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675 lines
25 KiB
Python
675 lines
25 KiB
Python
# Copyright 2024 Bingxin Ke, ETH Zurich and The HuggingFace Team. All rights reserved.
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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# --------------------------------------------------------------------------
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# If you find this code useful, we kindly ask you to cite our paper in your work.
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# Please find bibtex at: https://github.com/prs-eth/Marigold#-citation
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# More information about the method can be found at https://marigoldmonodepth.github.io
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# --------------------------------------------------------------------------
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import logging
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import math
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from typing import Dict, Union
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import matplotlib
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import numpy as np
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import torch
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from PIL import Image
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from PIL.Image import Resampling
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from scipy.optimize import minimize
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from torch.utils.data import DataLoader, TensorDataset
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from tqdm.auto import tqdm
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from transformers import CLIPTextModel, CLIPTokenizer
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from diffusers import (
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AutoencoderKL,
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DDIMScheduler,
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DiffusionPipeline,
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LCMScheduler,
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UNet2DConditionModel,
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)
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from diffusers.utils import BaseOutput, check_min_version
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# Will error if the minimal version of diffusers is not installed. Remove at your own risks.
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check_min_version("0.30.0.dev0")
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class MarigoldDepthOutput(BaseOutput):
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"""
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Output class for Marigold monocular depth prediction pipeline.
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Args:
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depth_np (`np.ndarray`):
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Predicted depth map, with depth values in the range of [0, 1].
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depth_colored (`None` or `PIL.Image.Image`):
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Colorized depth map, with the shape of [3, H, W] and values in [0, 1].
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uncertainty (`None` or `np.ndarray`):
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Uncalibrated uncertainty(MAD, median absolute deviation) coming from ensembling.
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"""
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depth_np: np.ndarray
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depth_colored: Union[None, Image.Image]
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uncertainty: Union[None, np.ndarray]
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def get_pil_resample_method(method_str: str) -> Resampling:
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resample_method_dic = {
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"bilinear": Resampling.BILINEAR,
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"bicubic": Resampling.BICUBIC,
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"nearest": Resampling.NEAREST,
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}
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resample_method = resample_method_dic.get(method_str, None)
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if resample_method is None:
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raise ValueError(f"Unknown resampling method: {resample_method}")
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else:
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return resample_method
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class MarigoldPipeline(DiffusionPipeline):
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"""
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Pipeline for monocular depth estimation using Marigold: https://marigoldmonodepth.github.io.
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This model inherits from [`DiffusionPipeline`]. Check the superclass documentation for the generic methods the
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library implements for all the pipelines (such as downloading or saving, running on a particular device, etc.)
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Args:
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unet (`UNet2DConditionModel`):
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Conditional U-Net to denoise the depth latent, conditioned on image latent.
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vae (`AutoencoderKL`):
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Variational Auto-Encoder (VAE) Model to encode and decode images and depth maps
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to and from latent representations.
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scheduler (`DDIMScheduler`):
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A scheduler to be used in combination with `unet` to denoise the encoded image latents.
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text_encoder (`CLIPTextModel`):
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Text-encoder, for empty text embedding.
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tokenizer (`CLIPTokenizer`):
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CLIP tokenizer.
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"""
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rgb_latent_scale_factor = 0.18215
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depth_latent_scale_factor = 0.18215
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def __init__(
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self,
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unet: UNet2DConditionModel,
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vae: AutoencoderKL,
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scheduler: DDIMScheduler,
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text_encoder: CLIPTextModel,
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tokenizer: CLIPTokenizer,
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):
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super().__init__()
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self.register_modules(
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unet=unet,
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vae=vae,
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scheduler=scheduler,
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text_encoder=text_encoder,
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tokenizer=tokenizer,
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)
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self.empty_text_embed = None
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@torch.no_grad()
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def __call__(
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self,
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input_image: Image,
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denoising_steps: int = 10,
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ensemble_size: int = 10,
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processing_res: int = 768,
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match_input_res: bool = True,
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resample_method: str = "bilinear",
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batch_size: int = 0,
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seed: Union[int, None] = None,
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color_map: str = "Spectral",
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show_progress_bar: bool = True,
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ensemble_kwargs: Dict = None,
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) -> MarigoldDepthOutput:
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"""
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Function invoked when calling the pipeline.
