moge/utils/geometry_torch.py

from typing import *
import math
from collections import namedtuple

import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F
import torch.types
import utils3d

from .tools import timeit
from .geometry_numpy import solve_optimal_focal_shift, solve_optimal_shift


def weighted_mean(x: torch.Tensor, w: torch.Tensor = None, dim: Union[int, torch.Size] = None, keepdim: bool = False, eps: float = 1e-7) -> torch.Tensor:
    if w is None:
        return x.mean(dim=dim, keepdim=keepdim)
    else:
        w = w.to(x.dtype)
        return (x * w).mean(dim=dim, keepdim=keepdim) / w.mean(dim=dim, keepdim=keepdim).add(eps)


def harmonic_mean(x: torch.Tensor, w: torch.Tensor = None, dim: Union[int, torch.Size] = None, keepdim: bool = False, eps: float = 1e-7) -> torch.Tensor:
    if w is None:
        return x.add(eps).reciprocal().mean(dim=dim, keepdim=keepdim).reciprocal()
    else:
        w = w.to(x.dtype)
        return weighted_mean(x.add(eps).reciprocal(), w, dim=dim, keepdim=keepdim, eps=eps).add(eps).reciprocal()


def geometric_mean(x: torch.Tensor, w: torch.Tensor = None, dim: Union[int, torch.Size] = None, keepdim: bool = False, eps: float = 1e-7) -> torch.Tensor:
    if w is None:
        return x.add(eps).log().mean(dim=dim).exp()
    else:
        w = w.to(x.dtype)
        return weighted_mean(x.add(eps).log(), w, dim=dim, keepdim=keepdim, eps=eps).exp()


def normalized_view_plane_uv(width: int, height: int, aspect_ratio: float = None, dtype: torch.dtype = None, device: torch.device = None) -> torch.Tensor:
    "UV with left-top corner as (-width / diagonal, -height / diagonal) and right-bottom corner as (width / diagonal, height / diagonal)"
    if aspect_ratio is None:
        aspect_ratio = width / height
    
    span_x = aspect_ratio / (1 + aspect_ratio ** 2) ** 0.5
    span_y = 1 / (1 + aspect_ratio ** 2) ** 0.5

    u = torch.linspace(-span_x * (width - 1) / width, span_x * (width - 1) / width, width, dtype=dtype, device=device)
    v = torch.linspace(-span_y * (height - 1) / height, span_y * (height - 1) / height, height, dtype=dtype, device=device)
    u, v = torch.meshgrid(u, v, indexing='xy')
    uv = torch.stack([u, v], dim=-1)
    return uv


def gaussian_blur_2d(input: torch.Tensor, kernel_size: int, sigma: float) -> torch.Tensor:
    kernel = torch.exp(-(torch.arange(-kernel_size // 2 + 1, kernel_size // 2 + 1, dtype=input.dtype, device=input.device) ** 2) / (2 * sigma ** 2))
    kernel = kernel / kernel.sum()
    kernel = (kernel[:, None] * kernel[None, :]).reshape(1, 1, kernel_size, kernel_size)
    input = F.pad(input, (kernel_size // 2, kernel_size // 2, kernel_size // 2, kernel_size // 2), mode='replicate')
    input = F.conv2d(input, kernel, groups=input.shape[1])
    return input


def focal_to_fov(focal: torch.Tensor):
    return 2 * torch.atan(0.5 / focal)


def fov_to_focal(fov: torch.Tensor):
    return 0.5 / torch.tan(fov / 2)


def angle_diff_vec3(v1: torch.Tensor, v2: torch.Tensor, eps: float = 1e-12):
    return torch.atan2(torch.cross(v1, v2, dim=-1).norm(dim=-1) + eps, (v1 * v2).sum(dim=-1))

def intrinsics_to_fov(intrinsics: torch.Tensor):
    """
    Returns field of view in radians from normalized intrinsics matrix.
    ### Parameters:
    - intrinsics: torch.Tensor of shape (..., 3, 3)

    ### Returns:
    - fov_x: torch.Tensor of shape (...)
    - fov_y: torch.Tensor of shape (...)
    """
    focal_x = intrinsics[..., 0, 0]
    focal_y = intrinsics[..., 1, 1]
    return 2 * torch.atan(0.5 / focal_x), 2 * torch.atan(0.5 / focal_y)


def point_map_to_depth_legacy(points: torch.Tensor):
    height, width = points.shape[-3:-1]
    diagonal = (height ** 2 + width ** 2) ** 0.5
    uv = normalized_view_plane_uv(width, height, dtype=points.dtype, device=points.device)  # (H, W, 2)

