///////////////////////////////////////////////////////////////////////
// C Implementation of Wu's Color Quantizer (v. 2)
// (see Graphics Gems vol. II, pp. 126-133)
//
// Author: Xiaolin Wu
// Dept. of Computer Science
// Univ. of Western Ontario
// London, Ontario N6A 5B7
// wu@csd.uwo.ca
//
// Algorithm: Greedy orthogonal bipartition of RGB space for variance
// minimization aided by inclusion-exclusion tricks.
// For speed no nearest neighbor search is done. Slightly
// better performance can be expected by more sophisticated
// but more expensive versions.
//
// The author thanks Tom Lane at Tom_Lane@G.GP.CS.CMU.EDU for much of
// additional documentation and a cure to a previous bug.
//
// Free to distribute, comments and suggestions are appreciated.
///////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////
// History
// -------
// July 2000: C++ Implementation of Wu's Color Quantizer
// and adaptation for the FreeImage 2 Library
// Author: Hervé Drolon (drolon@infonie.fr)
// March 2004: Adaptation for the FreeImage 3 library (port to big endian processors)
// Author: Hervé Drolon (drolon@infonie.fr)
///////////////////////////////////////////////////////////////////////
#include "../stdafx.h"
///////////////////////////////////////////////////////////////////////
// Size of a 3D array : 33 x 33 x 33
#define SIZE_3D 35937
// 3D array indexation
#define INDEX(r, g, b) ((r << 10) + (r << 6) + r + (g << 5) + g + b)
#define MAXCOLOR 256
// Constructor / Destructor
WuQuantizer::WuQuantizer(FIBITMAP *dib) {
width = FreeImage_GetWidth(dib);
height = FreeImage_GetHeight(dib);
pitch = FreeImage_GetPitch(dib);
m_dib = dib;
gm2 = NULL;
wt = mr = mg = mb = NULL;
Qadd = NULL;
// Allocate 3D arrays
gm2 = (float*)malloc(SIZE_3D * sizeof(float));
wt = (LONG*)malloc(SIZE_3D * sizeof(LONG));
mr = (LONG*)malloc(SIZE_3D * sizeof(LONG));
mg = (LONG*)malloc(SIZE_3D * sizeof(LONG));
mb = (LONG*)malloc(SIZE_3D * sizeof(LONG));
// Allocate Qadd
Qadd = (WORD *)malloc(sizeof(WORD) * width * height);
if(!gm2 || !wt || !mr || !mg || !mb || !Qadd) {
if(gm2) free(gm2);
if(wt) free(wt);
if(mr) free(mr);
if(mg) free(mg);
if(mb) free(mb);
if(Qadd) free(Qadd);
throw FI_MSG_ERROR_MEMORY;
}
memset(gm2, 0, SIZE_3D * sizeof(float));
memset(wt, 0, SIZE_3D * sizeof(LONG));
memset(mr, 0, SIZE_3D * sizeof(LONG));
memset(mg, 0, SIZE_3D * sizeof(LONG));
memset(mb, 0, SIZE_3D * sizeof(LONG));
memset(Qadd, 0, sizeof(WORD) * width * height);
}
WuQuantizer::~WuQuantizer() {
if(gm2) free(gm2);
if(wt) free(wt);
if(mr) free(mr);
if(mg) free(mg);
if(mb) free(mb);
if(Qadd) free(Qadd);
}
// Histogram is in elements 1..HISTSIZE along each axis,
// element 0 is for base or marginal value
// NB: these must start out 0!
