marigold_depth_estimation.py 25.4 KB
Newer Older
1
# Copyright 2024 Bingxin Ke, ETH Zurich and The HuggingFace Team. All rights reserved.
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# --------------------------------------------------------------------------
# If you find this code useful, we kindly ask you to cite our paper in your work.
# Please find bibtex at: https://github.com/prs-eth/Marigold#-citation
# More information about the method can be found at https://marigoldmonodepth.github.io
# --------------------------------------------------------------------------


21
import logging
22
23
24
25
26
27
28
import math
from typing import Dict, Union

import matplotlib
import numpy as np
import torch
from PIL import Image
29
from PIL.Image import Resampling
30
31
32
33
34
35
36
37
38
from scipy.optimize import minimize
from torch.utils.data import DataLoader, TensorDataset
from tqdm.auto import tqdm
from transformers import CLIPTextModel, CLIPTokenizer

from diffusers import (
    AutoencoderKL,
    DDIMScheduler,
    DiffusionPipeline,
39
    LCMScheduler,
40
41
42
43
44
45
    UNet2DConditionModel,
)
from diffusers.utils import BaseOutput, check_min_version


# Will error if the minimal version of diffusers is not installed. Remove at your own risks.
Sayak Paul's avatar
Sayak Paul committed
46
check_min_version("0.32.0.dev0")
47
48
49
50
51
52
53
54
55


class MarigoldDepthOutput(BaseOutput):
    """
    Output class for Marigold monocular depth prediction pipeline.

    Args:
        depth_np (`np.ndarray`):
            Predicted depth map, with depth values in the range of [0, 1].
56
        depth_colored (`None` or `PIL.Image.Image`):
57
58
59
60
61
62
            Colorized depth map, with the shape of [3, H, W] and values in [0, 1].
        uncertainty (`None` or `np.ndarray`):
            Uncalibrated uncertainty(MAD, median absolute deviation) coming from ensembling.
    """

    depth_np: np.ndarray
63
    depth_colored: Union[None, Image.Image]
64
65
66
    uncertainty: Union[None, np.ndarray]


67
68
69
70
71
72
73
74
75
76
77
78
79
def get_pil_resample_method(method_str: str) -> Resampling:
    resample_method_dic = {
        "bilinear": Resampling.BILINEAR,
        "bicubic": Resampling.BICUBIC,
        "nearest": Resampling.NEAREST,
    }
    resample_method = resample_method_dic.get(method_str, None)
    if resample_method is None:
        raise ValueError(f"Unknown resampling method: {resample_method}")
    else:
        return resample_method


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
class MarigoldPipeline(DiffusionPipeline):
    """
    Pipeline for monocular depth estimation using Marigold: https://marigoldmonodepth.github.io.

    This model inherits from [`DiffusionPipeline`]. Check the superclass documentation for the generic methods the
    library implements for all the pipelines (such as downloading or saving, running on a particular device, etc.)

    Args:
        unet (`UNet2DConditionModel`):
            Conditional U-Net to denoise the depth latent, conditioned on image latent.
        vae (`AutoencoderKL`):
            Variational Auto-Encoder (VAE) Model to encode and decode images and depth maps
            to and from latent representations.
        scheduler (`DDIMScheduler`):
            A scheduler to be used in combination with `unet` to denoise the encoded image latents.
        text_encoder (`CLIPTextModel`):
            Text-encoder, for empty text embedding.
        tokenizer (`CLIPTokenizer`):
            CLIP tokenizer.
    """

    rgb_latent_scale_factor = 0.18215
    depth_latent_scale_factor = 0.18215

    def __init__(
        self,
        unet: UNet2DConditionModel,
        vae: AutoencoderKL,
        scheduler: DDIMScheduler,
        text_encoder: CLIPTextModel,
        tokenizer: CLIPTokenizer,
    ):
        super().__init__()

        self.register_modules(
            unet=unet,
            vae=vae,
            scheduler=scheduler,
            text_encoder=text_encoder,
            tokenizer=tokenizer,
        )

        self.empty_text_embed = None

    @torch.no_grad()
    def __call__(
        self,
        input_image: Image,
        denoising_steps: int = 10,
        ensemble_size: int = 10,
        processing_res: int = 768,
        match_input_res: bool = True,
132
        resample_method: str = "bilinear",
133
        batch_size: int = 0,
134
        seed: Union[int, None] = None,
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
        color_map: str = "Spectral",
        show_progress_bar: bool = True,
        ensemble_kwargs: Dict = None,
    ) -> MarigoldDepthOutput:
        """
        Function invoked when calling the pipeline.