    # Solve least squares problem
    b = (uv * points[..., 2:]).flatten(-3, -1)                        # (..., H * W * 2)
    A = torch.stack([points[..., :2], -uv.expand_as(points[..., :2])], dim=-1).flatten(-4, -2)   # (..., H * W * 2, 2)

    M = A.transpose(-2, -1) @ A 
    solution = (torch.inverse(M + 1e-6 * torch.eye(2).to(A)) @ (A.transpose(-2, -1) @ b[..., None])).squeeze(-1)
    focal, shift = solution.unbind(-1)

    depth = points[..., 2] + shift[..., None, None]
    fov_x = torch.atan(width / diagonal / focal) * 2
    fov_y = torch.atan(height / diagonal / focal) * 2
    return depth, fov_x, fov_y, shift


def view_plane_uv_to_focal(uv: torch.Tensor):
    normed_uv = normalized_view_plane_uv(width=uv.shape[-2], height=uv.shape[-3], device=uv.device, dtype=uv.dtype)
    focal = (uv * normed_uv).sum() / uv.square().sum().add(1e-12)
    return focal


def recover_focal_shift(points: torch.Tensor, mask: torch.Tensor = None, focal: torch.Tensor = None, downsample_size: Tuple[int, int] = (64, 64)):
    """
    Recover the depth map and FoV from a point map with unknown z shift and focal.

    Note that it assumes:
    - the optical center is at the center of the map
    - the map is undistorted
    - the map is isometric in the x and y directions

    ### Parameters:
    - `points: torch.Tensor` of shape (..., H, W, 3)
    - `downsample_size: Tuple[int, int]` in (height, width), the size of the downsampled map. Downsampling produces approximate solution and is efficient for large maps.

    ### Returns:
    - `focal`: torch.Tensor of shape (...) the estimated focal length, relative to the half diagonal of the map
    - `shift`: torch.Tensor of shape (...) Z-axis shift to translate the point map to camera space
    """
    shape = points.shape
    height, width = points.shape[-3], points.shape[-2]
    diagonal = (height ** 2 + width ** 2) ** 0.5

    points = points.reshape(-1, *shape[-3:])
    mask = None if mask is None else mask.reshape(-1, *shape[-3:-1])
    focal = focal.reshape(-1) if focal is not None else None
    uv = normalized_view_plane_uv(width, height, dtype=points.dtype, device=points.device)  # (H, W, 2)

    points_lr = F.interpolate(points.permute(0, 3, 1, 2), downsample_size, mode='nearest').permute(0, 2, 3, 1)
    uv_lr = F.interpolate(uv.unsqueeze(0).permute(0, 3, 1, 2), downsample_size, mode='nearest').squeeze(0).permute(1, 2, 0)
    mask_lr = None if mask is None else F.interpolate(mask.to(torch.float32).unsqueeze(1), downsample_size, mode='nearest').squeeze(1) > 0
    
    uv_lr_np = uv_lr.cpu().numpy()
    points_lr_np = points_lr.detach().cpu().numpy()
    focal_np = focal.cpu().numpy() if focal is not None else None
    mask_lr_np = None if mask is None else mask_lr.cpu().numpy()
    optim_shift, optim_focal = [], []
    for i in range(points.shape[0]):
        points_lr_i_np = points_lr_np[i] if mask is None else points_lr_np[i][mask_lr_np[i]]
        uv_lr_i_np = uv_lr_np if mask is None else uv_lr_np[mask_lr_np[i]]
        if uv_lr_i_np.shape[0] < 2:
            optim_focal.append(1)
            optim_shift.append(0)
            continue
        if focal is None:
            optim_shift_i, optim_focal_i = solve_optimal_focal_shift(uv_lr_i_np, points_lr_i_np)
            optim_focal.append(float(optim_focal_i))
        else:
            optim_shift_i = solve_optimal_shift(uv_lr_i_np, points_lr_i_np, focal_np[i])
        optim_shift.append(float(optim_shift_i))
    optim_shift = torch.tensor(optim_shift, device=points.device, dtype=points.dtype).reshape(shape[:-3])

    if focal is None:
        optim_focal = torch.tensor(optim_focal, device=points.device, dtype=points.dtype).reshape(shape[:-3])
    else:
        optim_focal = focal.reshape(shape[:-3])

    return optim_focal, optim_shift


def mask_aware_nearest_resize(
    inputs: Union[torch.Tensor, Sequence[torch.Tensor], None],
    mask: torch.BoolTensor, 
    size: Tuple[int, int], 
    return_index: bool = False
) -> Tuple[Union[torch.Tensor, Sequence[torch.Tensor], None], torch.BoolTensor, Tuple[torch.LongTensor, ...]]:
    """
    Resize 2D map by nearest interpolation. Return the nearest neighbor index and mask of the resized map.

