/// <summary>
/// Computes the weighted variance of a box.
/// </summary>
/// <param name="cube">The cube.</param>
/// <returns>The result.</returns>
private double Variance(Box cube)
{
double dr = WuAlphaColorQuantizer.Volume(cube, this.vmr);
double dg = WuAlphaColorQuantizer.Volume(cube, this.vmg);
double db = WuAlphaColorQuantizer.Volume(cube, this.vmb);
double da = WuAlphaColorQuantizer.Volume(cube, this.vma);
double xx =
this.m2[WuAlphaColorQuantizer.GetIndex(cube.R1, cube.G1, cube.B1, cube.A1)]
- this.m2[WuAlphaColorQuantizer.GetIndex(cube.R1, cube.G1, cube.B1, cube.A0)]
- this.m2[WuAlphaColorQuantizer.GetIndex(cube.R1, cube.G1, cube.B0, cube.A1)]
+ this.m2[WuAlphaColorQuantizer.GetIndex(cube.R1, cube.G1, cube.B0, cube.A0)]
- this.m2[WuAlphaColorQuantizer.GetIndex(cube.R1, cube.G0, cube.B1, cube.A1)]
+ this.m2[WuAlphaColorQuantizer.GetIndex(cube.R1, cube.G0, cube.B1, cube.A0)]
+ this.m2[WuAlphaColorQuantizer.GetIndex(cube.R1, cube.G0, cube.B0, cube.A1)]
- this.m2[WuAlphaColorQuantizer.GetIndex(cube.R1, cube.G0, cube.B0, cube.A0)]
- this.m2[WuAlphaColorQuantizer.GetIndex(cube.R0, cube.G1, cube.B1, cube.A1)]
+ this.m2[WuAlphaColorQuantizer.GetIndex(cube.R0, cube.G1, cube.B1, cube.A0)]
+ this.m2[WuAlphaColorQuantizer.GetIndex(cube.R0, cube.G1, cube.B0, cube.A1)]
- this.m2[WuAlphaColorQuantizer.GetIndex(cube.R0, cube.G1, cube.B0, cube.A0)]
+ this.m2[WuAlphaColorQuantizer.GetIndex(cube.R0, cube.G0, cube.B1, cube.A1)]
- this.m2[WuAlphaColorQuantizer.GetIndex(cube.R0, cube.G0, cube.B1, cube.A0)]
- this.m2[WuAlphaColorQuantizer.GetIndex(cube.R0, cube.G0, cube.B0, cube.A1)]
+ this.m2[WuAlphaColorQuantizer.GetIndex(cube.R0, cube.G0, cube.B0, cube.A0)];
return(xx - (((dr * dr) + (dg * dg) + (db * db) + (da * da)) / WuAlphaColorQuantizer.Volume(cube, this.vwt)));
}
/// <summary>
/// Computes remainder of Volume(cube, moment), substituting position for r1, g1, or b1 (depending on direction).