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Args:
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input_image (`Image`):
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Input RGB (or gray-scale) image.
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processing_res (`int`, *optional*, defaults to `768`):
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Maximum resolution of processing.
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If set to 0: will not resize at all.
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match_input_res (`bool`, *optional*, defaults to `True`):
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Resize depth prediction to match input resolution.
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Only valid if `processing_res` > 0.
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resample_method: (`str`, *optional*, defaults to `bilinear`):
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Resampling method used to resize images and depth predictions. This can be one of `bilinear`, `bicubic` or `nearest`, defaults to: `bilinear`.
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denoising_steps (`int`, *optional*, defaults to `10`):
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Number of diffusion denoising steps (DDIM) during inference.
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ensemble_size (`int`, *optional*, defaults to `10`):
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Number of predictions to be ensembled.
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batch_size (`int`, *optional*, defaults to `0`):
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Inference batch size, no bigger than `num_ensemble`.
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If set to 0, the script will automatically decide the proper batch size.
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seed (`int`, *optional*, defaults to `None`)
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Reproducibility seed.
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show_progress_bar (`bool`, *optional*, defaults to `True`):
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Display a progress bar of diffusion denoising.
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color_map (`str`, *optional*, defaults to `"Spectral"`, pass `None` to skip colorized depth map generation):
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Colormap used to colorize the depth map.
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ensemble_kwargs (`dict`, *optional*, defaults to `None`):
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Arguments for detailed ensembling settings.
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Returns:
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`MarigoldDepthOutput`: Output class for Marigold monocular depth prediction pipeline, including:
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- **depth_np** (`np.ndarray`) Predicted depth map, with depth values in the range of [0, 1]
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- **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`
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- **uncertainty** (`None` or `np.ndarray`) Uncalibrated uncertainty(MAD, median absolute deviation)
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coming from ensembling. None if `ensemble_size = 1`
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"""
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device = self.device
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input_size = input_image.size
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if not match_input_res:
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assert processing_res is not None, "Value error: `resize_output_back` is only valid with "
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assert processing_res >= 0
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assert ensemble_size >= 1
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# Check if denoising step is reasonable
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self._check_inference_step(denoising_steps)
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resample_method: Resampling = get_pil_resample_method(resample_method)
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# ----------------- Image Preprocess -----------------
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# Resize image
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if processing_res > 0:
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input_image = self.resize_max_res(
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input_image,
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max_edge_resolution=processing_res,
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resample_method=resample_method,
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)
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# Convert the image to RGB, to 1.remove the alpha channel 2.convert B&W to 3-channel
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input_image = input_image.convert("RGB")
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image = np.asarray(input_image)
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# Normalize rgb values
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rgb = np.transpose(image, (2, 0, 1)) # [H, W, rgb] -> [rgb, H, W]
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rgb_norm = rgb / 255.0 * 2.0 - 1.0 # [0, 255] -> [-1, 1]
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rgb_norm = torch.from_numpy(rgb_norm).to(self.dtype)
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rgb_norm = rgb_norm.to(device)
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assert rgb_norm.min() >= -1.0 and rgb_norm.max() <= 1.0
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# ----------------- Predicting depth -----------------
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# Batch repeated input image
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duplicated_rgb = torch.stack([rgb_norm] * ensemble_size)
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single_rgb_dataset = TensorDataset(duplicated_rgb)
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if batch_size > 0:
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_bs = batch_size
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else:
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_bs = self._find_batch_size(
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ensemble_size=ensemble_size,
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input_res=max(rgb_norm.shape[1:]),
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dtype=self.dtype,
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)
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single_rgb_loader = DataLoader(single_rgb_dataset, batch_size=_bs, shuffle=False)
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# Predict depth maps (batched)
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depth_pred_ls = []
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if show_progress_bar:
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iterable = tqdm(single_rgb_loader, desc=" " * 2 + "Inference batches", leave=False)
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else:
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iterable = single_rgb_loader
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for batch in iterable:
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(batched_img,) = batch
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depth_pred_raw = self.single_infer(
