dustymax - 4 months ago 79

C++ Question

Given a set of N points in a 3D space, I am trying to find the best fitting plane using SVD and Eigen.

My algorithm is:

- Center data points around (0,0,0).
- Form 3xN matrix of point coordinates.
- Calculate SVD of the matrix.
- Set the smallest singular vector corresponding to the least singular value as normal of the plane.
- Set distance from origin to the plane as normalâˆ™centroid.

I can't figure out how to use Eigen's SVD Module to find the smallest singular vector corresponding to the least singular value of point coordinates matrix.

So far I have this code (steps 1, 2 and 5 of the algorithm):

`Eigen::Matrix<float, 3, 1> mean = points.rowwise().mean();`

const Eigen::Matrix3Xf points_centered = points.colwise() - mean;

int setting = Eigen::ComputeThinU | Eigen::ComputeThinV;

Eigen::JacobiSVD<Eigen::Matrix3Xf> svd = points_centered.jacobiSvd(setting);

Eigen::Vector3d normal = **???**

double d = normal.dot(mean);

Answer

Denoting `U = svd.matrixU()`

, the vectors `U.col(0)`

and `U.col(1)`

defines a base of your plane and `U.col(2)`

is normal to your plane.

`U.col(0)`

also defines the direction with the greatest standard deviation.

You should use the flag `ComputeFullU`

instead of `ComputeThinU`

to have the correct dimensions even if your points are coplanar.