/// </summary>
/// <param name="cube">The cube.</param>
/// <param name="direction">The direction.</param>
/// <param name="position">The position.</param>
/// <param name="moment">The moment.</param>
/// <returns>The result.</returns>
private static long Top(Box cube, int direction, int position, long[] moment)
{
switch (direction)
{
// Red
case 3:
return(moment[WuAlphaColorQuantizer.GetIndex(position, cube.G1, cube.B1, cube.A1)]
- moment[WuAlphaColorQuantizer.GetIndex(position, cube.G1, cube.B1, cube.A0)]
- moment[WuAlphaColorQuantizer.GetIndex(position, cube.G1, cube.B0, cube.A1)]
+ moment[WuAlphaColorQuantizer.GetIndex(position, cube.G1, cube.B0, cube.A0)]
- moment[WuAlphaColorQuantizer.GetIndex(position, cube.G0, cube.B1, cube.A1)]
+ moment[WuAlphaColorQuantizer.GetIndex(position, cube.G0, cube.B1, cube.A0)]
+ moment[WuAlphaColorQuantizer.GetIndex(position, cube.G0, cube.B0, cube.A1)]
- moment[WuAlphaColorQuantizer.GetIndex(position, cube.G0, cube.B0, cube.A0)]);
// Green
case 2:
return(moment[WuAlphaColorQuantizer.GetIndex(cube.R1, position, cube.B1, cube.A1)]
- moment[WuAlphaColorQuantizer.GetIndex(cube.R1, position, cube.B1, cube.A0)]
- moment[WuAlphaColorQuantizer.GetIndex(cube.R1, position, cube.B0, cube.A1)]
+ moment[WuAlphaColorQuantizer.GetIndex(cube.R1, position, cube.B0, cube.A0)]
- moment[WuAlphaColorQuantizer.GetIndex(cube.R0, position, cube.B1, cube.A1)]
+ moment[WuAlphaColorQuantizer.GetIndex(cube.R0, position, cube.B1, cube.A0)]
+ moment[WuAlphaColorQuantizer.GetIndex(cube.R0, position, cube.B0, cube.A1)]
- moment[WuAlphaColorQuantizer.GetIndex(cube.R0, position, cube.B0, cube.A0)]);
// Blue
case 1:
return(moment[WuAlphaColorQuantizer.GetIndex(cube.R1, cube.G1, position, cube.A1)]
- moment[WuAlphaColorQuantizer.GetIndex(cube.R1, cube.G1, position, cube.A0)]
- moment[WuAlphaColorQuantizer.GetIndex(cube.R1, cube.G0, position, cube.A1)]
+ moment[WuAlphaColorQuantizer.GetIndex(cube.R1, cube.G0, position, cube.A0)]
- moment[WuAlphaColorQuantizer.GetIndex(cube.R0, cube.G1, position, cube.A1)]
+ moment[WuAlphaColorQuantizer.GetIndex(cube.R0, cube.G1, position, cube.A0)]
+ moment[WuAlphaColorQuantizer.GetIndex(cube.R0, cube.G0, position, cube.A1)]
- moment[WuAlphaColorQuantizer.GetIndex(cube.R0, cube.G0, position, cube.A0)]);
// Alpha
case 0:
return(moment[WuAlphaColorQuantizer.GetIndex(cube.R1, cube.G1, cube.B1, position)]
- moment[WuAlphaColorQuantizer.GetIndex(cube.R1, cube.G1, cube.B0, position)]
- moment[WuAlphaColorQuantizer.GetIndex(cube.R1, cube.G0, cube.B1, position)]
+ moment[WuAlphaColorQuantizer.GetIndex(cube.R1, cube.G0, cube.B0, position)]
- moment[WuAlphaColorQuantizer.GetIndex(cube.R0, cube.G1, cube.B1, position)]
+ moment[WuAlphaColorQuantizer.GetIndex(cube.R0, cube.G1, cube.B0, position)]
+ moment[WuAlphaColorQuantizer.GetIndex(cube.R0, cube.G0, cube.B1, position)]
- moment[WuAlphaColorQuantizer.GetIndex(cube.R0, cube.G0, cube.B0, position)]);
default:
throw new ArgumentOutOfRangeException(nameof(direction));
}
}
/// <summary>
/// We want to minimize the sum of the variances of two sub-boxes.
/// The sum(c^2) terms can be ignored since their sum over both sub-boxes
/// is the same (the sum for the whole box) no matter where we split.
/// The remaining terms have a minus sign in the variance formula,
/// so we drop the minus sign and maximize the sum of the two terms.
