/// <summary>
/// Creates an homography matrix matching points
/// from a set of points to another.
/// </summary>
public static MatrixH Homography(PointH[] points1, PointH[] points2)
{
// Initial argument checkings
if (points1.Length != points2.Length)
{
throw new ArgumentException("The number of points should be equal.");
}
if (points1.Length < 4)
{
throw new ArgumentException("At least four points are required to fit an homography");
}
int N = points1.Length;
MatrixH T1, T2; // Normalize input points
points1 = points1.Normalize(out T1);
points2 = points2.Normalize(out T2);
// Create the matrix A
double[,] A = new double[3 * N, 9];
for (int i = 0; i < N; i++)
{
PointH X = points1[i];
double x = points2[i].X;
double y = points2[i].Y;
double w = points2[i].W;
int r = 3 * i;
A[r, 0] = 0;
A[r, 1] = 0;
A[r, 2] = 0;
A[r, 3] = -w * X.X;
A[r, 4] = -w * X.Y;
A[r, 5] = -w * X.W;
A[r, 6] = y * X.X;
A[r, 7] = y * X.Y;
A[r, 8] = y * X.W;
r++;
A[r, 0] = w * X.X;
A[r, 1] = w * X.Y;
A[r, 2] = w * X.W;
A[r, 3] = 0;
A[r, 4] = 0;
A[r, 5] = 0;
A[r, 6] = -x * X.X;
A[r, 7] = -x * X.Y;
A[r, 8] = -x * X.W;
r++;
A[r, 0] = -y * X.X;
A[r, 1] = -y * X.Y;
A[r, 2] = -y * X.W;
A[r, 3] = x * X.X;
A[r, 4] = x * X.Y;
A[r, 5] = x * X.W;
A[r, 6] = 0;
A[r, 7] = 0;
A[r, 8] = 0;
}
// Create the singular value decomposition
SingularValueDecomposition svd = new SingularValueDecomposition(A, false, true);
double[,] V = svd.RightSingularVectors;
// Extract the homography matrix
MatrixH H = new MatrixH((float)V[0, 8], (float)V[1, 8], (float)V[2, 8],
(float)V[3, 8], (float)V[4, 8], (float)V[5, 8],
(float)V[6, 8], (float)V[7, 8], (float)V[8, 8]);
// Denormalize
H = T2.Inverse().Multiply(H.Multiply(T1));
return(H);
}
