/// <summary>
/// Fit plane through points by linear orthogonal regression.
/// </summary>
/// <remarks>http://www.lsr.ei.tum.de/fileadmin/publications/K._Klasing/KlasingAlthoff-ComparisonOfSurfaceNormalEstimationMethodsForRangeSensingApplications_ICRA09.pdf</remarks>
/// <param name="points">Points to fit by plane</param>
/// <returns>Best-fit plane in terms of orthogonal least square regression.</returns>
public static bool FitByPCA(IEnumerable <Vector> points, out Plane plane)
{
// Perform orth lin regression by PCA which requires the estimation
// of the covariance matrix of the samples
// http://en.wikipedia.org/wiki/Estimation_of_covariance_matrices
plane = null;
int count = 0;
Vector mean = new Vector(3, 0.0);
foreach (Vector p in points)
{
mean.AddInplace(p); count++;
}
if (count < 3)
{
return(false);
}
mean /= (double)count;
Matrix cov = new Matrix(3, 3, 0.0);
foreach (Vector p in points)
{
Vector v = p - mean;
//code below is equivalent to
//cov += v.ToColumnMatrix() * v.ToRowMatrix();
//optimized
double v00 = v[0] * v[0];
double v01 = v[0] * v[1];
double v02 = v[0] * v[2];
double v11 = v[1] * v[1];
double v12 = v[1] * v[2];
double v22 = v[2] * v[2];
cov[0, 0] += v00;
cov[0, 1] += v01;
cov[0, 2] += v02;
cov[1, 0] += v01;
cov[1, 1] += v11;
cov[1, 2] += v12;
cov[2, 0] += v02;
cov[2, 1] += v12;
cov[2, 2] += v22;
}
// Skip normalization of matrix
try {
EigenvalueDecomposition decomp = cov.EigenvalueDecomposition;
plane = new Plane(mean, decomp.EigenVectors.GetColumnVector(0));
return(true);
} catch (IndexOutOfRangeException) {
return(false);
}
}
/// <summary>
/// Fit plane through points by linear orthogonal regression.
/// </summary>
/// <remarks>http://www.lsr.ei.tum.de/fileadmin/publications/K._Klasing/KlasingAlthoff-ComparisonOfSurfaceNormalEstimationMethodsForRangeSensingApplications_ICRA09.pdf</remarks>
/// <param name="points">Points to fit by plane</param>
/// <returns>Best-fit plane in terms of orthogonal least square regression.</returns>
public static bool FitByPCA(IEnumerable<Vector> points, out Plane plane) {
// Perform orth lin regression by PCA which requires the estimation
// of the covariance matrix of the samples
// http://en.wikipedia.org/wiki/Estimation_of_covariance_matrices
plane = null;
int count = 0;
Vector mean = new Vector(3, 0.0);
foreach (Vector p in points) {
mean.AddInplace(p); count++;
}
if (count < 3)
return false;
mean /= (double)count;
Matrix cov = new Matrix(3, 3, 0.0);
foreach (Vector p in points) {
Vector v = p - mean;
//code below is equivalent to
//cov += v.ToColumnMatrix() * v.ToRowMatrix();
//optimized
double v00 = v[0] * v[0];
double v01 = v[0] * v[1];
double v02 = v[0] * v[2];
double v11 = v[1] * v[1];
double v12 = v[1] * v[2];
double v22 = v[2] * v[2];
cov[0, 0] += v00;
cov[0, 1] += v01;
cov[0, 2] += v02;
cov[1, 0] += v01;
cov[1, 1] += v11;
cov[1, 2] += v12;
cov[2, 0] += v02;
cov[2, 1] += v12;
cov[2, 2] += v22;
}
// Skip normalization of matrix
try {
EigenvalueDecomposition decomp = cov.EigenvalueDecomposition;
plane = new Plane(mean, decomp.EigenVectors.GetColumnVector(0));
return true;
} catch (IndexOutOfRangeException) {
return false;
}
}