/// </summary>
/// <param name="cube">The cube.</param>
/// <param name="direction">The direction.</param>
/// <param name="first">The first position.</param>
/// <param name="last">The last position.</param>
/// <param name="cut">The cutting point.</param>
/// <param name="wholeR">The whole red.</param>
/// <param name="wholeG">The whole green.</param>
/// <param name="wholeB">The whole blue.</param>
/// <param name="wholeA">The whole alpha.</param>
/// <param name="wholeW">The whole weight.</param>
/// <returns>The result.</returns>
private double Maximize(Box cube, int direction, int first, int last, out int cut, double wholeR, double wholeG, double wholeB, double wholeA, double wholeW)
{
long baseR = WuAlphaColorQuantizer.Bottom(cube, direction, this.vmr);
long baseG = WuAlphaColorQuantizer.Bottom(cube, direction, this.vmg);
long baseB = WuAlphaColorQuantizer.Bottom(cube, direction, this.vmb);
long baseA = WuAlphaColorQuantizer.Bottom(cube, direction, this.vma);
long baseW = WuAlphaColorQuantizer.Bottom(cube, direction, this.vwt);
double max = 0.0;
cut = -1;
for (int i = first; i < last; i++)
{
double halfR = baseR + WuAlphaColorQuantizer.Top(cube, direction, i, this.vmr);
double halfG = baseG + WuAlphaColorQuantizer.Top(cube, direction, i, this.vmg);
double halfB = baseB + WuAlphaColorQuantizer.Top(cube, direction, i, this.vmb);
double halfA = baseA + WuAlphaColorQuantizer.Top(cube, direction, i, this.vma);
double halfW = baseW + WuAlphaColorQuantizer.Top(cube, direction, i, this.vwt);
if (halfW == 0)
{
continue;
}
double temp = ((halfR * halfR) + (halfG * halfG) + (halfB * halfB) + (halfA * halfA)) / halfW;
halfR = wholeR - halfR;
halfG = wholeG - halfG;
halfB = wholeB - halfB;
halfA = wholeA - halfA;
halfW = wholeW - halfW;
if (halfW == 0)
{
continue;
}
temp += ((halfR * halfR) + (halfG * halfG) + (halfB * halfB) + (halfA * halfA)) / halfW;
if (temp > max)
{
max = temp;
cut = i;
}
}
return(max);
}
/// <summary>
/// Marks a color space tag.
/// </summary>
/// <param name="cube">The cube.</param>
/// <param name="label">A label.</param>
private void Mark(Box cube, byte label)
{
for (int r = cube.R0 + 1; r <= cube.R1; r++)
{
for (int g = cube.G0 + 1; g <= cube.G1; g++)
{
for (int b = cube.B0 + 1; b <= cube.B1; b++)
{
for (int a = cube.A0 + 1; a <= cube.A1; a++)
{
this.tag[WuAlphaColorQuantizer.GetIndex(r, g, b, a)] = label;
}
}
}
}
}
/// <summary>
/// Computes sum over a box of any given statistic.
/// </summary>
/// <param name="cube">The cube.</param>
/// <param name="moment">The moment.</param>
/// <returns>The result.</returns>
private static double Volume(Box cube, long[] moment)
{
return(moment[WuAlphaColorQuantizer.GetIndex(cube.R1, cube.G1, cube.B1, cube.A1)]
- moment[WuAlphaColorQuantizer.GetIndex(cube.R1, cube.G1, cube.B1, cube.A0)]
- moment[WuAlphaColorQuantizer.GetIndex(cube.R1, cube.G1, cube.B0, cube.A1)]
+ moment[WuAlphaColorQuantizer.GetIndex(cube.R1, cube.G1, cube.B0, cube.A0)]
- moment[WuAlphaColorQuantizer.GetIndex(cube.R1, cube.G0, cube.B1, cube.A1)]
+ moment[WuAlphaColorQuantizer.GetIndex(cube.R1, cube.G0, cube.B1, cube.A0)]
+ moment[WuAlphaColorQuantizer.GetIndex(cube.R1, cube.G0, cube.B0, cube.A1)]
- moment[WuAlphaColorQuantizer.GetIndex(cube.R1, cube.G0, cube.B0, cube.A0)]
- moment[WuAlphaColorQuantizer.GetIndex(cube.R0, cube.G1, cube.B1, cube.A1)]
+ moment[WuAlphaColorQuantizer.GetIndex(cube.R0, cube.G1, cube.B1, cube.A0)]
+ moment[WuAlphaColorQuantizer.GetIndex(cube.R0, cube.G1, cube.B0, cube.A1)]
- moment[WuAlphaColorQuantizer.GetIndex(cube.R0, cube.G1, cube.B0, cube.A0)]
+ moment[WuAlphaColorQuantizer.GetIndex(cube.R0, cube.G0, cube.B1, cube.A1)]
- moment[WuAlphaColorQuantizer.GetIndex(cube.R0, cube.G0, cube.B1, cube.A0)]
- moment[WuAlphaColorQuantizer.GetIndex(cube.R0, cube.G0, cube.B0, cube.A1)]
+ moment[WuAlphaColorQuantizer.GetIndex(cube.R0, cube.G0, cube.B0, cube.A0)]);
}
/// <summary>
/// Builds a 3-D color histogram of <c>counts, r/g/b, c^2</c>.
