/// <summary>
/// What this process does to an image
/// </summary>
/// <param name="obj">Data pertaining to this image</param>
/// <param name="p_image">Image to be processed</param>
/// <seealso cref="http://www.cs.otago.ac.nz/cosc453/student_tutorials/principal_components.pdf"/>
protected override async void doWork(Object p_imgData)
{
//The point will be null if there were no points to observe
if (((ImageData)p_imgData).DataPoints.Count != 0)
{
//Narrow data set
List <Point> dataPoints = ((ImageData)p_imgData).DataPoints;
//Step 2 of PCA Step 1 is gathering data.
PCAData pcaData = getMeanValues(dataPoints);
//step 3 develop the coVariance matrix
genCoVarMatrix(dataPoints, ref pcaData);
//step 4 get eigenvectors and values
calculateEigens(ref pcaData);
//prepare variables for drawing later
((ImageData)p_imgData).EigenVectors = pcaData.eigenVectors;
((ImageData)p_imgData).Center = new Point((int)pcaData.XBar, (int)pcaData.YBar);
((ImageData)p_imgData).Orientation = getOrientation(pcaData.eigenVectors);
}
Processing.getInstance().ToGesturesImage = (ImageData)p_imgData;
}
/// <summary>
/// Gather info about the dataPoints
/// </summary>
/// <param name="p_dataPoints">dataset to evaluate</param>
private PCAData getMeanValues(List <Point> p_dataPoints)
{
if (p_dataPoints.Count == 0)
{
return(null);
}
PCAData pcaData = new PCAData();
//Populate data members of the PCAData object
foreach (Point point in p_dataPoints)
{
pcaData.Sumx += point.X;
pcaData.Sumy += point.Y;
}
pcaData.N = p_dataPoints.Count;
pcaData.XBar = pcaData.Sumx / pcaData.N;
pcaData.YBar = pcaData.Sumy / pcaData.N;
return(pcaData);
}
/// <summary>
/// This method is designed to create a covariance matrix.
/// </summary>
/// <param name="p_pcaData"></param>
private void genCoVarMatrix(List <Point> p_dataPoints, ref PCAData p_pcaData)
{
//Sum up the mean product
/*Parallel.ForEach(p_dataPoints, point =>
* {
* p_pcaData.XVar = (point.X - p_pcaData.XBar) * (point.X - p_pcaData.XBar);
* p_pcaData.YVar = (point.Y - p_pcaData.YBar) * (point.Y - p_pcaData.YBar);
* p_pcaData.CoVar = (point.X - p_pcaData.XBar) * (point.Y - p_pcaData.YBar);
* });*/
foreach (Point point in p_dataPoints)
{
p_pcaData.XVar += (point.X - p_pcaData.XBar) * (point.X - p_pcaData.XBar);
p_pcaData.YVar += (point.Y - p_pcaData.YBar) * (point.Y - p_pcaData.YBar);
p_pcaData.CoVar += (point.X - p_pcaData.XBar) * (point.Y - p_pcaData.YBar);
}
//perform the (n-1) division
p_pcaData.XVar /= (p_pcaData.N - 1);
p_pcaData.YVar /= (p_pcaData.N - 1);
p_pcaData.CoVar /= (p_pcaData.N - 1);
}
/// <summary>
/// This function first find the Eigen Values using discriminants
///
/// </summary>
/// <param name="p_pcaData"></param>
private void calculateEigens(ref PCAData p_pcaData)
{
/* let Oab equal covariance of ab so Oaa would be the variance
* This is after the A - lambda*I
* Oxx - lambda, Oxy
* Oxy, Oyy - lambda
* find the determinant
*
* lambda^2 + (-Oyy - Oxx)lambda + (OxxOyy - Oxy^2)
*/
//The following performs the quadratic formula on the above function
double diffVar = -p_pcaData.YVar - p_pcaData.XVar;
double discriminant = Math.Sqrt(diffVar * diffVar -
4 * (p_pcaData.XVar * p_pcaData.YVar - p_pcaData.CoVar * p_pcaData.CoVar));
double lambdaPlus = (-diffVar + discriminant) / 2;
double lambdaMinus = (-diffVar - discriminant) / 2;
p_pcaData.eigenValues[0] = lambdaPlus;
p_pcaData.eigenValues[1] = lambdaMinus;
//Now we have the eigen values time to get the eigenvectors that match them
/*
* Oxx - lambda, Oxy
* Oxy, Oyy - lambda
*
* convert to RRE format
*
* x, y
* 1, 0 : -Oxy / (Oxx - lambda)
* 0, 1 : -Oxy / (Oyy - lambda)
*/
//for some reason when the coVar is positive my primary is correct and secondary isn't normal
// and when it's negative secondary is correct and primary isn't normal
if (p_pcaData.CoVar > 0)
{
//first principal component
p_pcaData.eigenVectors[0, 0] = p_pcaData.CoVar / (p_pcaData.XVar - p_pcaData.eigenValues[0]);
p_pcaData.eigenVectors[0, 1] = p_pcaData.CoVar / (p_pcaData.YVar - p_pcaData.eigenValues[0]);
//second is normal to the first
p_pcaData.eigenVectors[1, 0] = -p_pcaData.eigenVectors[0, 1];
p_pcaData.eigenVectors[1, 1] = p_pcaData.eigenVectors[0, 0];
}
else
{
//second principal component
p_pcaData.eigenVectors[1, 0] = p_pcaData.CoVar / (p_pcaData.XVar - p_pcaData.eigenValues[1]);
p_pcaData.eigenVectors[1, 1] = p_pcaData.CoVar / (p_pcaData.YVar - p_pcaData.eigenValues[1]);
//first is normal to second
p_pcaData.eigenVectors[0, 0] = -p_pcaData.eigenVectors[1, 1];
p_pcaData.eigenVectors[0, 1] = p_pcaData.eigenVectors[1, 0];
}
//normalize component
//normX = x / sqrt(x*x + y*y) normY = y / sqrt(x*x + y*y)
double len = Math.Sqrt(p_pcaData.eigenVectors[0, 0] * p_pcaData.eigenVectors[0, 0] +
p_pcaData.eigenVectors[0, 1] * p_pcaData.eigenVectors[0, 1]);
p_pcaData.eigenVectors[0, 0] /= len;
p_pcaData.eigenVectors[0, 1] /= len;
len = Math.Sqrt(p_pcaData.eigenVectors[1, 0] * p_pcaData.eigenVectors[1, 0] +
p_pcaData.eigenVectors[1, 1] * p_pcaData.eigenVectors[1, 1]);
p_pcaData.eigenVectors[1, 0] /= len;
p_pcaData.eigenVectors[1, 1] /= len;
}
