Question

I am trying to use OpenCV’s estimateAffine3D() function to get the affine transformation between two sets of coplanar points in 3D. If I hold one variable constant, I find there is a constant error in the translation component of that variable.

My test code is:

std::vector<cv::Point3f> first, second;
std::vector<uchar> inliers;
cv::Mat aff(3,4,CV_64F);

for (int i = 0; i <6; i++)
{
    first.push_back(cv::Point3f(i,i%3,1));
    second.push_back(cv::Point3f(i,i%3,1));
}

int ret = cv::estimateAffine3D(first, second, aff, inliers);
std::cout << aff << std::endl;

The output I expect is:

[1 0 0 0]  
[0 1 0 0]  
[0 0 1 0]

Edit: My expectation is incorrect. The matrix does not decompose into [R|t] for the case of constant z-coordinates.

but what I get (with some rounding for readability) is:

[1 0 0 0]  
[0 1 0 0]  
[0 0 0.5 0.5]

Is there a way to fix this behavior? Is there a function which does the same on sets of 2D points?

Answer 1

No matter how I run your code I get fine output. For example when I run it exactly as you posted it I get.

[1,0,0 ,0]
[0,1,0 ,0]
[0,0,.5,.5]

which is correct because the 4th element of a homogeneous coordinate is assumed to be 1. When I run it with 2 as the z value I get

[1,0,0 ,0]
[0,1,0 ,0]
[0,0,.8,.4]

which also works (.8*2+.4 = 2). Are you sure you didn’t just read aff(2,2) wrong?