/// <summary>
/// Returns transformation parameters to coordinatesystem
/// Return an array with the six affine transformation parameters {a,b,c,d,e,f}
/// a,b defines vector 1 of coordinate system, d,e vector 2.
/// c,f defines image center.
/// Converting from input (X,Y) to output coordinate system (X',Y') is done by:
/// X' = a*X + b*Y + c, Y' = d*X + e*Y + f
/// Transformation based on Mikhail "Introduction to Modern Photogrammetry" p. 399-300
/// Extended to arbitrary number of points by M. Nielsen
/// </summary>
/// <returns>Six transformation parameters a,b,c,d,e,f for the affine transformation</returns>
public AffineTransformationParameters GetTransformation()
{
if (_inputs.Count < 3)
{
throw new System.Exception(ResourceLoader.GetForCurrentView().GetString("MeasurementsException"));
}
int count = _inputs.Count;
Point[] outputs = _outputs.ToArray();
Point[] inputs = _inputs.ToArray();
double[][] N = CreateMatrix(3, 3);
//Create normal equation: transpose(B)*B
//B: matrix of calibrated values. Example of row in B: [x , y , -1]
for (int i = 0; i < count; i++)
{
N[0][0] += Math.Pow(outputs[i].X, 2);
N[0][1] += outputs[i].X * outputs[i].Y;
N[0][2] += -outputs[i].X;
N[1][1] += Math.Pow(outputs[i].Y, 2);
N[1][2] += -outputs[i].Y;
}
N[2][2] = count;
double[] t1 = new double[3];
double[] t2 = new double[3];
for (int i = 0; i < count; i++)
{
t1[0] += outputs[i].X * inputs[i].X;
t1[1] += outputs[i].Y * inputs[i].X;
t1[2] += -inputs[i].X;
t2[0] += outputs[i].X * inputs[i].Y;
t2[1] += outputs[i].Y * inputs[i].Y;
t2[2] += -inputs[i].Y;
}
// Solve equation N = transpose(B)*t1
var result = new AffineTransformationParameters();
double frac = 1 / (-N[0][0] * N[1][1] * N[2][2] + N[0][0] * Math.Pow(N[1][2], 2) + Math.Pow(N[0][1], 2) * N[2][2] - 2 * N[1][2] * N[0][1] * N[0][2] + N[1][1] * Math.Pow(N[0][2], 2));
result.A = (-N[0][1] * N[1][2] * t1[2] + N[0][1] * t1[1] * N[2][2] - N[0][2] * N[1][2] * t1[1] + N[0][2] * N[1][1] * t1[2] - t1[0] * N[1][1] * N[2][2] + t1[0] * Math.Pow(N[1][2], 2)) * frac;
result.B = (-N[0][1] * N[0][2] * t1[2] + N[0][1] * t1[0] * N[2][2] + N[0][0] * N[1][2] * t1[2] - N[0][0] * t1[1] * N[2][2] - N[0][2] * N[1][2] * t1[0] + Math.Pow(N[0][2], 2) * t1[1]) * frac;
result.C = -(-N[1][2] * N[0][1] * t1[0] + Math.Pow(N[0][1], 2) * t1[2] + N[0][0] * N[1][2] * t1[1] - N[0][0] * N[1][1] * t1[2] - N[0][2] * N[0][1] * t1[1] + N[1][1] * N[0][2] * t1[0]) * frac;
// Solve equation N = transpose(B)*t2
result.D = (-N[0][1] * N[1][2] * t2[2] + N[0][1] * t2[1] * N[2][2] - N[0][2] * N[1][2] * t2[1] + N[0][2] * N[1][1] * t2[2] - t2[0] * N[1][1] * N[2][2] + t2[0] * Math.Pow(N[1][2], 2)) * frac;
result.E = (-N[0][1] * N[0][2] * t2[2] + N[0][1] * t2[0] * N[2][2] + N[0][0] * N[1][2] * t2[2] - N[0][0] * t2[1] * N[2][2] - N[0][2] * N[1][2] * t2[0] + Math.Pow(N[0][2], 2) * t2[1]) * frac;
result.F = -(-N[1][2] * N[0][1] * t2[0] + Math.Pow(N[0][1], 2) * t2[2] + N[0][0] * N[1][2] * t2[1] - N[0][0] * N[1][1] * t2[2] - N[0][2] * N[0][1] * t2[1] + N[1][1] * N[0][2] * t2[0]) * frac;
//Calculate s0
double s0 = 0;
for (int i = 0; i < this._inputs.Count; i++)
{
var tt = result.Transform(_outputs[i]);
s0 += Math.Pow(tt.X - _inputs[i].X, 2) + Math.Pow(tt.Y - _inputs[i].Y, 2);
}
result.S0 = Math.Sqrt(s0) / (this._inputs.Count);
return(result);
}
/// <summary>
/// Returns transformation parameters to coordinatesystem
/// Return an array with the six affine transformation parameters {a,b,c,d,e,f}
/// a,b defines vector 1 of coordinate system, d,e vector 2.
