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Add comments for fisheye::undistortPoints

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This commit is contained in:
MaximSmolskiy 2025-10-21 04:56:22 +03:00
parent c75cd1047b
commit b65d66e797
1 changed files with 18 additions and 1 deletions
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19
modules/calib3d/src/fisheye.cpp
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@ -429,8 +429,15 @@ void cv::fisheye::undistortPoints( InputArray distorted, OutputArray undistorted
for(size_t i = 0; i < n; i++ )
{
Vec2d pi = sdepth == CV_32F ? (Vec2d)srcf[i] : srcd[i]; // image point
// u = fx * x' + cx (alpha = 0), v = fy * y' + cy =>
// x' = (u - cx) / fx, y' = (v - cy) / fy
Vec2d pw((pi[0] - c[0])/f[0], (pi[1] - c[1])/f[1]); // world point
// x' = (theta_d / r) * a, y' = (theta_d / r) * b =>
// x'^2 + y'^2 = theta_d^2 * (a^2 + b^2) / r^2 =>
// (r^2 = a^2 + b^2)
// x'^2 + y'^2 = theta_d^2 =>
// theta_d = sqrt(x'^2 + y'^2)
double theta_d = sqrt(pw[0]*pw[0] + pw[1]*pw[1]);
// the current camera model is only valid up to 180 FOV
@ -449,9 +456,14 @@ void cv::fisheye::undistortPoints( InputArray distorted, OutputArray undistorted
for (int j = 0; j < maxCount; j++)
{
// theta_d = theta * (1 + k1 * theta^2 + k2 * theta^4 + k3 * theta^6 + k4 * theta^8) =>
// f(theta) := theta * (1 + k1 * theta^2 + k2 * theta^4 + k3 * theta^6 + k4 * theta^8) - theta_d = 0
// Newton's method: new_theta = theta - theta_fix, theta_fix := f(theta) / f'(theta)
// f'(theta) = (theta * (1 + k1 * theta^2 + k2 * theta^4 + k3 * theta^6 + k4 * theta^8) - theta_d)' =
// (theta + k1 * theta^3 + k2 * theta^5 + k3 * theta^7 + k4 * theta^9 - theta_d)' =
// 1 + 3 * k1 * theta^2 + 5 * k2 * theta^4 + 7 * k3 * theta^6 + 9 * k4 * theta^8
double theta2 = theta*theta, theta4 = theta2*theta2, theta6 = theta4*theta2, theta8 = theta6*theta2;
double k0_theta2 = k[0] * theta2, k1_theta4 = k[1] * theta4, k2_theta6 = k[2] * theta6, k3_theta8 = k[3] * theta8;
/* new_theta = theta - theta_fix, theta_fix = f0(theta) / f0'(theta) */
double theta_fix = (theta * (1 + k0_theta2 + k1_theta4 + k2_theta6 + k3_theta8) - theta_d) /
(1 + 3*k0_theta2 + 5*k1_theta4 + 7*k2_theta6 + 9*k3_theta8);
theta = theta - theta_fix;
@ -463,6 +475,10 @@ void cv::fisheye::undistortPoints( InputArray distorted, OutputArray undistorted
}
}
// x' = (theta_d / r) * a, y' = (theta_d / r) * b =>
// a = x' * r / theta_d, b = y' * r / theta_d =>
// (theta = atan(r) => r = tan(theta), scale := r / theta_d = tan(theta) / theta_d)
// a = x' * scale, b = y' * scale
scale = std::tan(theta) / theta_d;
}
else
@ -477,6 +493,7 @@ void cv::fisheye::undistortPoints( InputArray distorted, OutputArray undistorted
if ((converged || !isEps) && !theta_flipped)
{
// a = x' * scale, b = y' * scale
Vec2d pu = pw * scale; //undistorted point
Vec2d fi;