// Build 3-D color histogram of counts, r/g/b, c^2
void
WuQuantizer::Hist3D(LONG *vwt, LONG *vmr, LONG *vmg, LONG *vmb, float *m2, int ReserveSize, RGBQUAD *ReservePalette) {
int ind = 0;
int inr, ing, inb, table[256];
int i;
unsigned y, x;
for(i = 0; i < 256; i++)
table[i] = i * i;
if (FreeImage_GetBPP(m_dib) == 24) {
for(y = 0; y < height; y++) {
BYTE *bits = FreeImage_GetScanLine(m_dib, y);
for(x = 0; x < width; x++) {
inr = (bits[FI_RGBA_RED] >> 3) + 1;
ing = (bits[FI_RGBA_GREEN] >> 3) + 1;
inb = (bits[FI_RGBA_BLUE] >> 3) + 1;
ind = INDEX(inr, ing, inb);
Qadd[y*width + x] = (WORD)ind;
// [inr][ing][inb]
vwt[ind]++;
vmr[ind] += bits[FI_RGBA_RED];
vmg[ind] += bits[FI_RGBA_GREEN];
vmb[ind] += bits[FI_RGBA_BLUE];
m2[ind] += (float)(table[bits[FI_RGBA_RED]] + table[bits[FI_RGBA_GREEN]] + table[bits[FI_RGBA_BLUE]]);
bits += 3;
}
}
} else {
for(y = 0; y < height; y++) {
BYTE *bits = FreeImage_GetScanLine(m_dib, y);
for(x = 0; x < width; x++) {
inr = (bits[FI_RGBA_RED] >> 3) + 1;
ing = (bits[FI_RGBA_GREEN] >> 3) + 1;
inb = (bits[FI_RGBA_BLUE] >> 3) + 1;
ind = INDEX(inr, ing, inb);
Qadd[y*width + x] = (WORD)ind;
// [inr][ing][inb]
vwt[ind]++;
vmr[ind] += bits[FI_RGBA_RED];
vmg[ind] += bits[FI_RGBA_GREEN];
vmb[ind] += bits[FI_RGBA_BLUE];
m2[ind] += (float)(table[bits[FI_RGBA_RED]] + table[bits[FI_RGBA_GREEN]] + table[bits[FI_RGBA_BLUE]]);
bits += 4;
}
}
}
if( ReserveSize > 0 ) {
int max = 0;
for(i = 0; i < SIZE_3D; i++) {
if( vwt[i] > max ) max = vwt[i];
}
max++;
for(i = 0; i < ReserveSize; i++) {
inr = (ReservePalette[i].rgbRed >> 3) + 1;
ing = (ReservePalette[i].rgbGreen >> 3) + 1;
inb = (ReservePalette[i].rgbBlue >> 3) + 1;
ind = INDEX(inr, ing, inb);
wt[ind] = max;
mr[ind] = max * ReservePalette[i].rgbRed;
mg[ind] = max * ReservePalette[i].rgbGreen;
mb[ind] = max * ReservePalette[i].rgbBlue;
gm2[ind] = (float)max * (float)(table[ReservePalette[i].rgbRed] + table[ReservePalette[i].rgbGreen] + table[ReservePalette[i].rgbBlue]);
}
}
}
// At conclusion of the histogram step, we can interpret
// wt[r][g][b] = sum over voxel of P(c)
// mr[r][g][b] = sum over voxel of r*P(c) , similarly for mg, mb
// m2[r][g][b] = sum over voxel of c^2*P(c)
// Actually each of these should be divided by 'ImageSize' to give the usual
// interpretation of P() as ranging from 0 to 1, but we needn't do that here.
// We now convert histogram into moments so that we can rapidly calculate
// the sums of the above quantities over any desired box.
