_masks[dilated_mask > 0] = i
    return dilated_masks


def get_perimeter(points):
    """
    Calculate the perimeter of a set of points.

    Parameters:
        points (ndarray): An array of points with shape (npoints, ndim).

    Returns:
        float: The perimeter of the points.

    """
    if points.shape[0] > 4:
        points = np.append(points, points[:1], axis=0)
        return ((np.diff(points, axis=0)**2).sum(axis=1)**0.5).sum()
    else:
        return 0


def get_mask_compactness(masks):
    """
    Calculate the compactness of masks.
    
    Parameters:
        masks (ndarray): Binary masks representing objects.
        
    Returns:
        ndarray: Array of compactness values for each mask.
    """
    perimeters = get_mask_perimeters(masks)
    npoints = np.unique(masks, return_counts=True)[1][1:]
    areas = npoints
    compactness = 4 * np.pi * areas / perimeters**2
    compactness[perimeters == 0] = 0
    compactness[compactness > 1.0] = 1.0
    return compactness


def get_mask_perimeters(masks):
    """
    Calculate the perimeters of the given masks.

    Parameters:
        masks (numpy.ndarray): Binary masks representing objects.

    Returns:
        numpy.ndarray: Array containing the perimeters of each mask.
    """
    perimeters = np.zeros(masks.max())
    for n in range(masks.max()):
        mn = masks == (n + 1)
        if mn.sum() > 0:
            contours = cv2.findContours(mn.astype(np.uint8), mode=cv2.RETR_EXTERNAL,
                                        method=cv2.CHAIN_APPROX_NONE)[-2]
            perimeters[n] = np.array(
                [get_perimeter(c.astype(int).squeeze()) for c in contours]).sum()

    return perimeters


def circleMask(d0):
    """
    Creates an array with indices which are the radius of that x,y point.

    Args:
        d0 (tuple): Patch of (-d0, d0+1) over which radius is computed.

    Returns:
        tuple: A tuple containing:
            - rs (ndarray): Array of radii with shape (2*d0[0]+1, 2*d0[1]+1).
            - dx (ndarray): Indices of the patch along the x-axis.
            - dy (ndarray): Indices of the patch along the y-axis.
    """
    dx = np.tile(np.arange(-d0[1], d0[1] + 1), (2 * d0[0] + 1, 1))
    dy = np.tile(np.arange(-d0[0], d0[0] + 1), (2 * d0[1] + 1, 1))
    dy = dy.transpose()

    rs = (dy**2 + dx**2)**0.5
    return rs, dx, dy


def get_mask_stats(masks_true):
    """
    Calculate various statistics for the given binary masks.

    Parameters:
        masks_true (ndarray): masks (0=no cells, 1=first cell, 2=second cell,...)

    Returns:
        convexity (ndarray): Convexity values for each mask.
        solidity (ndarray): Solidity values for each mask.
        compactness (ndarray): Compactness values for each mask.
    """
    mask_perimeters = get_mask_perimeters(masks_true)

    # disk for compactness
    rs, dy, dx = circleMask(np.array([100, 100]))
    rsort = np.sort(rs.flatten())

    # area for solidity
    npoints = np.unique(masks_true, return_counts=True)[1][1:]
    areas = npoints - mask_perimeters / 2 - 1

    compactness = np.zeros(masks_true.max())
    convexity = np.zeros(masks_true.max())
    solidity = np.zeros(masks_true.max())
    convex_perimeters = np.zeros(masks_true.max())
    convex_areas = np.zeros(masks_true.max())
    for ic in range(masks_true.max()):
        points = np.array(np.nonzero(masks_true == (ic + 1))).T
        if len(points) > 15 and mask_perimeters[ic] > 0:
            med = np.median(points, axis=0)
            # compute compactness of ROI
            r2 = ((points - med)**2).sum(axis=1)**0.5
            compactness[ic] = (rsort[:r2.size].mean() + 1e-10) / r2.mean()
            try:
                hull = ConvexHull(points)
                convex_perimeters[ic] = hull.area
                convex_areas[ic] = hull.volume
            except:
                convex_perimeters[ic] = 0