        Args:
            input_image (`Image`):
                Input RGB (or gray-scale) image.
            processing_res (`int`, *optional*, defaults to `768`):
                Maximum resolution of processing.
                If set to 0: will not resize at all.
            match_input_res (`bool`, *optional*, defaults to `True`):
                Resize depth prediction to match input resolution.
150
151
152
                Only valid if `processing_res` > 0.
            resample_method: (`str`, *optional*, defaults to `bilinear`):
                Resampling method used to resize images and depth predictions. This can be one of `bilinear`, `bicubic` or `nearest`, defaults to: `bilinear`.
153
154
155
156
157
158
159
            denoising_steps (`int`, *optional*, defaults to `10`):
                Number of diffusion denoising steps (DDIM) during inference.
            ensemble_size (`int`, *optional*, defaults to `10`):
                Number of predictions to be ensembled.
            batch_size (`int`, *optional*, defaults to `0`):
                Inference batch size, no bigger than `num_ensemble`.
                If set to 0, the script will automatically decide the proper batch size.
160
161
            seed (`int`, *optional*, defaults to `None`)
                Reproducibility seed.
162
163
            show_progress_bar (`bool`, *optional*, defaults to `True`):
                Display a progress bar of diffusion denoising.
164
            color_map (`str`, *optional*, defaults to `"Spectral"`, pass `None` to skip colorized depth map generation):
165
166
167
168
169
170
                Colormap used to colorize the depth map.
            ensemble_kwargs (`dict`, *optional*, defaults to `None`):
                Arguments for detailed ensembling settings.
        Returns:
            `MarigoldDepthOutput`: Output class for Marigold monocular depth prediction pipeline, including:
            - **depth_np** (`np.ndarray`) Predicted depth map, with depth values in the range of [0, 1]
171
            - **depth_colored** (`PIL.Image.Image`) Colorized depth map, with the shape of [3, H, W] and values in [0, 1], None if `color_map` is `None`
172
173
174
175
176
177
178
179
180
181
182
183
            - **uncertainty** (`None` or `np.ndarray`) Uncalibrated uncertainty(MAD, median absolute deviation)
                    coming from ensembling. None if `ensemble_size = 1`
        """

        device = self.device
        input_size = input_image.size

        if not match_input_res:
            assert processing_res is not None, "Value error: `resize_output_back` is only valid with "
        assert processing_res >= 0
        assert ensemble_size >= 1

184
185
186
187
188
        # Check if denoising step is reasonable
        self._check_inference_step(denoising_steps)

        resample_method: Resampling = get_pil_resample_method(resample_method)

189
190
191
        # ----------------- Image Preprocess -----------------
        # Resize image
        if processing_res > 0:
192
193
194
195
196
            input_image = self.resize_max_res(
                input_image,
                max_edge_resolution=processing_res,
                resample_method=resample_method,
            )
197
198
199
200
201
202
        # Convert the image to RGB, to 1.remove the alpha channel 2.convert B&W to 3-channel
        input_image = input_image.convert("RGB")
        image = np.asarray(input_image)

        # Normalize rgb values
        rgb = np.transpose(image, (2, 0, 1))  # [H, W, rgb] -> [rgb, H, W]
203
        rgb_norm = rgb / 255.0 * 2.0 - 1.0  #  [0, 255] -> [-1, 1]
204
205
        rgb_norm = torch.from_numpy(rgb_norm).to(self.dtype)
        rgb_norm = rgb_norm.to(device)
206
        assert rgb_norm.min() >= -1.0 and rgb_norm.max() <= 1.0
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

        # ----------------- Predicting depth -----------------
        # Batch repeated input image
        duplicated_rgb = torch.stack([rgb_norm] * ensemble_size)
        single_rgb_dataset = TensorDataset(duplicated_rgb)
        if batch_size > 0:
            _bs = batch_size
        else:
            _bs = self._find_batch_size(
                ensemble_size=ensemble_size,
                input_res=max(rgb_norm.shape[1:]),
                dtype=self.dtype,
            )

        single_rgb_loader = DataLoader(single_rgb_dataset, batch_size=_bs, shuffle=False)