    ### Parameters
    - `inputs`: a single or a list of input 2D map(s) of shape (..., H, W, ...). 
    - `mask`: input 2D mask of shape (..., H, W)
    - `size`: target size (target_width, target_height)

    ### Returns
    - `*resized_maps`: resized map(s) of shape (..., target_height, target_width, ...). 
    - `resized_mask`: mask of the resized map of shape (..., target_height, target_width)
    - `nearest_idx`: if return_index is True, nearest neighbor index of the resized map of shape (..., target_height, target_width) for each dimension, .
    """
    height, width = mask.shape[-2:]
    target_width, target_height = size
    device = mask.device
    filter_h_f, filter_w_f = max(1, height / target_height), max(1, width / target_width)
    filter_h_i, filter_w_i = math.ceil(filter_h_f), math.ceil(filter_w_f)
    filter_size = filter_h_i * filter_w_i
    padding_h, padding_w = filter_h_i // 2 + 1, filter_w_i // 2 + 1

    # Window the original mask and uv
    uv = utils3d.torch.image_pixel_center(width=width, height=height, dtype=torch.float32, device=device)
    indices = torch.arange(height * width, dtype=torch.long, device=device).reshape(height, width)
    padded_uv = torch.full((height + 2 * padding_h, width + 2 * padding_w, 2), 0, dtype=torch.float32, device=device)
    padded_uv[padding_h:padding_h + height, padding_w:padding_w + width] = uv
    padded_mask = torch.full((*mask.shape[:-2], height + 2 * padding_h, width + 2 * padding_w), False, dtype=torch.bool, device=device)
    padded_mask[..., padding_h:padding_h + height, padding_w:padding_w + width] = mask
    padded_indices = torch.full((height + 2 * padding_h, width + 2 * padding_w), 0, dtype=torch.long, device=device)
    padded_indices[padding_h:padding_h + height, padding_w:padding_w + width] = indices
    windowed_uv = utils3d.torch.sliding_window_2d(padded_uv, (filter_h_i, filter_w_i), 1, dim=(0, 1))
    windowed_mask = utils3d.torch.sliding_window_2d(padded_mask, (filter_h_i, filter_w_i), 1, dim=(-2, -1))
    windowed_indices = utils3d.torch.sliding_window_2d(padded_indices, (filter_h_i, filter_w_i), 1, dim=(0, 1))

    # Gather the target pixels's local window
    target_uv = utils3d.torch.image_uv(width=target_width, height=target_height, dtype=torch.float32, device=device) * torch.tensor([width, height], dtype=torch.float32, device=device)
    target_lefttop = target_uv - torch.tensor((filter_w_f / 2, filter_h_f / 2), dtype=torch.float32, device=device)
    target_window = torch.round(target_lefttop).long() + torch.tensor((padding_w, padding_h), dtype=torch.long, device=device)

    target_window_uv = windowed_uv[target_window[..., 1], target_window[..., 0], :, :, :].reshape(target_height, target_width, 2, filter_size)                          # (target_height, tgt_width, 2, filter_size)
    target_window_mask = windowed_mask[..., target_window[..., 1], target_window[..., 0], :, :].reshape(*mask.shape[:-2], target_height, target_width, filter_size)     # (..., target_height, tgt_width, filter_size)
    target_window_indices = windowed_indices[target_window[..., 1], target_window[..., 0], :, :].reshape(target_height, target_width, filter_size)                      # (target_height, tgt_width, filter_size)
    target_window_indices = target_window_indices.expand_as(target_window_mask)

    # Compute nearest neighbor in the local window for each pixel 
    dist = torch.where(target_window_mask, torch.norm(target_window_uv - target_uv[..., None], dim=-2), torch.inf)  # (..., target_height, tgt_width, filter_size)
    nearest = torch.argmin(dist, dim=-1, keepdim=True)                                                              # (..., target_height, tgt_width, 1)
    nearest_idx = torch.gather(target_window_indices, index=nearest, dim=-1).squeeze(-1)                            # (..., target_height, tgt_width)
    target_mask = torch.any(target_window_mask, dim=-1)
    nearest_i, nearest_j = nearest_idx // width, nearest_idx % width
    batch_indices = [torch.arange(n, device=device).reshape([1] * i + [n] + [1] * (mask.dim() - i - 1)) for i, n in enumerate(mask.shape[:-2])]
    
    index = (*batch_indices, nearest_i, nearest_j)
    
