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| # Copyright (C) 2024-present Naver Corporation. All rights reserved. | |
| # Licensed under CC BY-NC-SA 4.0 (non-commercial use only). | |
| # | |
| # -------------------------------------------------------- | |
| # utilities for interpreting the DUST3R output | |
| # -------------------------------------------------------- | |
| import numpy as np | |
| import torch | |
| from dust3r.utils.geometry import xy_grid | |
| # 估计焦距f，即论文中的《3.3.Downstream Applications-Recovering intrinsics.》章节的公式 | |
| def estimate_focal_knowing_depth(pts3d, pp, focal_mode='median', min_focal=0.5, max_focal=3.5): | |
| """ Reprojection method, for when the absolute depth is known: | |
| 1) estimate the camera focal using a robust estimator | |
| 2) reproject points onto true rays, minimizing a certain error | |
| """ | |
| B, H, W, THREE = pts3d.shape | |
| assert THREE == 3 | |
| # pixels即论文中的图像坐标系下的坐标(i`,j`)：i` = i - W/2 , j` = j - H/2 | |
| pixels = xy_grid(W, H, device=pts3d.device).view(1, -1, 2) - pp.view(-1, 1, 2) # B,HW,2 | |
| pts3d = pts3d.flatten(1, 2) # (B, H*W, 3) | |
| if focal_mode == 'median': | |
| with torch.no_grad(): | |
| # direct estimation of focal | |
| u, v = pixels.unbind(dim=-1) | |
| x, y, z = pts3d.unbind(dim=-1) | |
| fx_votes = (u * z) / x | |
| fy_votes = (v * z) / y | |
| # assume square pixels, hence same focal for X and Y | |
| f_votes = torch.cat((fx_votes.view(B, -1), fy_votes.view(B, -1)), dim=-1) | |
| focal = torch.nanmedian(f_votes, dim=-1).values | |
| elif focal_mode == 'weiszfeld': # 参考链接：https://blog.csdn.net/qianlinjun/article/details/53852306 | |
| # init focal with l2 closed form | |
| # we try to find focal = argmin Sum | pixel - focal * (x,y)/z| | |
| xy_over_z = (pts3d[..., :2] / pts3d[..., 2:3]).nan_to_num(posinf=0, neginf=0) # 转齐次坐标，即x，y除以z坐标 | |
| # 1、初始化第一轮迭代时的focal | |
| dot_xy_px = (xy_over_z * pixels).sum(dim=-1) | |
| dot_xy_xy = xy_over_z.square().sum(dim=-1) | |
| focal = dot_xy_px.mean(dim=1) / dot_xy_xy.mean(dim=1) | |
| # 2、基于weiszfeld算法迭代 | |
| # iterative re-weighted least-squares | |
| for iter in range(10): | |
| # re-weighting by inverse of distance | |
| dis = (pixels - focal.view(-1, 1, 1) * xy_over_z).norm(dim=-1) # norm：求第二范式 | |
| # print(dis.nanmean(-1)) | |
| w = dis.clip(min=1e-8).reciprocal() # 求倒数 | |
| # update the scaling with the new weights | |
| focal = (w * dot_xy_px).mean(dim=1) / (w * dot_xy_xy).mean(dim=1) | |
| else: | |
| raise ValueError(f'bad {focal_mode=}') | |
| focal_base = max(H, W) / (2 * np.tan(np.deg2rad(60) / 2)) # size / 1.1547005383792515 | |
| focal = focal.clip(min=min_focal*focal_base, max=max_focal*focal_base) | |
| # print(focal) | |
| return focal | |