        # Predict depth maps (batched)
        depth_pred_ls = []
        if show_progress_bar:
            iterable = tqdm(single_rgb_loader, desc=" " * 2 + "Inference batches", leave=False)
        else:
            iterable = single_rgb_loader
        for batch in iterable:
            (batched_img,) = batch
            depth_pred_raw = self.single_infer(
                rgb_in=batched_img,
                num_inference_steps=denoising_steps,
                show_pbar=show_progress_bar,
235
                seed=seed,
236
            )
237
238
            depth_pred_ls.append(depth_pred_raw.detach())
        depth_preds = torch.concat(depth_pred_ls, dim=0).squeeze()
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
        torch.cuda.empty_cache()  # clear vram cache for ensembling

        # ----------------- Test-time ensembling -----------------
        if ensemble_size > 1:
            depth_pred, pred_uncert = self.ensemble_depths(depth_preds, **(ensemble_kwargs or {}))
        else:
            depth_pred = depth_preds
            pred_uncert = None

        # ----------------- Post processing -----------------
        # Scale prediction to [0, 1]
        min_d = torch.min(depth_pred)
        max_d = torch.max(depth_pred)
        depth_pred = (depth_pred - min_d) / (max_d - min_d)

        # Convert to numpy
        depth_pred = depth_pred.cpu().numpy().astype(np.float32)

        # Resize back to original resolution
        if match_input_res:
            pred_img = Image.fromarray(depth_pred)
260
            pred_img = pred_img.resize(input_size, resample=resample_method)
261
262
263
264
265
266
            depth_pred = np.asarray(pred_img)

        # Clip output range
        depth_pred = depth_pred.clip(0, 1)

        # Colorize
267
268
269
270
271
272
273
274
275
        if color_map is not None:
            depth_colored = self.colorize_depth_maps(
                depth_pred, 0, 1, cmap=color_map
            ).squeeze()  # [3, H, W], value in (0, 1)
            depth_colored = (depth_colored * 255).astype(np.uint8)
            depth_colored_hwc = self.chw2hwc(depth_colored)
            depth_colored_img = Image.fromarray(depth_colored_hwc)
        else:
            depth_colored_img = None
276

277
278
279
280
281
282
        return MarigoldDepthOutput(
            depth_np=depth_pred,
            depth_colored=depth_colored_img,
            uncertainty=pred_uncert,
        )

283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
    def _check_inference_step(self, n_step: int):
        """
        Check if denoising step is reasonable
        Args:
            n_step (`int`): denoising steps
        """
        assert n_step >= 1

        if isinstance(self.scheduler, DDIMScheduler):
            if n_step < 10:
                logging.warning(
                    f"Too few denoising steps: {n_step}. Recommended to use the LCM checkpoint for few-step inference."
                )
        elif isinstance(self.scheduler, LCMScheduler):
            if not 1 <= n_step <= 4:
                logging.warning(f"Non-optimal setting of denoising steps: {n_step}. Recommended setting is 1-4 steps.")
        else:
            raise RuntimeError(f"Unsupported scheduler type: {type(self.scheduler)}")

302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
    def _encode_empty_text(self):
        """
        Encode text embedding for empty prompt.
        """
        prompt = ""
        text_inputs = self.tokenizer(
            prompt,
            padding="do_not_pad",
            max_length=self.tokenizer.model_max_length,
            truncation=True,
            return_tensors="pt",
        )
        text_input_ids = text_inputs.input_ids.to(self.text_encoder.device)
        self.empty_text_embed = self.text_encoder(text_input_ids)[0].to(self.dtype)

    @torch.no_grad()
318
319
320
321
322
323
324
    def single_infer(
        self,
        rgb_in: torch.Tensor,
        num_inference_steps: int,
        seed: Union[int, None],
        show_pbar: bool,
    ) -> torch.Tensor:
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
        """
        Perform an individual depth prediction without ensembling.