    convexity[mask_perimeters > 0.0] = (convex_perimeters[mask_perimeters > 0.0] /
                                        mask_perimeters[mask_perimeters > 0.0])
    solidity[convex_areas > 0.0] = (areas[convex_areas > 0.0] /
                                    convex_areas[convex_areas > 0.0])
    convexity = np.clip(convexity, 0.0, 1.0)
    solidity = np.clip(solidity, 0.0, 1.0)
    compactness = np.clip(compactness, 0.0, 1.0)
    return convexity, solidity, compactness


def get_masks_unet(output, cell_threshold=0, boundary_threshold=0):
    """Create masks using cell probability and cell boundary.

    Args:
        output (ndarray): The output array containing cell probability and cell boundary.
        cell_threshold (float, optional): The threshold value for cell probability. Defaults to 0.
        boundary_threshold (float, optional): The threshold value for cell boundary. Defaults to 0.

    Returns:
        ndarray: The masks representing the segmented cells.

    """
    cells = (output[..., 1] - output[..., 0]) > cell_threshold
    selem = generate_binary_structure(cells.ndim, connectivity=1)
    labels, nlabels = label(cells, selem)

    if output.shape[-1] > 2:
        slices = find_objects(labels)
        dists = 10000 * np.ones(labels.shape, np.float32)
        mins = np.zeros(labels.shape, np.int32)
        borders = np.logical_and(~(labels > 0), output[..., 2] > boundary_threshold)
        pad = 10
        for i, slc in enumerate(slices):
            if slc is not None:
                slc_pad = tuple([
                    slice(max(0, sli.start - pad), min(labels.shape[j], sli.stop + pad))
                    for j, sli in enumerate(slc)
                ])
                msk = (labels[slc_pad] == (i + 1)).astype(np.float32)
                msk = 1 - gaussian_filter(msk, 5)
                dists[slc_pad] = np.minimum(dists[slc_pad], msk)
                mins[slc_pad][dists[slc_pad] == msk] = (i + 1)
        labels[labels == 0] = borders[labels == 0] * mins[labels == 0]

    masks = labels
    shape0 = masks.shape
    _, masks = np.unique(masks, return_inverse=True)
    masks = np.reshape(masks, shape0)
    return masks


def stitch3D(masks, stitch_threshold=0.25):
    """
    Stitch 2D masks into a 3D volume using a stitch_threshold on IOU.

    Args:
        masks (list or ndarray): List of 2D masks.
        stitch_threshold (float, optional): Threshold value for stitching. Defaults to 0.25.

    Returns:
        list: List of stitched 3D masks.
    """
    mmax = masks[0].max()
    empty = 0
    for i in trange(len(masks) - 1):
        iou = metrics._intersection_over_union(masks[i + 1], masks[i])[1:, 1:]
        if not iou.size and empty == 0:
            masks[i + 1] = masks[i + 1]
            mmax = masks[i + 1].max()
        elif not iou.size and not empty == 0:
            icount = masks[i + 1].max()
            istitch = np.arange(mmax + 1, mmax + icount + 1, 1, masks.dtype)
            mmax += icount
            istitch = np.append(np.array(0), istitch)
            masks[i + 1] = istitch[masks[i + 1]]
        else:
            iou[iou < stitch_threshold] = 0.0
            iou[iou < iou.max(axis=0)] = 0.0
            istitch = iou.argmax(axis=1) + 1
            ino = np.nonzero(iou.max(axis=1) == 0.0)[0]
            istitch[ino] = np.arange(mmax + 1, mmax + len(ino) + 1, 1, masks.dtype)
            mmax += len(ino)
            istitch = np.append(np.array(0), istitch)
            masks[i + 1] = istitch[masks[i + 1]]
            empty = 1

    return masks


def diameters(masks):
    """
    Calculate the diameters of the objects in the given masks.