// Compute cumulative moments
void
WuQuantizer::M3D(LONG *vwt, LONG *vmr, LONG *vmg, LONG *vmb, float *m2) {
unsigned ind1, ind2;
BYTE i, r, g, b;
LONG line, line_r, line_g, line_b;
LONG area[33], area_r[33], area_g[33], area_b[33];
float line2, area2[33];
for(r = 1; r <= 32; r++) {
for(i = 0; i <= 32; i++) {
area2[i] = 0;
area[i] = area_r[i] = area_g[i] = area_b[i] = 0;
}
for(g = 1; g <= 32; g++) {
line2 = 0;
line = line_r = line_g = line_b = 0;
for(b = 1; b <= 32; b++) {
ind1 = INDEX(r, g, b); // [r][g][b]
line += vwt[ind1];
line_r += vmr[ind1];
line_g += vmg[ind1];
line_b += vmb[ind1];
line2 += m2[ind1];
area[b] += line;
area_r[b] += line_r;
area_g[b] += line_g;
area_b[b] += line_b;
area2[b] += line2;
ind2 = ind1 - 1089; // [r-1][g][b]
vwt[ind1] = vwt[ind2] + area[b];
vmr[ind1] = vmr[ind2] + area_r[b];
vmg[ind1] = vmg[ind2] + area_g[b];
vmb[ind1] = vmb[ind2] + area_b[b];
m2[ind1] = m2[ind2] + area2[b];
}
}
}
}
// Compute sum over a box of any given statistic
LONG
WuQuantizer::Vol( Box *cube, LONG *mmt ) {
return( mmt[INDEX(cube->r1, cube->g1, cube->b1)]
- mmt[INDEX(cube->r1, cube->g1, cube->b0)]
- mmt[INDEX(cube->r1, cube->g0, cube->b1)]
+ mmt[INDEX(cube->r1, cube->g0, cube->b0)]
- mmt[INDEX(cube->r0, cube->g1, cube->b1)]
+ mmt[INDEX(cube->r0, cube->g1, cube->b0)]
+ mmt[INDEX(cube->r0, cube->g0, cube->b1)]
- mmt[INDEX(cube->r0, cube->g0, cube->b0)] );
}
// The next two routines allow a slightly more efficient calculation
// of Vol() for a proposed subbox of a given box. The sum of Top()
// and Bottom() is the Vol() of a subbox split in the given direction
// and with the specified new upper bound.
// Compute part of Vol(cube, mmt) that doesn't depend on r1, g1, or b1
// (depending on dir)
LONG
WuQuantizer::Bottom(Box *cube, BYTE dir, LONG *mmt) {
switch(dir)
{
case FI_RGBA_RED:
return( - mmt[INDEX(cube->r0, cube->g1, cube->b1)]
+ mmt[INDEX(cube->r0, cube->g1, cube->b0)]
+ mmt[INDEX(cube->r0, cube->g0, cube->b1)]
- mmt[INDEX(cube->r0, cube->g0, cube->b0)] );
break;
case FI_RGBA_GREEN:
return( - mmt[INDEX(cube->r1, cube->g0, cube->b1)]
+ mmt[INDEX(cube->r1, cube->g0, cube->b0)]
+ mmt[INDEX(cube->r0, cube->g0, cube->b1)]
- mmt[INDEX(cube->r0, cube->g0, cube->b0)] );
break;
case FI_RGBA_BLUE:
return( - mmt[INDEX(cube->r1, cube->g1, cube->b0)]
+ mmt[INDEX(cube->r1, cube->g0, cube->b0)]
+ mmt[INDEX(cube->r0, cube->g1, cube->b0)]
- mmt[INDEX(cube->r0, cube->g0, cube->b0)] );
break;
}
return 0;
}
// Compute remainder of Vol(cube, mmt), substituting pos for
// r1, g1, or b1 (depending on dir)
LONG
WuQuantizer::Top(Box *cube, BYTE dir, int pos, LONG *mmt) {
switch(dir)
{
case FI_RGBA_RED:
return( mmt[INDEX(pos, cube->g1, cube->b1)]
-mmt[INDEX(pos, cube->g1, cube->b0)]
-mmt[INDEX(pos, cube->g0, cube->b1)]
+mmt[INDEX(pos, cube->g0, cube->b0)] );
break;
case FI_RGBA_GREEN:
return( mmt[INDEX(cube->r1, pos, cube->b1)]
-mmt[INDEX(cube->r1, pos, cube->b0)]
-mmt[INDEX(cube->r0, pos, cube->b1)]
+mmt[INDEX(cube->r0, pos, cube->b0)] );
break;
case FI_RGBA_BLUE:
return( mmt[INDEX(cube->r1, cube->g1, pos)]
-mmt[INDEX(cube->r1, cube->g0, pos)]
-mmt[INDEX(cube->r0, cube->g1, pos)]
+mmt[INDEX(cube->r0, cube->g0, pos)] );
break;
}
return 0;
}
// Compute the weighted variance of a box
// NB: as with the raw statistics, this is really the variance * ImageSize
float
WuQuantizer::Var(Box *cube) {
float dr = (float) Vol(cube, mr);
float dg = (float) Vol(cube, mg);
float db = (float) Vol(cube, mb);
float xx = gm2[INDEX(cube->r1, cube->g1, cube->b1)]
-gm2[INDEX(cube->r1, cube->g1, cube->b0)]
-gm2[INDEX(cube->r1, cube->g0, cube->b1)]
+gm2[INDEX(cube->r1, cube->g0, cube->b0)]
-gm2[INDEX(cube->r0, cube->g1, cube->b1)]
+gm2[INDEX(cube->r0, cube->g1, cube->b0)]
+gm2[INDEX(cube->r0, cube->g0, cube->b1)]
-gm2[INDEX(cube->r0, cube->g0, cube->b0)];
return (xx - (dr*dr+dg*dg+db*db)/(float)Vol(cube,wt));
}
// We want to minimize the sum of the variances of two subboxes.