        Args:
            rgb_in (`torch.Tensor`):
                Input RGB image.
            num_inference_steps (`int`):
                Number of diffusion denoisign steps (DDIM) during inference.
            show_pbar (`bool`):
                Display a progress bar of diffusion denoising.
        Returns:
            `torch.Tensor`: Predicted depth map.
        """
        device = rgb_in.device

        # Set timesteps
        self.scheduler.set_timesteps(num_inference_steps, device=device)
        timesteps = self.scheduler.timesteps  # [T]

        # Encode image
345
        rgb_latent = self.encode_rgb(rgb_in)
346
347

        # Initial depth map (noise)
348
349
350
351
352
353
354
355
356
357
358
        if seed is None:
            rand_num_generator = None
        else:
            rand_num_generator = torch.Generator(device=device)
            rand_num_generator.manual_seed(seed)
        depth_latent = torch.randn(
            rgb_latent.shape,
            device=device,
            dtype=self.dtype,
            generator=rand_num_generator,
        )  # [B, 4, h, w]
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382

        # Batched empty text embedding
        if self.empty_text_embed is None:
            self._encode_empty_text()
        batch_empty_text_embed = self.empty_text_embed.repeat((rgb_latent.shape[0], 1, 1))  # [B, 2, 1024]

        # Denoising loop
        if show_pbar:
            iterable = tqdm(
                enumerate(timesteps),
                total=len(timesteps),
                leave=False,
                desc=" " * 4 + "Diffusion denoising",
            )
        else:
            iterable = enumerate(timesteps)

        for i, t in iterable:
            unet_input = torch.cat([rgb_latent, depth_latent], dim=1)  # this order is important

            # predict the noise residual
            noise_pred = self.unet(unet_input, t, encoder_hidden_states=batch_empty_text_embed).sample  # [B, 4, h, w]

            # compute the previous noisy sample x_t -> x_t-1
383
384
385
            depth_latent = self.scheduler.step(noise_pred, t, depth_latent, generator=rand_num_generator).prev_sample

        depth = self.decode_depth(depth_latent)
386
387
388
389
390
391
392
393

        # clip prediction
        depth = torch.clip(depth, -1.0, 1.0)
        # shift to [0, 1]
        depth = (depth + 1.0) / 2.0

        return depth

394
    def encode_rgb(self, rgb_in: torch.Tensor) -> torch.Tensor:
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
        """
        Encode RGB image into latent.

        Args:
            rgb_in (`torch.Tensor`):
                Input RGB image to be encoded.

        Returns:
            `torch.Tensor`: Image latent.
        """
        # encode
        h = self.vae.encoder(rgb_in)
        moments = self.vae.quant_conv(h)
        mean, logvar = torch.chunk(moments, 2, dim=1)
        # scale latent
        rgb_latent = mean * self.rgb_latent_scale_factor
        return rgb_latent

413
    def decode_depth(self, depth_latent: torch.Tensor) -> torch.Tensor:
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
        """
        Decode depth latent into depth map.

        Args:
            depth_latent (`torch.Tensor`):
                Depth latent to be decoded.

        Returns:
            `torch.Tensor`: Decoded depth map.
        """
        # scale latent
        depth_latent = depth_latent / self.depth_latent_scale_factor
        # decode
        z = self.vae.post_quant_conv(depth_latent)
        stacked = self.vae.decoder(z)
        # mean of output channels
        depth_mean = stacked.mean(dim=1, keepdim=True)
        return depth_mean

    @staticmethod
434
    def resize_max_res(img: Image.Image, max_edge_resolution: int, resample_method=Resampling.BILINEAR) -> Image.Image:
435
436
437
438
439
440
441
442
        """
        Resize image to limit maximum edge length while keeping aspect ratio.

        Args:
            img (`Image.Image`):
                Image to be resized.
            max_edge_resolution (`int`):
                Maximum edge length (pixel).
443
444
            resample_method (`PIL.Image.Resampling`):
                Resampling method used to resize images.
445
446
447
448
449
450
451
452
453
454

        Returns:
            `Image.Image`: Resized image.
        """
        original_width, original_height = img.size
        downscale_factor = min(max_edge_resolution / original_width, max_edge_resolution / original_height)

        new_width = int(original_width * downscale_factor)
        new_height = int(original_height * downscale_factor)

455
        resized_img = img.resize((new_width, new_height), resample=resample_method)
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
669
670
671
672
673
674
        return resized_img

    @staticmethod
    def colorize_depth_maps(depth_map, min_depth, max_depth, cmap="Spectral", valid_mask=None):
        """
        Colorize depth maps.
        """
        assert len(depth_map.shape) >= 2, "Invalid dimension"

        if isinstance(depth_map, torch.Tensor):
            depth = depth_map.detach().clone().squeeze().numpy()
        elif isinstance(depth_map, np.ndarray):
            depth = depth_map.copy().squeeze()
        # reshape to [ (B,) H, W ]
        if depth.ndim < 3:
            depth = depth[np.newaxis, :, :]