    Parameters:
    masks (ndarray): masks (0=no cells, 1=first cell, 2=second cell,...)

    Returns:
        tuple: A tuple containing the median diameter and an array of diameters for each object.

    Examples:
    >>> masks = np.array([[0, 1, 1], [1, 0, 0], [1, 1, 0]])
    >>> diameters(masks)
    (1.0, array([1.41421356, 1.0, 1.0]))
    """
    uniq, counts = fastremap.unique(masks.astype("int32"), return_counts=True)
    counts = counts[1:]
    md = np.median(counts**0.5)
    if np.isnan(md):
        md = 0
    md /= (np.pi**0.5) / 2
    return md, counts**0.5


def radius_distribution(masks, bins):
    """
    Calculate the radius distribution of masks.

    Args:
        masks (ndarray): masks (0=no cells, 1=first cell, 2=second cell,...)
        bins (int): Number of bins for the histogram.

    Returns:
        A tuple containing a normalized histogram of radii, median radius, array of radii.

    """
    unique, counts = np.unique(masks, return_counts=True)
    counts = counts[unique != 0]
    nb, _ = np.histogram((counts**0.5) * 0.5, bins)
    nb = nb.astype(np.float32)
    if nb.sum() > 0:
        nb = nb / nb.sum()
    md = np.median(counts**0.5) * 0.5
    if np.isnan(md):
        md = 0
    md /= (np.pi**0.5) / 2
    return nb, md, (counts**0.5) / 2


def size_distribution(masks):
    """
    Calculates the size distribution of masks.

    Args:
        masks (ndarray): masks (0=no cells, 1=first cell, 2=second cell,...)

    Returns:
        float: The ratio of the 25th percentile of mask sizes to the 75th percentile of mask sizes.
    """
    counts = np.unique(masks, return_counts=True)[1][1:]
    return np.percentile(counts, 25) / np.percentile(counts, 75)


def fill_holes_and_remove_small_masks(masks, min_size=15):
    """ Fills holes in masks (2D/3D) and discards masks smaller than min_size.

    This function fills holes in each mask using fill_voids.fill.
    It also removes masks that are smaller than the specified min_size.

    Parameters:
    masks (ndarray): Int, 2D or 3D array of labelled masks.
        0 represents no mask, while positive integers represent mask labels.
        The size can be [Ly x Lx] or [Lz x Ly x Lx].
    min_size (int, optional): Minimum number of pixels per mask.
        Masks smaller than min_size will be removed.
        Set to -1 to turn off this functionality. Default is 15.

    Returns:
        ndarray: Int, 2D or 3D array of masks with holes filled and small masks removed.
            0 represents no mask, while positive integers represent mask labels.
            The size is [Ly x Lx] or [Lz x Ly x Lx].
    """

    if masks.ndim > 3 or masks.ndim < 2:
        raise ValueError("masks_to_outlines takes 2D or 3D array, not %dD array" %
                         masks.ndim)

    # Filter small masks
    if min_size > 0:
        counts = fastremap.unique(masks, return_counts=True)[1][1:]
        masks = fastremap.mask(masks, np.nonzero(counts < min_size)[0] + 1)
        fastremap.renumber(masks, in_place=True)
        
    slices = find_objects(masks)
    j = 0
    for i, slc in enumerate(slices):
        if slc is not None:
            msk = masks[slc] == (i + 1)
            msk = fill_voids.fill(msk)
            masks[slc][msk] = (j + 1)
            j += 1

    if min_size > 0:
        counts = fastremap.unique(masks, return_counts=True)[1][1:]
        masks = fastremap.mask(masks, np.nonzero(counts < min_size)[0] + 1)
        fastremap.renumber(masks, in_place=True)
    
    return masks