    if inputs is None:
        outputs = None
    elif isinstance(inputs, torch.Tensor):
        outputs = inputs[index]
    elif isinstance(inputs, Sequence):
        outputs = tuple(x[index] for x in inputs)
    else:
        raise ValueError(f'Invalid input type: {type(inputs)}')
    
    if return_index:
        return outputs, target_mask, index
    else:
        return outputs, target_mask


def theshold_depth_change(depth: torch.Tensor, mask: torch.Tensor, pooler: Literal['min', 'max'], rtol: float = 0.2, kernel_size: int = 3):
    *batch_shape, height, width = depth.shape
    depth = depth.reshape(-1, 1, height, width)
    mask = mask.reshape(-1, 1, height, width)
    if pooler =='max':
        pooled_depth = F.max_pool2d(torch.where(mask, depth, -torch.inf), kernel_size, stride=1, padding=kernel_size // 2)
        output_mask = pooled_depth > depth * (1 + rtol)
    elif pooler =='min':
        pooled_depth = -F.max_pool2d(-torch.where(mask, depth, torch.inf), kernel_size, stride=1, padding=kernel_size // 2)
        output_mask =  pooled_depth < depth * (1 - rtol)
    else:
        raise ValueError(f'Unsupported pooler: {pooler}')
    output_mask = output_mask.reshape(*batch_shape, height, width)
    return output_mask


def depth_occlusion_edge(depth: torch.FloatTensor, mask: torch.BoolTensor, kernel_size: int = 3, tol: float = 0.1):
    device, dtype = depth.device, depth.dtype

    disp = torch.where(mask, 1 / depth, 0)
    disp_pad = F.pad(disp, (kernel_size // 2, kernel_size // 2, kernel_size // 2, kernel_size // 2), value=0)
    mask_pad = F.pad(mask, (kernel_size // 2, kernel_size // 2, kernel_size // 2, kernel_size // 2), value=False)
    disp_window = utils3d.torch.sliding_window_2d(disp_pad, (kernel_size, kernel_size), 1, dim=(-2, -1)).flatten(-2)  # [..., H, W, kernel_size ** 2]
    mask_window = utils3d.torch.sliding_window_2d(mask_pad, (kernel_size, kernel_size), 1, dim=(-2, -1)).flatten(-2)            # [..., H, W, kernel_size ** 2]

    x = torch.linspace(-kernel_size // 2, kernel_size // 2, kernel_size, device=device, dtype=dtype)
    A = torch.stack([*torch.meshgrid(x, x, indexing='xy'), torch.ones((kernel_size, kernel_size), device=device, dtype=dtype)], dim=-1).reshape(kernel_size ** 2, 3)        # [kernel_size ** 2, 3]
    A = mask_window[..., None] * A
    I = torch.eye(3, device=device, dtype=dtype)
    
    affine_disp_window = (disp_window[..., None, :] @ A @ torch.inverse(A.mT @ A + 1e-5 * I) @ A.mT).clamp_min(1e-12)[..., 0, :]  # [..., H, W, kernel_size ** 2]
    diff = torch.where(mask_window, torch.maximum(affine_disp_window, disp_window) / torch.minimum(affine_disp_window, disp_window) - 1, 0)

    edge_mask = mask & (diff > tol).any(dim=-1)

    disp_mean = weighted_mean(disp_window, mask_window, dim=-1)
    fg_edge_mask = edge_mask & (disp > disp_mean)
    # fg_edge_mask = edge_mask & theshold_depth_change(depth, mask, pooler='max', rtol=tol, kernel_size=kernel_size)
    bg_edge_mask = edge_mask & ~fg_edge_mask
    return fg_edge_mask, bg_edge_mask


def depth_occlusion_edge(depth: torch.FloatTensor, mask: torch.BoolTensor, kernel_size: int = 3, tol: float = 0.1):
    device, dtype = depth.device, depth.dtype

    disp = torch.where(mask, 1 / depth, 0)
    disp_pad = F.pad(disp, (kernel_size // 2, kernel_size // 2, kernel_size // 2, kernel_size // 2), value=0)
    mask_pad = F.pad(mask, (kernel_size // 2, kernel_size // 2, kernel_size // 2, kernel_size // 2), value=False)
    disp_window = utils3d.torch.sliding_window_2d(disp_pad, (kernel_size, kernel_size), 1, dim=(-2, -1))  # [..., H, W, kernel_size ** 2]
    mask_window = utils3d.torch.sliding_window_2d(mask_pad, (kernel_size, kernel_size), 1, dim=(-2, -1))  # [..., H, W, kernel_size ** 2]

