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#!/usr/bin/env python3
# Converts Windows Mixed Reality (Reverb G2 and Odyssey+) calibrations in to
# basalt calibrations.
# Run with ./wmr2bslt_calib.py your_wmrcalib.json > your_calib.json
import json
import argparse
import numpy as np
from numpy.linalg import inv
from math import sqrt
def get(j, name):
assert name in ["HT0", "HT1", "Gyro", "Accelerometer"]
is_imu = name in ["Gyro", "Accelerometer"]
calib = j["CalibrationInformation"]
sensors = calib["InertialSensors" if is_imu else "Cameras"]
name_key = "SensorType" if is_imu else "Location"
sensor = next(filter(lambda s: s[name_key].endswith(name), sensors))
return sensor
def rt2mat(rt):
R33 = np.array(rt["Rotation"]).reshape(3, 3)
t31 = np.array(rt["Translation"]).reshape(3, 1)
T34 = np.hstack((R33, t31))
T44 = np.vstack((T34, [0, 0, 0, 1]))
return T44
def rmat2quat(r):
w = sqrt(1 + r[0, 0] + r[1, 1] + r[2, 2]) / 2
w4 = 4 * w
x = (r[2, 1] - r[1, 2]) / w4
y = (r[0, 2] - r[2, 0]) / w4
z = (r[1, 0] - r[0, 1]) / w4
return np.array([x, y, z, w])
def project(intrinsics, x, y, z):
fx, fy, cx, cy, k1, k2, k3, k4, k5, k6, p1, p2 = (
intrinsics["fx"],
intrinsics["fy"],
intrinsics["cx"],
intrinsics["cy"],
intrinsics["k1"],
intrinsics["k2"],
intrinsics["k3"],
intrinsics["k4"],
intrinsics["k5"],
intrinsics["k6"],
intrinsics["p1"],
intrinsics["p2"],
)
xp = x / z
yp = y / z
r2 = xp * xp + yp * yp
cdist = (1 + r2 * (k1 + r2 * (k2 + r2 * k3))) / (
1 + r2 * (k4 + r2 * (k5 + r2 * k6))
)
deltaX = 2 * p1 * xp * yp + p2 * (r2 + 2 * xp * xp)
deltaY = 2 * p2 * xp * yp + p1 * (r2 + 2 * yp * yp)
xpp = xp * cdist + deltaX
ypp = yp * cdist + deltaY
u = fx * xpp + cx
v = fy * ypp + cy
return u, v
def extrinsics(j, cam):
# NOTE: The `Rt` field seems to be a transform from the sensor to HT0 (i.e.,
# from HT0 space to sensor space). For basalt we need the transforms
# expressed w.r.t IMU origin.
# NOTE: The gyro and magnetometer translations are 0, probably because an
# HMD is a rigid body. Therefore the accelerometer is considered as the IMU
# origin.
imu = get(j, "Accelerometer")
T_i_c0 = rt2mat(imu["Rt"])
T = None
if cam == "HT0":
T = T_i_c0
elif cam == "HT1":
cam1 = get(j, "HT1")
T_c1_c0 = rt2mat(cam1["Rt"])
T_c0_c1 = inv(T_c1_c0)
T_i_c1 = T_i_c0 @ T_c0_c1
T = T_i_c1
else:
assert False
q = rmat2quat(T[0:3, 0:3])
p = T[0:3, 3]
return {
"px": p[0],
"py": p[1],
"pz": p[2],
"qx": q[0],
"qy": q[1],
"qz": q[2],
"qw": q[3],
}
def resolution(j, cam):
camera = get(j, cam)
width = camera["SensorWidth"]
height = camera["SensorHeight"]
return [width, height]
def intrinsics(j, cam):
# https://github.com/microsoft/Azure-Kinect-Sensor-SDK/blob/2feb3425259bf803749065bb6d628c6c180f8e77/include/k4a/k4atypes.h#L1024-L1046
camera = get(j, cam)
model_params = camera["Intrinsics"]["ModelParameters"]
assert (
camera["Intrinsics"]["ModelType"]
== "CALIBRATION_LensDistortionModelRational6KT"
)
width = camera["SensorWidth"]
height = camera["SensorHeight"]
return {
"camera_type": "pinhole-radtan8",
"intrinsics": {
"fx": model_params[2] * width,
"fy": model_params[3] * height,
"cx": model_params[0] * width,
"cy": model_params[1] * height,
"k1": model_params[4],
"k2": model_params[5],
"p1": model_params[13],
"p2": model_params[12],
"k3": model_params[6],
"k4": model_params[7],
"k5": model_params[8],
"k6": model_params[9],
"rpmax": model_params[14],
},
}
def view_offset(j):
"""
This is a very rough offset in pixels between the two cameras. Originally we
needed to manually estimate it like explained and shown here
https://youtu.be/jyQKjyRVMS4?t=670.
