/**********************************************************************
C Implementation of Wu's Color Quantizer (v. 2)
(see Graphics Gems vol. II, pp. 126-133)
Author: 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.
**********************************************************************/
#include "Tquant.h"
#include "gobject.hpp"
#define MAXCOLOR 256
#define RED 2
#define GREEN 1
#define BLUE 0
struct box {
int r0; /* min value, exclusive */
int r1; /* max value, inclusive */
int g0;
int g1;
int b0;
int b1;
int vol;
};
/* Histogram is in elements 1..HISTSIZE along each axis,
* element 0 is for base or marginal value
* NB: these must start out 0!
*/
float gm2[33][33][33];
long int wt[33][33][33], mr[33][33][33], mg[33][33][33], mb[33][33][33];
unsigned char *Ir, *Ig, *Ib;
//int size; /*image size*/
//int K; /*color look-up table size*/
unsigned short int *Qadd;
void ClearTables(void);
void ClearTables(void)
{
for (int x=0;x<33;x++)
for (int y=0;y<33;y++)
for (int z=0;z<33;z++)
{
gm2[x][y][z]=0;
wt[x][y][z]=0;
mr[x][y][z]=0;
mg[x][y][z]=0;
mb[x][y][z]=0;
}
}
/* build 3-D color histogram of counts, r/g/b, c^2 */
void Hist3d(long int* vwt, long int *vmr, long int *vmg, long int *vmb, float *m2, int size)
{
register int ind, r, g, b;
int inr, ing, inb, table[256];
register long int i;
for(i=0; i<256; ++i) table[i]=i*i;
Qadd = (unsigned short int *)malloc(sizeof(short int)*size);
if (Qadd==NULL)
GObject::Error(ERM_OUTOFMEM);
for(i=0; i<size; ++i)
{
r = Ir[i]; g = Ig[i]; b = Ib[i];
inr=(r>>3)+1;
ing=(g>>3)+1;
inb=(b>>3)+1;
Qadd[i]=ind=(inr<<10)+(inr<<6)+inr+(ing<<5)+ing+inb;
/*[inr][ing][inb]*/
++vwt[ind];
vmr[ind] += r;
vmg[ind] += g;
vmb[ind] += b;
m2[ind] += (float)(table[r]+table[g]+table[b]);
}
}
/* 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 'size' 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 M3d(long int *vwt, long int *vmr, long int *vmg, long int *vmb, float *m2)
{
register unsigned short int ind1, ind2;
register unsigned char i, r, g, b;
long int line, line_r, line_g, line_b;
long int 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)
{
area[i]=area_r[i]=area_g[i]=area_b[i]=0;
area2[i]=0.f;
}
for(g=1; g<=32; ++g)
{
line = line_r = line_g = line_b = 0;
line2 = 0.f;
for(b=1; b<=32; ++b)
{
ind1 = (r<<10) + (r<<6) + r + (g<<5) + 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 int Vol(box *cube, long int *mmt)
{
return( mmt[((cube->r1)*33*33)+((cube->g1)*33)+(cube->b1)]
-mmt[((cube->r1)*33*33)+((cube->g1)*33)+(cube->b0)]
-mmt[((cube->r1)*33*33)+((cube->g0)*33)+(cube->b1)]
+mmt[((cube->r1)*33*33)+((cube->g0)*33)+(cube->b0)]
-mmt[((cube->r0)*33*33)+((cube->g1)*33)+(cube->b1)]
+mmt[((cube->r0)*33*33)+((cube->g1)*33)+(cube->b0)]
+mmt[((cube->r0)*33*33)+((cube->g0)*33)+(cube->b1)]
-mmt[((cube->r0)*33*33)+((cube->g0)*33)+(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 int Bottom(box *cube, unsigned char dir, long int *mmt)
{
switch(dir){
case RED:
return( -mmt[((cube->r0)*33*33)+((cube->g1)*33)+(cube->b1)]
+mmt[((cube->r0)*33*33)+((cube->g1)*33)+(cube->b0)]
+mmt[((cube->r0)*33*33)+((cube->g0)*33)+(cube->b1)]
-mmt[((cube->r0)*33*33)+((cube->g0)*33)+(cube->b0)] );
break;
case GREEN:
return( -mmt[((cube->r1)*33*33)+((cube->g0)*33)+(cube->b1)]
+mmt[((cube->r1)*33*33)+((cube->g0)*33)+(cube->b0)]
+mmt[((cube->r0)*33*33)+((cube->g0)*33)+(cube->b1)]
-mmt[((cube->r0)*33*33)+((cube->g0)*33)+(cube->b0)] );
break;
case BLUE:
return( -mmt[((cube->r1)*33*33)+((cube->g1)*33)+(cube->b0)]
+mmt[((cube->r1)*33*33)+((cube->g0)*33)+(cube->b0)]
+mmt[((cube->r0)*33*33)+((cube->g1)*33)+(cube->b0)]
-mmt[((cube->r0)*33*33)+((cube->g0)*33)+(cube->b0)] );
break;
default:
return NULL;
}
}
/* Compute remainder of Vol(cube, mmt), substituting pos for */