        # colorize
        cm = matplotlib.colormaps[cmap]
        depth = ((depth - min_depth) / (max_depth - min_depth)).clip(0, 1)
        img_colored_np = cm(depth, bytes=False)[:, :, :, 0:3]  # value from 0 to 1
        img_colored_np = np.rollaxis(img_colored_np, 3, 1)

        if valid_mask is not None:
            if isinstance(depth_map, torch.Tensor):
                valid_mask = valid_mask.detach().numpy()
            valid_mask = valid_mask.squeeze()  # [H, W] or [B, H, W]
            if valid_mask.ndim < 3:
                valid_mask = valid_mask[np.newaxis, np.newaxis, :, :]
            else:
                valid_mask = valid_mask[:, np.newaxis, :, :]
            valid_mask = np.repeat(valid_mask, 3, axis=1)
            img_colored_np[~valid_mask] = 0

        if isinstance(depth_map, torch.Tensor):
            img_colored = torch.from_numpy(img_colored_np).float()
        elif isinstance(depth_map, np.ndarray):
            img_colored = img_colored_np

        return img_colored

    @staticmethod
    def chw2hwc(chw):
        assert 3 == len(chw.shape)
        if isinstance(chw, torch.Tensor):
            hwc = torch.permute(chw, (1, 2, 0))
        elif isinstance(chw, np.ndarray):
            hwc = np.moveaxis(chw, 0, -1)
        return hwc

    @staticmethod
    def _find_batch_size(ensemble_size: int, input_res: int, dtype: torch.dtype) -> int:
        """
        Automatically search for suitable operating batch size.

        Args:
            ensemble_size (`int`):
                Number of predictions to be ensembled.
            input_res (`int`):
                Operating resolution of the input image.

        Returns:
            `int`: Operating batch size.
        """
        # Search table for suggested max. inference batch size
        bs_search_table = [
            # tested on A100-PCIE-80GB
            {"res": 768, "total_vram": 79, "bs": 35, "dtype": torch.float32},
            {"res": 1024, "total_vram": 79, "bs": 20, "dtype": torch.float32},
            # tested on A100-PCIE-40GB
            {"res": 768, "total_vram": 39, "bs": 15, "dtype": torch.float32},
            {"res": 1024, "total_vram": 39, "bs": 8, "dtype": torch.float32},
            {"res": 768, "total_vram": 39, "bs": 30, "dtype": torch.float16},
            {"res": 1024, "total_vram": 39, "bs": 15, "dtype": torch.float16},
            # tested on RTX3090, RTX4090
            {"res": 512, "total_vram": 23, "bs": 20, "dtype": torch.float32},
            {"res": 768, "total_vram": 23, "bs": 7, "dtype": torch.float32},
            {"res": 1024, "total_vram": 23, "bs": 3, "dtype": torch.float32},
            {"res": 512, "total_vram": 23, "bs": 40, "dtype": torch.float16},
            {"res": 768, "total_vram": 23, "bs": 18, "dtype": torch.float16},
            {"res": 1024, "total_vram": 23, "bs": 10, "dtype": torch.float16},
            # tested on GTX1080Ti
            {"res": 512, "total_vram": 10, "bs": 5, "dtype": torch.float32},
            {"res": 768, "total_vram": 10, "bs": 2, "dtype": torch.float32},
            {"res": 512, "total_vram": 10, "bs": 10, "dtype": torch.float16},
            {"res": 768, "total_vram": 10, "bs": 5, "dtype": torch.float16},
            {"res": 1024, "total_vram": 10, "bs": 3, "dtype": torch.float16},
        ]

        if not torch.cuda.is_available():
            return 1

        total_vram = torch.cuda.mem_get_info()[1] / 1024.0**3
        filtered_bs_search_table = [s for s in bs_search_table if s["dtype"] == dtype]
        for settings in sorted(
            filtered_bs_search_table,
            key=lambda k: (k["res"], -k["total_vram"]),
        ):
            if input_res <= settings["res"] and total_vram >= settings["total_vram"]:
                bs = settings["bs"]
                if bs > ensemble_size:
                    bs = ensemble_size
                elif bs > math.ceil(ensemble_size / 2) and bs < ensemble_size:
                    bs = math.ceil(ensemble_size / 2)
                return bs