With this calculation we get a similar number without the need to open Gimp.
In reality this offset changes based on distance to the point, nonetheless
it helps to get some features tracked in the right camera.
"""
# Rough approximation of how far from the cameras features will likely be in your room
DISTANCE_TO_WALL = 2 # In meters
cam1 = get(j, "HT1")
width = cam1["SensorWidth"]
height = cam1["SensorHeight"]
cam1_intrinsics = intrinsics(j, "HT1")["intrinsics"]
T_c1_c0 = rt2mat(cam1["Rt"]) # Maps a point in c0 space to c1 space
p = np.array([0, 0, DISTANCE_TO_WALL, 1]) # Fron tof c0, in homogeneous coords
p_in_c1 = T_c1_c0 @ p # Point in c1 coordinates
u, v = project(cam1_intrinsics, *p_in_c1[0:3])
view_offset = [width / 2 - u, height / 2 - v] # We used a point in the middle of c0
return view_offset
def calib_accel_bias(j):
# https://github.com/microsoft/Azure-Kinect-Sensor-SDK/blob/2feb3425259bf803749065bb6d628c6c180f8e77/include/k4ainternal/calibration.h#L48-L77
# https://vladyslavusenko.gitlab.io/basalt-headers/classbasalt_1_1CalibAccelBias.html#details
# https://gitlab.com/VladyslavUsenko/basalt-headers/-/issues/8
accel = get(j, "Accelerometer")
bias = accel["BiasTemperatureModel"]
align = accel["MixingMatrixTemperatureModel"]
return [
-bias[0 * 4],
-bias[1 * 4],
-bias[2 * 4],
align[0 * 4] - 1, # [0, 0]
align[3 * 4], # [1, 0]
align[6 * 4], # [2, 0]
align[4 * 4] - 1, # [1, 1]
align[7 * 4], # [2, 1]
align[8 * 4] - 1, # [2, 2]
]
def calib_gyro_bias(j):
# https://github.com/microsoft/Azure-Kinect-Sensor-SDK/blob/2feb3425259bf803749065bb6d628c6c180f8e77/include/k4ainternal/calibration.h#L48-L77
# https://vladyslavusenko.gitlab.io/basalt-headers/classbasalt_1_1CalibGyroBias.html#details
gyro = get(j, "Gyro")
bias = gyro["BiasTemperatureModel"]
align = gyro["MixingMatrixTemperatureModel"]
return [
-bias[0 * 4],
-bias[1 * 4],
-bias[2 * 4],
align[0 * 4] - 1, # [0, 0]
align[3 * 4], # [1, 0]
align[6 * 4], # [2, 0]
align[1 * 4], # [0, 1]
align[4 * 4] - 1, # [1, 1]
align[7 * 4], # [2, 1]
align[2 * 4], # [0, 2]
align[5 * 4], # [1, 2]
align[8 * 4] - 1, # [2, 2]
]
def noise_std(j, name):
imu = get(j, name)
return imu["Noise"][0:3]
def bias_std(j, name):
imu = get(j, name)
return list(map(sqrt, imu["BiasUncertainty"]))
def main():
parser = argparse.ArgumentParser()
parser.add_argument("wmr_json_file", help="Input WMR json calibration file")
args = parser.parse_args()
in_fn = args.wmr_json_file
with open(in_fn) as f:
j = json.load(f)
# We get 250 packets with 4 samples each per second, totalling 1000 samples per second.
# But in monado we just average those 4 samples to reduce the noise. So we have 250hz.
IMU_UPDATE_RATE = 250
out_calib = {
"value0": {
"T_imu_cam": [extrinsics(j, "HT0"), extrinsics(j, "HT1")],
"intrinsics": [intrinsics(j, "HT0"), intrinsics(j, "HT1")],
"resolution": [resolution(j, "HT0"), resolution(j, "HT1")],
"calib_accel_bias": calib_accel_bias(j),
"calib_gyro_bias": calib_gyro_bias(j),
"imu_update_rate": IMU_UPDATE_RATE,
"accel_noise_std": noise_std(j, "Accelerometer"),
"gyro_noise_std": noise_std(j, "Gyro"),
"accel_bias_std": bias_std(j, "Accelerometer"),
"gyro_bias_std": bias_std(j, "Gyro"),
"cam_time_offset_ns": 0,
# "view_offset": view_offset(j),
"vignette": [],
}
}
print(json.dumps(out_calib, indent=4))
if __name__ == "__main__":
main()
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