DLT求外方位元素代码,MATLAB
时间: 2023-12-20 17:14:12 浏览: 22
下面是一个简单的 MATLAB 代码示例,用于求解摄像机的外部方位元素(外参):
```matlab
function [R, t] = solve_exterior_orientation(points_3d, points_2d, intrinsic_matrix)
% 将3D点和2D点转换为齐次坐标
points_3d_homogeneous = [points_3d, ones(size(points_3d, 1), 1)];
points_2d_homogeneous = [points_2d, ones(size(points_2d, 1), 1)];
% 使用DLT算法求解外参矩阵
A = [];
for i = 1:size(points_3d, 1)
X = points_3d_homogeneous(i, 1);
Y = points_3d_homogeneous(i, 2);
Z = points_3d_homogeneous(i, 3);
u = points_2d_homogeneous(i, 1);
v = points_2d_homogeneous(i, 2);
A = [A; X, Y, Z, 1, 0, 0, 0, 0, -u*X, -u*Y, -u*Z, -u;
0, 0, 0, 0, X, Y, Z, 1, -v*X, -v*Y, -v*Z, -v];
end
[~, ~, V] = svd(A);
P = reshape(V(:, end), 4, 3)';
% 使用QR分解分解相机矩阵
[K, R] = qr(intrinsic_matrix);
T = inv(K) * P(:, 1:3);
scale = norm(T(:, 3));
T = T / scale;
R = inv(K) * P(:, 1:3) / scale;
% 将旋转矩阵转换为欧拉角(yaw, pitch, roll)
yaw = atan2(R(2, 1), R(1, 1));
pitch = atan2(-R(3, 1), sqrt(R(3, 2)^2 + R(3, 3)^2));
roll = atan2(R(3, 2), R(3, 3));
% 返回外参元素
t = T(:, 3);
R = [yaw, pitch, roll];
end
```
这个函数 `solve_exterior_orientation` 接受三个参数:三维点的坐标、对应的二维点的坐标和相机的内参矩阵。它将使用DLT算法求解相机的外参矩阵,并将其转换为相机的平移向量和旋转欧拉角。在这个代码示例中,我们使用了 MATLAB 自带的矩阵计算函数来进行计算。