如何使用已知的相机参数在 Matlab 中消除图像畸变？

这很容易做到OpenCV http://docs.opencv.org/modules/calib3d/doc/camera_calibration_and_3d_reconstruction.html但是我想要一个相当高效并且可以轻松更改的本机 Matlab 实现。该方法应该能够获取上述链接中指定的相机参数。

进行去畸变（也称为去畸变或补偿镜头畸变）的最简单和最常见的方法是对选定的输出照片尺寸进行前向畸变，然后使用双线性插值进行反向映射。

这是我为执行此操作而编写的代码：

function I = undistort(Idistorted, params)
fx = params.fx;
fy = params.fy;
cx = params.cx;
cy = params.cy;
k1 = params.k1;
k2 = params.k2;
k3 = params.k3;
p1 = params.p1;
p2 = params.p2;

K = [fx 0 cx; 0 fy cy; 0 0 1];

I = zeros(size(Idistorted));
[i j] = find(~isnan(I));

% Xp = the xyz vals of points on the z plane
Xp = inv(K)*[j i ones(length(i),1)]';

% Now we calculate how those points distort i.e forward map them through the distortion
r2 = Xp(1,:).^2+Xp(2,:).^2;
x = Xp(1,:);
y = Xp(2,:);

x = x.*(1+k1*r2 + k2*r2.^2) + 2*p1.*x.*y + p2*(r2 + 2*x.^2);
y = y.*(1+k1*r2 + k2*r2.^2) + 2*p2.*x.*y + p1*(r2 + 2*y.^2);

% u and v are now the distorted cooridnates
u = reshape(fx*x + cx,size(I));
v = reshape(fy*y + cy,size(I));

% Now we perform a backward mapping in order to undistort the warped image coordinates
I = interp2(Idistorted, u, v);

要使用它，需要了解所使用相机的相机参数。 我目前正在使用 PMD CamboardNano，根据 Cayim.com 论坛，它具有此处使用的参数：

params = struct('fx',104.119, 'fy', 103.588, 'cx', 81.9494, 'cy', 59.4392, 'k1', -0.222609, 'k2', 0.063022, 'k3', 0, 'p1', 0.002865, 'p2', -0.001446);

I = undistort(Idistorted, params);

subplot(121); imagesc(Idistorted);
subplot(122); imagesc(I);

Here is an example of the output from the Camboard Nano. Note: I artificially added border lines to see what the effect was of the distortion close to the edges (its much more pronounced):