/// </summary>
/// <param name="image">The image.</param>
private void Build3DHistogram(Color[] image)
{
foreach (var color in image)
{
int a = color.A;
int r = color.R;
int g = color.G;
int b = color.B;
int inr = r >> (8 - IndexBits);
int ing = g >> (8 - IndexBits);
int inb = b >> (8 - IndexBits);
int ina = a >> (8 - IndexAlphaBits);
int ind = WuAlphaColorQuantizer.GetIndex(inr + 1, ing + 1, inb + 1, ina + 1);
this.vwt[ind]++;
this.vmr[ind] += r;
this.vmg[ind] += g;
this.vmb[ind] += b;
this.vma[ind] += a;
this.m2[ind] += (r * r) + (g * g) + (b * b) + (a * a);
}
}
/// <summary>
/// Generates the quantized result.
/// </summary>
/// <param name="image">The image.</param>
/// <param name="colorCount">The color count.</param>
/// <param name="cube">The cube.</param>
/// <returns>The result.</returns>
private void GenerateResult(Color[] image, int colorCount, Box[] cube)
{
List <Color> palette = new List <Color>();
for (int k = 0; k < colorCount; k++)
{
this.Mark(cube[k], (byte)k);
double weight = WuAlphaColorQuantizer.Volume(cube[k], this.vwt);
byte A;
byte R;
byte G;
byte B;
if (weight != 0)
{
A = (byte)(Volume(cube[k], this.vma) / weight);
R = (byte)(Volume(cube[k], this.vmr) / weight);
G = (byte)(Volume(cube[k], this.vmg) / weight);
B = (byte)(Volume(cube[k], this.vmb) / weight);
}
else
{
A = 0xff;
R = 0;
G = 0;
B = 0;
}
palette.Add(Color.FromArgb(A, R, G, B));
}
QuantPalette = palette.ToArray();
var length = colorCount == 256 ? image.Length : colorCount == 16 ? image.Length / 2 : throw new Exception("IndexedPixels: unknown pixelformat");
var returned = new byte[length];
for (int i = 0; i < image.Length; i++)
{
var color = image[i];
int a = color.A >> (8 - IndexAlphaBits);
int r = color.R >> (8 - IndexBits);
int g = color.G >> (8 - IndexBits);
int b = color.B >> (8 - IndexBits);
int ind = GetIndex(r + 1, g + 1, b + 1, a + 1);
var value = tag[ind];
switch (colorCount)
{
case 256:
returned[i] = value;
break;
case 16:
if (i % 2 == 0)
{
returned[i / 2] = (byte)(value << 4);
}
else
{
returned[i / 2] |= (byte)(value & 0x0F);
}
break;
case 2:
if (i % 8 == 0)
{
returned[i / 8] = (byte)(value << 7);
}
else
{
returned[i / 8] |= (byte)((value & 0x01) << (7 - (i % 8)));
}
break;
}
}
QuantData = returned;
}
/// <summary>
/// Cuts a box.