    disp_mean = weighted_mean(disp_window, mask_window, dim=(-2, -1))
    fg_edge_mask = mask & (disp / disp_mean > 1 + tol)
    bg_edge_mask = mask & (disp_mean / disp > 1 + tol)

    fg_edge_mask = fg_edge_mask & F.max_pool2d(bg_edge_mask.float(), kernel_size + 2, stride=1, padding=kernel_size // 2 + 1).bool()
    bg_edge_mask = bg_edge_mask & F.max_pool2d(fg_edge_mask.float(), kernel_size + 2, stride=1, padding=kernel_size // 2 + 1).bool()

    return fg_edge_mask, bg_edge_mask


def dilate_with_mask(input: torch.Tensor, mask: torch.BoolTensor, filter: Literal['min', 'max', 'mean', 'median'] = 'mean', iterations: int = 1) -> torch.Tensor:
    kernel = torch.tensor([[False, True, False], [True, True, True], [False, True, False]], device=input.device, dtype=torch.bool)
    for _ in range(iterations):
        input_window = utils3d.torch.sliding_window_2d(F.pad(input, (1, 1, 1, 1), mode='constant', value=0), window_size=3, stride=1, dim=(-2, -1))
        mask_window = kernel & utils3d.torch.sliding_window_2d(F.pad(mask, (1, 1, 1, 1), mode='constant', value=False), window_size=3, stride=1, dim=(-2, -1))    
        if filter =='min':
            input = torch.where(mask, input, torch.where(mask_window, input_window, torch.inf).min(dim=(-2, -1)).values)
        elif filter =='max':
            input = torch.where(mask, input, torch.where(mask_window, input_window, -torch.inf).max(dim=(-2, -1)).values)
        elif filter == 'mean':
            input = torch.where(mask, input, torch.where(mask_window, input_window, torch.nan).nanmean(dim=(-2, -1)))
        elif filter =='median':
            input = torch.where(mask, input, torch.where(mask_window, input_window, torch.nan).flatten(-2).nanmedian(dim=-1).values)
        mask = mask_window.any(dim=(-2, -1))
    return input, mask


def refine_depth_with_normal(depth: torch.Tensor, normal: torch.Tensor, intrinsics: torch.Tensor, iterations: int = 10, damp: float = 1e-3, eps: float = 1e-12, kernel_size: int = 5) -> torch.Tensor:
    device, dtype = depth.device, depth.dtype
    height, width = depth.shape[-2:]
    radius = kernel_size // 2

    duv = torch.stack(torch.meshgrid(torch.linspace(-radius / width, radius / width, kernel_size, device=device, dtype=dtype), torch.linspace(-radius / height, radius / height, kernel_size, device=device, dtype=dtype), indexing='xy'), dim=-1).to(dtype=dtype, device=device)

    log_depth = depth.clamp_min_(eps).log()
    log_depth_diff = utils3d.torch.sliding_window_2d(log_depth, window_size=kernel_size, stride=1, dim=(-2, -1)) - log_depth[..., radius:-radius, radius:-radius, None, None] 
    
    weight = torch.exp(-(log_depth_diff / duv.norm(dim=-1).clamp_min_(eps) / 10).square())
    tot_weight = weight.sum(dim=(-2, -1)).clamp_min_(eps)

    uv = utils3d.torch.image_uv(height=height, width=width, device=device, dtype=dtype)
    K_inv = torch.inverse(intrinsics)

    grad = -(normal[..., None, :2] @ K_inv[..., None, None, :2, :2]).squeeze(-2) \
            / (normal[..., None, 2:] + normal[..., None, :2] @ (K_inv[..., None, None, :2, :2] @ uv[..., :, None] + K_inv[..., None, None, :2, 2:])).squeeze(-2)
    laplacian = (weight * ((utils3d.torch.sliding_window_2d(grad, window_size=kernel_size, stride=1, dim=(-3, -2)) + grad[..., radius:-radius, radius:-radius, :, None, None]) * (duv.permute(2, 0, 1) / 2)).sum(dim=-3)).sum(dim=(-2, -1))
    
    laplacian = laplacian.clamp(-0.1, 0.1)
    log_depth_refine = log_depth.clone()

    for _ in range(iterations):
        log_depth_refine[..., radius:-radius, radius:-radius] = 0.1 * log_depth_refine[..., radius:-radius, radius:-radius] + 0.9 * (damp * log_depth[..., radius:-radius, radius:-radius] - laplacian + (weight * utils3d.torch.sliding_window_2d(log_depth_refine, window_size=kernel_size, stride=1, dim=(-2, -1))).sum(dim=(-2, -1))) / (tot_weight + damp) 

    depth_refine = log_depth_refine.exp()

    return depth_refine