/// <summary>
/// Superimpose a monochrome image, and return the resulting image.
/// </summary>
/// <param name="img">A monochrome image.</param>
/// <param name="reference">A reference to img1 for downsampling and rotation.</param>
/// <returns></returns>
public static Image SaveSuperimposedImage(Image img, Image reference)
{
//If image isn't monochrome format, throw exception
if (img.PixelFormat != PixelFormat.Format1bppIndexed)
{
throw new Exception(imageFormatNotMonochrome);
}
//Construct two ImageAsPointCollection instances.
ImageAsPointCollection pointCollection1 = new ImageAsPointCollection(img);
ImageAsPointCollection pointCollection2 = new ImageAsPointCollection(reference);
//Downsample
pointCollection1 = DownSampling(pointCollection1, Math.Min(pointCollection1.listOfPoints.Count, pointCollection2.listOfPoints.Count));
pointCollection2 = DownSampling(pointCollection2, Math.Min(pointCollection1.listOfPoints.Count, pointCollection2.listOfPoints.Count));
//Translate
pointCollection1 = Translate(pointCollection1);
pointCollection2 = Translate(pointCollection2);
//Uniform scale
pointCollection1 = UniformScale(pointCollection1);
pointCollection2 = UniformScale(pointCollection2);
//Rotate
pointCollection1 = RotateToReference(pointCollection2, pointCollection1);
Image superimposedImage1 = pointCollection1.ToMonoImage();
return superimposedImage1;
}
private static string imageNotSameDimension = "Images have different sizes; computation aborted."; //Exception message.
#endregion Fields
#region Methods
/// <summary>
/// Given two images, compute their square differences.
/// No superimposition function is applied in this step.
/// To compare superimposed images, they must be superimposed before input into this function.
/// </summary>
/// <param name="img1">A monochrome image. Must have same dimensions with img2.</param>
/// <param name="img2">A monochrome image. Must have same dimensions with img1.</param>
/// <returns></returns>
public static double ComputeHausdroffDistance(Image img1, Image img2)
{
//If any image isn't monochrome format, throw exception
if (img1.PixelFormat != PixelFormat.Format1bppIndexed || img2.PixelFormat != PixelFormat.Format1bppIndexed)
{
throw new Exception(imageFormatNotMonochrome);
}
//If images aren't of same dimension, throw exception
if (img1.Width != img2.Width || img1.Height != img2.Height)
{
throw new Exception(imageNotSameDimension);
}
//Construct two ImageAsPointCollection instances.
ImageAsPointCollection pointCollection1 = new ImageAsPointCollection(img1);
ImageAsPointCollection pointCollection2 = new ImageAsPointCollection(img2);
//Calculate difference of two superimposed images.
double difference = 0;
for(int i = 0; i < pointCollection1.listOfPoints.Count; i++)
{
double min_difference = double.MaxValue;
for(int j = 0; j < pointCollection2.listOfPoints.Count; j++)
{
double temp_difference = Math.Pow((pointCollection1.listOfPoints[i].x - pointCollection2.listOfPoints[j].x), 2)
+ Math.Pow((pointCollection1.listOfPoints[i].y - pointCollection2.listOfPoints[j].y), 2);
if (temp_difference < min_difference)
min_difference = temp_difference;
}
difference += min_difference;
}
difference = Math.Sqrt(difference/(pointCollection1.listOfPoints.Count * pointCollection2.listOfPoints.Count));
return difference;
}
/// <summary>
/// Calculates the root mean square distance (RMSD) of a set of points,
/// then scale them.
/// </summary>
/// <param name="original"></param>
/// <returns></returns>
private static ImageAsPointCollection UniformScale(ImageAsPointCollection original)
{
ImageAsPointCollection result = original;
//Get list's length
int k = original.listOfPoints.Count;
//Calculate sum of x's and y's
double x_sum = 0;
double y_sum = 0;
for (int i = 0; i < k; i++)
{
x_sum += original.listOfPoints[i].x;
y_sum += original.listOfPoints[i].y;
}
//Calculate averages of x's and y's
double x_bar = x_sum / k;
double y_bar = y_sum / k;
//Calculate RMSD
double rmsd = 0;
for (int i = 0; i < k; i++)
{
rmsd += (original.listOfPoints[i].x - x_bar) * (original.listOfPoints[i].x - x_bar);
rmsd += (original.listOfPoints[i].y - y_bar) * (original.listOfPoints[i].y - y_bar);
}
rmsd = Math.Sqrt(rmsd / k);
//Apply scaling
for (int i = 0; i < k; i++)
{
result.listOfPoints[i].x = ((original.listOfPoints[i].x - x_bar)/rmsd);
result.listOfPoints[i].y = ((original.listOfPoints[i].y - y_bar)/rmsd);
}
return result;
}
/// <summary>
/// Takes an ImageAsPointCollection instance, return its translated version.