// The sum(c^2) terms can be ignored since their sum over both subboxes
// 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.
float
WuQuantizer::Maximize(Box *cube, BYTE dir, int first, int last , int *cut, LONG whole_r, LONG whole_g, LONG whole_b, LONG whole_w) {
LONG half_r, half_g, half_b, half_w;
int i;
float temp;
LONG base_r = Bottom(cube, dir, mr);
LONG base_g = Bottom(cube, dir, mg);
LONG base_b = Bottom(cube, dir, mb);
LONG base_w = Bottom(cube, dir, wt);
float max = 0.0;
*cut = -1;
for (i = first; i < last; i++) {
half_r = base_r + Top(cube, dir, i, mr);
half_g = base_g + Top(cube, dir, i, mg);
half_b = base_b + Top(cube, dir, i, mb);
half_w = base_w + Top(cube, dir, i, wt);
// now half_x is sum over lower half of box, if split at i
if (half_w == 0) { // subbox could be empty of pixels!
continue; // never split into an empty box
} else {
temp = ((float)half_r*half_r + (float)half_g*half_g + (float)half_b*half_b)/half_w;
}
half_r = whole_r - half_r;
half_g = whole_g - half_g;
half_b = whole_b - half_b;
half_w = whole_w - half_w;
if (half_w == 0) { // subbox could be empty of pixels!
continue; // never split into an empty box
} else {
temp += ((float)half_r*half_r + (float)half_g*half_g + (float)half_b*half_b)/half_w;
}
if (temp > max) {
max=temp;
*cut=i;
}
}
return max;
}
bool
WuQuantizer::Cut(Box *set1, Box *set2) {
BYTE dir;
int cutr, cutg, cutb;
LONG whole_r = Vol(set1, mr);
LONG whole_g = Vol(set1, mg);
LONG whole_b = Vol(set1, mb);
LONG whole_w = Vol(set1, wt);
float maxr = Maximize(set1, FI_RGBA_RED, set1->r0+1, set1->r1, &cutr, whole_r, whole_g, whole_b, whole_w);
float maxg = Maximize(set1, FI_RGBA_GREEN, set1->g0+1, set1->g1, &cutg, whole_r, whole_g, whole_b, whole_w);
float maxb = Maximize(set1, FI_RGBA_BLUE, set1->b0+1, set1->b1, &cutb, whole_r, whole_g, whole_b, whole_w);
if ((maxr >= maxg) && (maxr >= maxb)) {
dir = FI_RGBA_RED;
if (cutr < 0) {
return false; // can't split the box
}
} else if ((maxg >= maxr) && (maxg>=maxb)) {
dir = FI_RGBA_GREEN;
} else {
dir = FI_RGBA_BLUE;
}
set2->r1 = set1->r1;
set2->g1 = set1->g1;
set2->b1 = set1->b1;
switch (dir) {
case FI_RGBA_RED:
set2->r0 = set1->r1 = cutr;
set2->g0 = set1->g0;
set2->b0 = set1->b0;
break;
case FI_RGBA_GREEN:
set2->g0 = set1->g1 = cutg;
set2->r0 = set1->r0;
set2->b0 = set1->b0;
break;
case FI_RGBA_BLUE:
set2->b0 = set1->b1 = cutb;
set2->r0 = set1->r0;
set2->g0 = set1->g0;
break;
}
set1->vol = (set1->r1-set1->r0)*(set1->g1-set1->g0)*(set1->b1-set1->b0);