/// </summary>
/// <param name="set1">The first set.</param>
/// <param name="set2">The second set.</param>
/// <returns>Returns a value indicating whether the box has been split.</returns>
private bool Cut(Box set1, Box set2)
{
double wholeR = WuAlphaColorQuantizer.Volume(set1, this.vmr);
double wholeG = WuAlphaColorQuantizer.Volume(set1, this.vmg);
double wholeB = WuAlphaColorQuantizer.Volume(set1, this.vmb);
double wholeA = WuAlphaColorQuantizer.Volume(set1, this.vma);
double wholeW = WuAlphaColorQuantizer.Volume(set1, this.vwt);
int cutr;
int cutg;
int cutb;
int cuta;
double maxr = this.Maximize(set1, 3, set1.R0 + 1, set1.R1, out cutr, wholeR, wholeG, wholeB, wholeA, wholeW);
double maxg = this.Maximize(set1, 2, set1.G0 + 1, set1.G1, out cutg, wholeR, wholeG, wholeB, wholeA, wholeW);
double maxb = this.Maximize(set1, 1, set1.B0 + 1, set1.B1, out cutb, wholeR, wholeG, wholeB, wholeA, wholeW);
double maxa = this.Maximize(set1, 0, set1.A0 + 1, set1.A1, out cuta, wholeR, wholeG, wholeB, wholeA, wholeW);
int dir;
if ((maxr >= maxg) && (maxr >= maxb) && (maxr >= maxa))
{
dir = 3;
if (cutr < 0)
{
return(false);
}
}
else if ((maxg >= maxr) && (maxg >= maxb) && (maxg >= maxa))
{
dir = 2;
}
else if ((maxb >= maxr) && (maxb >= maxg) && (maxb >= maxa))
{
dir = 1;
}
else
{
dir = 0;
}
set2.R1 = set1.R1;
set2.G1 = set1.G1;
set2.B1 = set1.B1;
set2.A1 = set1.A1;
switch (dir)
{
// Red
case 3:
set2.R0 = set1.R1 = cutr;
set2.G0 = set1.G0;
set2.B0 = set1.B0;
set2.A0 = set1.A0;
break;
// Green
case 2:
set2.G0 = set1.G1 = cutg;
set2.R0 = set1.R0;
set2.B0 = set1.B0;
set2.A0 = set1.A0;
break;
// Blue
case 1:
set2.B0 = set1.B1 = cutb;
set2.R0 = set1.R0;
set2.G0 = set1.G0;
set2.A0 = set1.A0;
break;
// Alpha
case 0:
set2.A0 = set1.A1 = cuta;
set2.R0 = set1.R0;
set2.G0 = set1.G0;
set2.B0 = set1.B0;
break;
}
set1.Volume = (set1.R1 - set1.R0) * (set1.G1 - set1.G0) * (set1.B1 - set1.B0) * (set1.A1 - set1.A0);
set2.Volume = (set2.R1 - set2.R0) * (set2.G1 - set2.G0) * (set2.B1 - set2.B0) * (set2.A1 - set2.A0);
return(true);
}
/// <summary>
/// Converts the histogram into moments so that we can rapidly calculate
/// the sums of the above quantities over any desired box.