/// </summary>
/// <param name="original"></param>
/// <returns></returns>
private static ImageAsPointCollection Translate(ImageAsPointCollection original)
{
ImageAsPointCollection result = original;
//Get list's length
int k = original.listOfPoints.Count;
double x_sum = 0;
double y_sum = 0;
for (int i = 0; i < k; i++)
{
x_sum += original.listOfPoints[i].x;
y_sum += original.listOfPoints[i].y;
}
double x_bar = x_sum / k;
double y_bar = y_sum / k;
for(int i = 0; i < k; i++)
{
result.listOfPoints[i].x = (original.listOfPoints[i].x - x_bar);
result.listOfPoints[i].y = (original.listOfPoints[i].y - y_bar);
}
return result;
}
/// <summary>
/// Rotates original image relative to reference image.
/// </summary>
/// <param name="original"></param>
/// <param name="reference"></param>
/// <returns></returns>
private static ImageAsPointCollection RotateToReference(ImageAsPointCollection reference, ImageAsPointCollection original)
{
ImageAsPointCollection result = original;
//Get list's length
int k = Math.Min(reference.listOfPoints.Count, original.listOfPoints.Count);
//Calculate theta
double numerator = 0;
double denominator = 0;
for(int i = 0; i < k; i++)
{
numerator += original.listOfPoints[i].x * reference.listOfPoints[i].y - original.listOfPoints[i].y * reference.listOfPoints[i].x;
denominator += original.listOfPoints[i].x * reference.listOfPoints[i].x + original.listOfPoints[i].y * reference.listOfPoints[i].y;
}
double theta = Math.Atan(numerator/denominator);
//Do rotation
for(int i = 0; i < result.listOfPoints.Count; i++)
{
result.listOfPoints[i].x = (Math.Cos(theta) * original.listOfPoints[i].x - Math.Sin(theta) * original.listOfPoints[i].y);
result.listOfPoints[i].y = (Math.Sin(theta) * original.listOfPoints[i].x + Math.Cos(theta) * original.listOfPoints[i].y);
}
return result;
}
//--------------------------------------------Helper methods--------------------------------------------
/// <summary>
/// Downsample a set of data to a desired size.
/// </summary>
/// <param name="original"></param>
/// <param name="desiredNumberOfPoints"></param>
/// <returns></returns>
private static ImageAsPointCollection DownSampling(ImageAsPointCollection original, int desiredNumberOfPoints)
{
ImageAsPointCollection result = original;
//Get list's length
int k = original.listOfPoints.Count;
if(k <= desiredNumberOfPoints)
{
return original;
}
while(result.listOfPoints.Count > desiredNumberOfPoints)
{
for(int i = 0; i < result.listOfPoints.Count; i += (int)((double)result.listOfPoints.Count/desiredNumberOfPoints))
{
result.listOfPoints.RemoveAt(i);
if(result.listOfPoints.Count <= desiredNumberOfPoints)
{
return result;
}
}
}
return result;
}
/// <summary>
/// Returns the translated version of a given image.
/// </summary>
/// <param name="img">A monochrome image.</param>
/// <returns></returns>
public static Image SaveTranslatedImage(Image img)
{
//If image isn't monochrome format, throw exception
if (img.PixelFormat != PixelFormat.Format1bppIndexed)
{
throw new Exception(imageFormatNotMonochrome);
}
//Construct ImageAsPointCollection instance.
ImageAsPointCollection pointCollection1 = new ImageAsPointCollection(img);
//Translate
pointCollection1 = Translate(pointCollection1);
Image superimposedImage1 = pointCollection1.ToMonoImage();
return superimposedImage1;
}