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rgb_in=batched_img,
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num_inference_steps=denoising_steps,
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show_pbar=show_progress_bar,
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seed=seed,
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)
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depth_pred_ls.append(depth_pred_raw.detach())
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depth_preds = torch.concat(depth_pred_ls, dim=0).squeeze()
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torch.cuda.empty_cache() # clear vram cache for ensembling
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# ----------------- Test-time ensembling -----------------
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if ensemble_size > 1:
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depth_pred, pred_uncert = self.ensemble_depths(depth_preds, **(ensemble_kwargs or {}))
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else:
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depth_pred = depth_preds
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pred_uncert = None
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# ----------------- Post processing -----------------
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# Scale prediction to [0, 1]
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min_d = torch.min(depth_pred)
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max_d = torch.max(depth_pred)
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depth_pred = (depth_pred - min_d) / (max_d - min_d)
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# Convert to numpy
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depth_pred = depth_pred.cpu().numpy().astype(np.float32)
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# Resize back to original resolution
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if match_input_res:
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pred_img = Image.fromarray(depth_pred)
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pred_img = pred_img.resize(input_size, resample=resample_method)
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depth_pred = np.asarray(pred_img)
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# Clip output range
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depth_pred = depth_pred.clip(0, 1)
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# Colorize
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if color_map is not None:
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depth_colored = self.colorize_depth_maps(
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depth_pred, 0, 1, cmap=color_map
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).squeeze() # [3, H, W], value in (0, 1)
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depth_colored = (depth_colored * 255).astype(np.uint8)
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depth_colored_hwc = self.chw2hwc(depth_colored)
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depth_colored_img = Image.fromarray(depth_colored_hwc)
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else:
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depth_colored_img = None
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return MarigoldDepthOutput(
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depth_np=depth_pred,
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depth_colored=depth_colored_img,
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uncertainty=pred_uncert,
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)
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def _check_inference_step(self, n_step: int):
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"""
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Check if denoising step is reasonable
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Args:
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n_step (`int`): denoising steps
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"""
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assert n_step >= 1
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if isinstance(self.scheduler, DDIMScheduler):
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if n_step < 10:
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logging.warning(
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f"Too few denoising steps: {n_step}. Recommended to use the LCM checkpoint for few-step inference."
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)
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elif isinstance(self.scheduler, LCMScheduler):
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if not 1 <= n_step <= 4:
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logging.warning(f"Non-optimal setting of denoising steps: {n_step}. Recommended setting is 1-4 steps.")
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else:
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raise RuntimeError(f"Unsupported scheduler type: {type(self.scheduler)}")
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def _encode_empty_text(self):
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"""
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Encode text embedding for empty prompt.
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"""
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prompt = ""
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text_inputs = self.tokenizer(
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prompt,
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padding="do_not_pad",
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max_length=self.tokenizer.model_max_length,
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truncation=True,
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return_tensors="pt",
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)
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text_input_ids = text_inputs.input_ids.to(self.text_encoder.device)
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self.empty_text_embed = self.text_encoder(text_input_ids)[0].to(self.dtype)
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@torch.no_grad()
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def single_infer(
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self,
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rgb_in: torch.Tensor,
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num_inference_steps: int,
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seed: Union[int, None],
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show_pbar: bool,
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) -> torch.Tensor:
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"""
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Perform an individual depth prediction without ensembling.
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Args:
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rgb_in (`torch.Tensor`):
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Input RGB image.
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num_inference_steps (`int`):
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Number of diffusion denoisign steps (DDIM) during inference.
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show_pbar (`bool`):
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Display a progress bar of diffusion denoising.
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Returns:
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`torch.Tensor`: Predicted depth map.
