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import numpy as np
import torch
from tools.utils import wrap
from common.quaternion import qort, qinverse
def normalize_screen_coordinates(X, w, h):
assert X.shape[-1] == 2
# Normalize so that [0, w] is mapped to [-1, 1], while preserving the aspect ratio
return X/w*2 - [1, h/w]
def image_coordinates(X, w, h):
assert X.shape[-1] == 2
# Reverse camera frame normalization
return (X + [1, h/w]) * w / 2
def world_to_camera(X, R, t):
Rt = wrap(qinverse, R) # Invert rotation
return wrap(qort, np.tile(Rt, (*X.shape[:-1], 1)), X - t) # Rotate and translate
def camera_to_world(X, R, t):
return wrap(qort, np.tile(R, (*X.shape[:-1], 1)), X) + t
def project_to_2d(X, camera_params):
"""
Project 3D points to 2D using the Human3.6M camera projection function.
This is a differentiable and batched reimplementation of the original MATLAB script.
Arguments:
X -- 3D points in *camera space* to transform (N, *, 3)
camera_params -- intrinsic parameteres (N, 2+2+3+2=9)
"""
assert X.shape[-1] == 3
assert len(camera_params.shape) == 2
assert camera_params.shape[-1] == 9
assert X.shape[0] == camera_params.shape[0]
while len(camera_params.shape) < len(X.shape):
camera_params = camera_params.unsqueeze(1)
f = camera_params[..., :2]
c = camera_params[..., 2:4]
k = camera_params[..., 4:7]
p = camera_params[..., 7:]
# XX = torch.clamp(X[..., :2] / X[..., 2:], min=-1, max=1)
XX = X[..., :2] / X[..., 2:]
r2 = torch.sum(XX[..., :2]**2, dim=len(XX.shape)-1, keepdim=True)
radial = 1 + torch.sum(k * torch.cat((r2, r2**2, r2**3), dim=len(r2.shape)-1), dim=len(r2.shape)-1, keepdim=True)
tan = torch.sum(p*XX, dim=len(XX.shape)-1, keepdim=True)
XXX = XX*(radial + tan) + p*r2
return f*XXX + c
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