private static double ComputeSSIM(Grid img1, Grid img2)
{
// uses notation from paper
// automatic downsampling
int f = (int)Math.Max(1, Math.Round(Math.Min(img1.Width, img1.Height) / 256.0));
if (f > 1)
{
// downsampling by f
// use a simple low-pass filter and subsample by f
img1 = Grid.SubSample(img1, f);
img2 = Grid.SubSample(img2, f);
}
// normalize window - todo - do in window set {}
double scale = 1.0 / window.Total;
Grid.Op((i, j) => window[i, j] * scale, window);
// image statistics
var mu1 = Grid.Filter(img1, window);
var mu2 = Grid.Filter(img2, window);
var mu1mu2 = mu1 * mu2;
var mu1SQ = mu1 * mu1;
var mu2SQ = mu2 * mu2;
var sigma12 = Grid.Filter(img1 * img2, window) - mu1mu2;
var sigma1SQ = Grid.Filter(img1 * img1, window) - mu1SQ;
var sigma2SQ = Grid.Filter(img2 * img2, window) - mu2SQ;
// constants from the paper
double C1 = K1 * L; C1 *= C1;
double C2 = K2 * L; C2 *= C2;
Grid ssimMap = null;
if ((C1 > 0) && (C2 > 0))
{
ssimMap = Grid.Op((i, j) =>
(2 * mu1mu2[i, j] + C1) * (2 * sigma12[i, j] + C2) /
(mu1SQ[i, j] + mu2SQ[i, j] + C1) / (sigma1SQ[i, j] + sigma2SQ[i, j] + C2),
new Grid(mu1mu2.Width, mu1mu2.Height));
}
else
{
var num1 = Grid.Linear(2, mu1mu2, C1);
var num2 = Grid.Linear(2, sigma12, C2);
var den1 = Grid.Linear(1, mu1SQ + mu2SQ, C1);
var den2 = Grid.Linear(1, sigma1SQ + sigma2SQ, C2);
var den = den1 * den2; // total denominator
ssimMap = new Grid(mu1.Width, mu1.Height);
for (int i = 0; i < ssimMap.Width; ++i)
for (int j = 0; j < ssimMap.Height; ++j)
{
ssimMap[i, j] = 1;
if (den[i, j] > 0)
{
ssimMap[i, j] = num1[i, j] * num2[i, j] / (den1[i, j] * den2[i, j]);
}
else if ((den1[i, j] != 0) && (den2[i, j] == 0))
{
ssimMap[i, j] = num1[i, j] / den1[i, j];
}
}
}
// average all values
return ssimMap.Total / (ssimMap.Width * ssimMap.Height);
}
public static Grid SubSample(Grid img, int skip)
{
int width = img.Width;
int height = img.Height;
double scale = 1.0 / (skip * skip);
var ans = new Grid(width / skip, height / skip);
for (int i = 0; i < width - skip; i += skip)
{
for (int j = 0; j < height - skip; j += skip)
{
double sum = 0;
for (int x = i; x < i + skip; ++x)
{
for (int y = j; y < j + skip; ++y)
{
sum += img[x, y];
}
}
ans[i / skip, j / skip] = sum * scale;
}
}
return ans;
}
public static Grid Op(Func<int, int, double> f, Grid g)
{
int width = g._width;
int height = g._height;
for (int i = 0; i < width; i++)
{
for (int j = 0; j < height; j++)
{
g[i, j] = f(i, j);
}
}
return g;
}
public static Grid Linear(double s, Grid a, double c)
{
return Grid.Op((i, j) => s * a[i, j] + c, new Grid(a.Width, a.Height));
}
public static Grid Filter(Grid firstGrid, Grid secondGrid)
{
int ax = firstGrid.Width;
int ay = firstGrid.Height;
int bx = secondGrid.Width;
int by = secondGrid.Height;
int bcx = (bx + 1) / 2, bcy = (by + 1) / 2;
var thirdGrid = new Grid(ax - bx + 1, ay - by + 1);
for (int i = bx - bcx + 1; i < ax - bx; ++i)
{
for (int j = by - bcy + 1; j < ay - by; ++j)
{
double sum = 0;
for (int x = bcx - bx + 1 + i; x < 1 + i + bcx; ++x)
{
for (int y = bcy - by + 1 + j; y < 1 + j + bcy; ++y)
{
sum += firstGrid[x, y] * secondGrid[bx - bcx - 1 - i + x, by - bcy - 1 - j + y];
}
}
thirdGrid[i - bcx, j - bcy] = sum;
}
}
return thirdGrid;
}
public static Grid CreateGaussianGrid(int size, double sigma)
{
var filter = new Grid(size, size);
double s2 = sigma * sigma, c = (size - 1) / 2.0, dx, dy;
Grid.Op(
(i, j) =>
{
dx = i - c;
dy = j - c;
return Math.Exp(-(dx * dx + dy * dy) / (2 * s2));
},
filter
);
var scale = 1.0 / filter.Total;
Grid.Op((i, j) => filter[i, j] * scale, filter);
return filter;
}