/// c,f defines image center.
/// Converting from input (X,Y) to output coordinate system (X',Y') is done by:
/// X' = a*X + b*Y + c, Y' = d*X + e*Y + f
/// Transformation based on Mikhail "Introduction to Modern Photogrammetry" p. 399-300
/// Extended to arbitrary number of points by M. Nielsen
/// </summary>
/// <returns>Six transformation parameters a,b,c,d,e,f for the affine transformation</returns>
public AffineTransformationParameters GetTransformation()
{
if (_inputs.Count < 3)
throw (new System.Exception("At least 3 measurements required to calculate affine transformation"));
int count = _inputs.Count;
Point[] outputs = _outputs.ToArray();
Point[] inputs = _inputs.ToArray();
double[][] N = CreateMatrix(3, 3);
//Create normal equation: transpose(B)*B
//B: matrix of calibrated values. Example of row in B: [x , y , -1]
for (int i = 0; i < count; i++)
{
N[0][0] += Math.Pow(outputs[i].X, 2);
N[0][1] += outputs[i].X * outputs[i].Y;
N[0][2] += -outputs[i].X;
N[1][1] += Math.Pow(outputs[i].Y, 2);
N[1][2] += -outputs[i].Y;
}
N[2][2] = count;
double[] t1 = new double[3];
double[] t2 = new double[3];
for (int i = 0; i < count; i++)
{
t1[0] += outputs[i].X * inputs[i].X;
t1[1] += outputs[i].Y * inputs[i].X;
t1[2] += -inputs[i].X;
t2[0] += outputs[i].X * inputs[i].Y;
t2[1] += outputs[i].Y * inputs[i].Y;
t2[2] += -inputs[i].Y;
}
// Solve equation N = transpose(B)*t1
var result = new AffineTransformationParameters();
double frac = 1 / (-N[0][0] * N[1][1] * N[2][2] + N[0][0] * Math.Pow(N[1][2], 2) + Math.Pow(N[0][1], 2) * N[2][2] - 2 * N[1][2] * N[0][1] * N[0][2] + N[1][1] * Math.Pow(N[0][2], 2));
result.A = (-N[0][1] * N[1][2] * t1[2] + N[0][1] * t1[1] * N[2][2] - N[0][2] * N[1][2] * t1[1] + N[0][2] * N[1][1] * t1[2] - t1[0] * N[1][1] * N[2][2] + t1[0] * Math.Pow(N[1][2], 2)) * frac;
result.B = (-N[0][1] * N[0][2] * t1[2] + N[0][1] * t1[0] * N[2][2] + N[0][0] * N[1][2] * t1[2] - N[0][0] * t1[1] * N[2][2] - N[0][2] * N[1][2] * t1[0] + Math.Pow(N[0][2], 2) * t1[1]) * frac;
result.C = -(-N[1][2] * N[0][1] * t1[0] + Math.Pow(N[0][1], 2) * t1[2] + N[0][0] * N[1][2] * t1[1] - N[0][0] * N[1][1] * t1[2] - N[0][2] * N[0][1] * t1[1] + N[1][1] * N[0][2] * t1[0]) * frac;
// Solve equation N = transpose(B)*t2
result.D = (-N[0][1] * N[1][2] * t2[2] + N[0][1] * t2[1] * N[2][2] - N[0][2] * N[1][2] * t2[1] + N[0][2] * N[1][1] * t2[2] - t2[0] * N[1][1] * N[2][2] + t2[0] * Math.Pow(N[1][2], 2)) * frac;
result.E = (-N[0][1] * N[0][2] * t2[2] + N[0][1] * t2[0] * N[2][2] + N[0][0] * N[1][2] * t2[2] - N[0][0] * t2[1] * N[2][2] - N[0][2] * N[1][2] * t2[0] + Math.Pow(N[0][2], 2) * t2[1]) * frac;
result.F = -(-N[1][2] * N[0][1] * t2[0] + Math.Pow(N[0][1], 2) * t2[2] + N[0][0] * N[1][2] * t2[1] - N[0][0] * N[1][1] * t2[2] - N[0][2] * N[0][1] * t2[1] + N[1][1] * N[0][2] * t2[0]) * frac;
//Calculate s0
double s0 = 0;
for (int i = 0; i < this._inputs.Count; i++)
{
var tt = result.Transform(_outputs[i]);
s0 += Math.Pow(tt.X - _inputs[i].X, 2) + Math.Pow(tt.Y - _inputs[i].Y, 2);
}
result.s0 = Math.Sqrt(s0) / (this._inputs.Count);
return result;
}