set2->vol = (set2->r1-set2->r0)*(set2->g1-set2->g0)*(set2->b1-set2->b0);
return true;
}
void
WuQuantizer::Mark(Box *cube, int label, BYTE *tag) {
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++) {
tag[INDEX(r, g, b)] = (BYTE)label;
}
}
}
}
// Wu Quantization algorithm
FIBITMAP *
WuQuantizer::Quantize(int PaletteSize, int ReserveSize, RGBQUAD *ReservePalette) {
BYTE *tag = NULL;
try {
Box cube[MAXCOLOR];
int next;
LONG i, weight;
int k;
float vv[MAXCOLOR], temp;
// Compute 3D histogram
Hist3D(wt, mr, mg, mb, gm2, ReserveSize, ReservePalette);
// Compute moments
M3D(wt, mr, mg, mb, gm2);
cube[0].r0 = cube[0].g0 = cube[0].b0 = 0;
cube[0].r1 = cube[0].g1 = cube[0].b1 = 32;
next = 0;
for (i = 1; i < PaletteSize; i++) {
if(Cut(&cube[next], &cube[i])) {
// volume test ensures we won't try to cut one-cell box
vv[next] = (cube[next].vol > 1) ? Var(&cube[next]) : 0;
vv[i] = (cube[i].vol > 1) ? Var(&cube[i]) : 0;
} else {
vv[next] = 0.0; // don't try to split this box again
i--; // didn't create box i
}
next = 0; temp = vv[0];
for (k = 1; k <= i; k++) {
if (vv[k] > temp) {
temp = vv[k]; next = k;
}
}
if (temp <= 0.0) {
PaletteSize = i + 1;
// Error: "Only got 'PaletteSize' boxes"
break;
}
}
// Partition done
// the space for array gm2 can be freed now
free(gm2);
gm2 = NULL;
// Allocate a new dib
FIBITMAP *new_dib = FreeImage_Allocate(width, height, 8);
if (new_dib == NULL) {
throw FI_MSG_ERROR_MEMORY;
}
// create an optimized palette
RGBQUAD *new_pal = FreeImage_GetPalette(new_dib);
tag = (BYTE*) malloc(SIZE_3D * sizeof(BYTE));
if (tag == NULL) {
throw FI_MSG_ERROR_MEMORY;
}
memset(tag, 0, SIZE_3D * sizeof(BYTE));
for (k = 0; k < PaletteSize ; k++) {
Mark(&cube[k], k, tag);
weight = Vol(&cube[k], wt);
if (weight) {
new_pal[k].rgbRed = (BYTE)(((float)Vol(&cube[k], mr) / (float)weight) + 0.5f);
new_pal[k].rgbGreen = (BYTE)(((float)Vol(&cube[k], mg) / (float)weight) + 0.5f);
new_pal[k].rgbBlue = (BYTE)(((float)Vol(&cube[k], mb) / (float)weight) + 0.5f);
} else {
// Error: bogus box 'k'
new_pal[k].rgbRed = new_pal[k].rgbGreen = new_pal[k].rgbBlue = 0;
}
}
int npitch = FreeImage_GetPitch(new_dib);
for (unsigned y = 0; y < height; y++) {
BYTE *new_bits = FreeImage_GetBits(new_dib) + (y * npitch);
for (unsigned x = 0; x < width; x++) {
new_bits[x] = tag[Qadd[y*width + x]];
}
}
// output 'new_pal' as color look-up table contents,
// 'new_bits' as the quantized image (array of table addresses).
free(tag);
return (FIBITMAP*) new_dib;
} catch(...) {
free(tag);
}
return NULL;
}