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"""
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device = rgb_in.device
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# Set timesteps
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self.scheduler.set_timesteps(num_inference_steps, device=device)
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timesteps = self.scheduler.timesteps # [T]
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# Encode image
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rgb_latent = self.encode_rgb(rgb_in)
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# Initial depth map (noise)
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if seed is None:
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rand_num_generator = None
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else:
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rand_num_generator = torch.Generator(device=device)
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rand_num_generator.manual_seed(seed)
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depth_latent = torch.randn(
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rgb_latent.shape,
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device=device,
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dtype=self.dtype,
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generator=rand_num_generator,
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) # [B, 4, h, w]
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# Batched empty text embedding
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if self.empty_text_embed is None:
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self._encode_empty_text()
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batch_empty_text_embed = self.empty_text_embed.repeat((rgb_latent.shape[0], 1, 1)) # [B, 2, 1024]
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# Denoising loop
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if show_pbar:
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iterable = tqdm(
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enumerate(timesteps),
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total=len(timesteps),
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leave=False,
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desc=" " * 4 + "Diffusion denoising",
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)
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else:
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iterable = enumerate(timesteps)
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for i, t in iterable:
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unet_input = torch.cat([rgb_latent, depth_latent], dim=1) # this order is important
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# predict the noise residual
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noise_pred = self.unet(unet_input, t, encoder_hidden_states=batch_empty_text_embed).sample # [B, 4, h, w]
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# compute the previous noisy sample x_t -> x_t-1
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depth_latent = self.scheduler.step(noise_pred, t, depth_latent, generator=rand_num_generator).prev_sample
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depth = self.decode_depth(depth_latent)
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# clip prediction
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depth = torch.clip(depth, -1.0, 1.0)
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# shift to [0, 1]
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depth = (depth + 1.0) / 2.0
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return depth
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def encode_rgb(self, rgb_in: torch.Tensor) -> torch.Tensor:
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"""
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Encode RGB image into latent.
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Args:
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rgb_in (`torch.Tensor`):
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Input RGB image to be encoded.
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Returns:
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`torch.Tensor`: Image latent.
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"""
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# encode
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h = self.vae.encoder(rgb_in)
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moments = self.vae.quant_conv(h)
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mean, logvar = torch.chunk(moments, 2, dim=1)
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# scale latent
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rgb_latent = mean * self.rgb_latent_scale_factor
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return rgb_latent
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def decode_depth(self, depth_latent: torch.Tensor) -> torch.Tensor:
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"""
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Decode depth latent into depth map.
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Args:
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depth_latent (`torch.Tensor`):
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Depth latent to be decoded.
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Returns:
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`torch.Tensor`: Decoded depth map.
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"""
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# scale latent
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depth_latent = depth_latent / self.depth_latent_scale_factor
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# decode
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z = self.vae.post_quant_conv(depth_latent)
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stacked = self.vae.decoder(z)
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# mean of output channels
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depth_mean = stacked.mean(dim=1, keepdim=True)
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return depth_mean
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@staticmethod
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def resize_max_res(img: Image.Image, max_edge_resolution: int, resample_method=Resampling.BILINEAR) -> Image.Image:
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"""
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Resize image to limit maximum edge length while keeping aspect ratio.
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Args:
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img (`Image.Image`):
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Image to be resized.
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max_edge_resolution (`int`):
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Maximum edge length (pixel).
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resample_method (`PIL.Image.Resampling`):
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Resampling method used to resize images.
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Returns:
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`Image.Image`: Resized image.
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"""
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original_width, original_height = img.size
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downscale_factor = min(max_edge_resolution / original_width, max_edge_resolution / original_height)
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new_width = int(original_width * downscale_factor)
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new_height = int(original_height * downscale_factor)
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resized_img = img.resize((new_width, new_height), resample=resample_method)
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return resized_img
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@staticmethod
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def colorize_depth_maps(depth_map, min_depth, max_depth, cmap="Spectral", valid_mask=None):
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"""
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Colorize depth maps.
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"""
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assert len(depth_map.shape) >= 2, "Invalid dimension"
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if isinstance(depth_map, torch.Tensor):
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depth = depth_map.detach().clone().squeeze().numpy()
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elif isinstance(depth_map, np.ndarray):
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depth = depth_map.copy().squeeze()
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# reshape to [ (B,) H, W ]
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if depth.ndim < 3:
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depth = depth[np.newaxis, :, :]
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# colorize
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cm = matplotlib.colormaps[cmap]
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depth = ((depth - min_depth) / (max_depth - min_depth)).clip(0, 1)
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img_colored_np = cm(depth, bytes=False)[:, :, :, 0:3] # value from 0 to 1
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img_colored_np = np.rollaxis(img_colored_np, 3, 1)
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if valid_mask is not None:
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if isinstance(depth_map, torch.Tensor):
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valid_mask = valid_mask.detach().numpy()
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valid_mask = valid_mask.squeeze() # [H, W] or [B, H, W]
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if valid_mask.ndim < 3:
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valid_mask = valid_mask[np.newaxis, np.newaxis, :, :]
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else:
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|
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
|