/// </summary>
private void Get3DMoments()
{
long[] volume = new long[WuAlphaColorQuantizer.IndexCount * WuAlphaColorQuantizer.IndexAlphaCount];
long[] volumeR = new long[WuAlphaColorQuantizer.IndexCount * WuAlphaColorQuantizer.IndexAlphaCount];
long[] volumeG = new long[WuAlphaColorQuantizer.IndexCount * WuAlphaColorQuantizer.IndexAlphaCount];
long[] volumeB = new long[WuAlphaColorQuantizer.IndexCount * WuAlphaColorQuantizer.IndexAlphaCount];
long[] volumeA = new long[WuAlphaColorQuantizer.IndexCount * WuAlphaColorQuantizer.IndexAlphaCount];
double[] volume2 = new double[WuAlphaColorQuantizer.IndexCount * WuAlphaColorQuantizer.IndexAlphaCount];
long[] area = new long[WuAlphaColorQuantizer.IndexAlphaCount];
long[] areaR = new long[WuAlphaColorQuantizer.IndexAlphaCount];
long[] areaG = new long[WuAlphaColorQuantizer.IndexAlphaCount];
long[] areaB = new long[WuAlphaColorQuantizer.IndexAlphaCount];
long[] areaA = new long[WuAlphaColorQuantizer.IndexAlphaCount];
double[] area2 = new double[WuAlphaColorQuantizer.IndexAlphaCount];
for (int r = 1; r < WuAlphaColorQuantizer.IndexCount; r++)
{
Array.Clear(volume, 0, WuAlphaColorQuantizer.IndexCount * WuAlphaColorQuantizer.IndexAlphaCount);
Array.Clear(volumeR, 0, WuAlphaColorQuantizer.IndexCount * WuAlphaColorQuantizer.IndexAlphaCount);
Array.Clear(volumeG, 0, WuAlphaColorQuantizer.IndexCount * WuAlphaColorQuantizer.IndexAlphaCount);
Array.Clear(volumeB, 0, WuAlphaColorQuantizer.IndexCount * WuAlphaColorQuantizer.IndexAlphaCount);
Array.Clear(volumeA, 0, WuAlphaColorQuantizer.IndexCount * WuAlphaColorQuantizer.IndexAlphaCount);
Array.Clear(volume2, 0, WuAlphaColorQuantizer.IndexCount * WuAlphaColorQuantizer.IndexAlphaCount);
for (int g = 1; g < WuAlphaColorQuantizer.IndexCount; g++)
{
Array.Clear(area, 0, WuAlphaColorQuantizer.IndexAlphaCount);
Array.Clear(areaR, 0, WuAlphaColorQuantizer.IndexAlphaCount);
Array.Clear(areaG, 0, WuAlphaColorQuantizer.IndexAlphaCount);
Array.Clear(areaB, 0, WuAlphaColorQuantizer.IndexAlphaCount);
Array.Clear(areaA, 0, WuAlphaColorQuantizer.IndexAlphaCount);
Array.Clear(area2, 0, WuAlphaColorQuantizer.IndexAlphaCount);
for (int b = 1; b < WuAlphaColorQuantizer.IndexCount; b++)
{
long line = 0;
long lineR = 0;
long lineG = 0;
long lineB = 0;
long lineA = 0;
double line2 = 0;
for (int a = 1; a < WuAlphaColorQuantizer.IndexAlphaCount; a++)
{
int ind1 = WuAlphaColorQuantizer.GetIndex(r, g, b, a);
line += this.vwt[ind1];
lineR += this.vmr[ind1];
lineG += this.vmg[ind1];
lineB += this.vmb[ind1];
lineA += this.vma[ind1];
line2 += this.m2[ind1];
area[a] += line;
areaR[a] += lineR;
areaG[a] += lineG;
areaB[a] += lineB;
areaA[a] += lineA;
area2[a] += line2;
int inv = (b * WuAlphaColorQuantizer.IndexAlphaCount) + a;
volume[inv] += area[a];
volumeR[inv] += areaR[a];
volumeG[inv] += areaG[a];
volumeB[inv] += areaB[a];
volumeA[inv] += areaA[a];
volume2[inv] += area2[a];
int ind2 = ind1 - WuAlphaColorQuantizer.GetIndex(1, 0, 0, 0);
this.vwt[ind1] = this.vwt[ind2] + volume[inv];
this.vmr[ind1] = this.vmr[ind2] + volumeR[inv];
this.vmg[ind1] = this.vmg[ind2] + volumeG[inv];
this.vmb[ind1] = this.vmb[ind2] + volumeB[inv];
this.vma[ind1] = this.vma[ind2] + volumeA[inv];
this.m2[ind1] = this.m2[ind2] + volume2[inv];
}
}
}
}
}