        return 1

    @staticmethod
    def ensemble_depths(
        input_images: torch.Tensor,
        regularizer_strength: float = 0.02,
        max_iter: int = 2,
        tol: float = 1e-3,
        reduction: str = "median",
        max_res: int = None,
    ):
        """
        To ensemble multiple affine-invariant depth images (up to scale and shift),
            by aligning estimating the scale and shift
        """

        def inter_distances(tensors: torch.Tensor):
            """
            To calculate the distance between each two depth maps.
            """
            distances = []
            for i, j in torch.combinations(torch.arange(tensors.shape[0])):
                arr1 = tensors[i : i + 1]
                arr2 = tensors[j : j + 1]
                distances.append(arr1 - arr2)
            dist = torch.concatenate(distances, dim=0)
            return dist

        device = input_images.device
        dtype = input_images.dtype
        np_dtype = np.float32

        original_input = input_images.clone()
        n_img = input_images.shape[0]
        ori_shape = input_images.shape

        if max_res is not None:
            scale_factor = torch.min(max_res / torch.tensor(ori_shape[-2:]))
            if scale_factor < 1:
                downscaler = torch.nn.Upsample(scale_factor=scale_factor, mode="nearest")
                input_images = downscaler(torch.from_numpy(input_images)).numpy()

        # init guess
        _min = np.min(input_images.reshape((n_img, -1)).cpu().numpy(), axis=1)
        _max = np.max(input_images.reshape((n_img, -1)).cpu().numpy(), axis=1)
        s_init = 1.0 / (_max - _min).reshape((-1, 1, 1))
        t_init = (-1 * s_init.flatten() * _min.flatten()).reshape((-1, 1, 1))
        x = np.concatenate([s_init, t_init]).reshape(-1).astype(np_dtype)

        input_images = input_images.to(device)

        # objective function
        def closure(x):
            l = len(x)
            s = x[: int(l / 2)]
            t = x[int(l / 2) :]
            s = torch.from_numpy(s).to(dtype=dtype).to(device)
            t = torch.from_numpy(t).to(dtype=dtype).to(device)

            transformed_arrays = input_images * s.view((-1, 1, 1)) + t.view((-1, 1, 1))
            dists = inter_distances(transformed_arrays)
            sqrt_dist = torch.sqrt(torch.mean(dists**2))

            if "mean" == reduction:
                pred = torch.mean(transformed_arrays, dim=0)
            elif "median" == reduction:
                pred = torch.median(transformed_arrays, dim=0).values
            else:
                raise ValueError

            near_err = torch.sqrt((0 - torch.min(pred)) ** 2)
            far_err = torch.sqrt((1 - torch.max(pred)) ** 2)

            err = sqrt_dist + (near_err + far_err) * regularizer_strength
            err = err.detach().cpu().numpy().astype(np_dtype)
            return err

        res = minimize(
            closure,
            x,
            method="BFGS",
            tol=tol,
            options={"maxiter": max_iter, "disp": False},
        )
        x = res.x
        l = len(x)
        s = x[: int(l / 2)]
        t = x[int(l / 2) :]

        # Prediction
        s = torch.from_numpy(s).to(dtype=dtype).to(device)
        t = torch.from_numpy(t).to(dtype=dtype).to(device)
        transformed_arrays = original_input * s.view(-1, 1, 1) + t.view(-1, 1, 1)
        if "mean" == reduction:
            aligned_images = torch.mean(transformed_arrays, dim=0)
            std = torch.std(transformed_arrays, dim=0)
            uncertainty = std
        elif "median" == reduction:
            aligned_images = torch.median(transformed_arrays, dim=0).values
            # MAD (median absolute deviation) as uncertainty indicator
            abs_dev = torch.abs(transformed_arrays - aligned_images)
            mad = torch.median(abs_dev, dim=0).values
            uncertainty = mad
        else:
            raise ValueError(f"Unknown reduction method: {reduction}")

        # Scale and shift to [0, 1]
        _min = torch.min(aligned_images)
        _max = torch.max(aligned_images)
        aligned_images = (aligned_images - _min) / (_max - _min)
        uncertainty /= _max - _min

        return aligned_images, uncertainty