/* r1, g1, or b1 (depending on dir) */
long int Top(box *cube, unsigned char dir, int pos, long int *mmt)
{
switch(dir){
case RED:
return( mmt[(pos*33*33)+(cube->g1*33)+cube->b1]
-mmt[(pos*33*33)+(cube->g1*33)+cube->b0]
-mmt[(pos*33*33)+(cube->g0*33)+cube->b1]
+mmt[(pos*33*33)+(cube->g0*33)+cube->b0] );
break;
case GREEN:
return( mmt[((cube->r1)*33*33)+(pos*33)+cube->b1]
-mmt[((cube->r1)*33*33)+(pos*33)+cube->b0]
-mmt[((cube->r0)*33*33)+(pos*33)+cube->b1]
+mmt[((cube->r0)*33*33)+(pos*33)+cube->b0] );
break;
case BLUE:
return( mmt[(cube->r1*33*33)+(cube->g1*33)+pos]
-mmt[(cube->r1*33*33)+(cube->g0*33)+pos]
-mmt[(cube->r0*33*33)+(cube->g1*33)+pos]
+mmt[(cube->r0*33*33)+(cube->g0*33)+pos] );
break;
default:
return NULL;
}
}
/* Compute the weighted variance of a box */
/* NB: as with the raw statistics, this is really the variance * size */
float Var(box *cube)
{
float dr, dg, db, xx;
dr = (float)Vol(cube, &mr[0][0][0]);
dg = (float)Vol(cube, &mg[0][0][0]);
db = (float)Vol(cube, &mb[0][0][0]);
xx = gm2[cube->r1][cube->g1][cube->b1]
-gm2[cube->r1][cube->g1][cube->b0]
-gm2[cube->r1][cube->g0][cube->b1]
+gm2[cube->r1][cube->g0][cube->b0]
-gm2[cube->r0][cube->g1][cube->b1]
+gm2[cube->r0][cube->g1][cube->b0]
+gm2[cube->r0][cube->g0][cube->b1]
-gm2[cube->r0][cube->g0][cube->b0];
return( xx - (dr*dr+dg*dg+db*db)/(float)Vol(cube,&wt[0][0][0]) );
}
/* 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 Maximize(box *cube, unsigned char dir, int first, int last, int *cut,long int whole_r, long int whole_g, long int whole_b, long int whole_w)
{
register long int half_r, half_g, half_b, half_w;
long int base_r, base_g, base_b, base_w;
register int i;
register float temp, max;
base_r = Bottom(cube, dir, &mr[0][0][0]);
base_g = Bottom(cube, dir, &mg[0][0][0]);
base_b = Bottom(cube, dir, &mb[0][0][0]);
base_w = Bottom(cube, dir, &wt[0][0][0]);
max = 0.0;
*cut = -1;
for(i=first; i<last; ++i)
{
half_r = base_r + Top(cube, dir, i, &mr[0][0][0]);
half_g = base_g + Top(cube, dir, i, &mg[0][0][0]);
half_b = base_b + Top(cube, dir, i, &mb[0][0][0]);
half_w = base_w + Top(cube, dir, i, &wt[0][0][0]);
/* 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);
}
int Cut(box *set1, box *set2)
{
unsigned char dir;
int cutr, cutg, cutb;
float maxr, maxg, maxb;
long int whole_r, whole_g, whole_b, whole_w;
whole_r = Vol(set1, &mr[0][0][0]);
whole_g = Vol(set1, &mg[0][0][0]);
whole_b = Vol(set1, &mb[0][0][0]);
whole_w = Vol(set1, &wt[0][0][0]);
maxr = Maximize(set1, RED, set1->r0+1, set1->r1, &cutr,
whole_r, whole_g, whole_b, whole_w);
maxg = Maximize(set1, GREEN, set1->g0+1, set1->g1, &cutg,
whole_r, whole_g, whole_b, whole_w);
maxb = Maximize(set1, BLUE, set1->b0+1, set1->b1, &cutb,
whole_r, whole_g, whole_b, whole_w);
if( (maxr>=maxg)&&(maxr>=maxb) )
{
dir = RED;
if (cutr < 0) return 0; /* can't split the box */
}else
if( (maxg>=maxr)&&(maxg>=maxb) )
dir = GREEN;
else
dir = BLUE;
set2->r1 = set1->r1;
set2->g1 = set1->g1;
set2->b1 = set1->b1;
switch (dir){
case RED:
set2->r0 = set1->r1 = cutr;
set2->g0 = set1->g0;
set2->b0 = set1->b0;
break;
case GREEN:
set2->g0 = set1->g1 = cutg;
set2->r0 = set1->r0;
set2->b0 = set1->b0;
break;
case 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 1;
}
void Mark(box *cube, int label, unsigned char *tag)
{
register int r, g, b;
for(r=cube->r0+1; r<=cube->r1; ++r)
for(g=cube->g0+1; g<=cube->g1; ++g)
for(b=cube->b0+1; b<=cube->b1; ++b)
tag[(r<<10) + (r<<6) + r + (g<<5) + g + b] = label;
}
void tquant(BYTE* Src, BYTE* Dst, BYTE* Pal, int K, int size)
{
struct box cube[MAXCOLOR];
unsigned char *tag;
unsigned char lut_r[MAXCOLOR], lut_g[MAXCOLOR], lut_b[MAXCOLOR];
int next;
register long int i, weight;
register int k;
float vv[MAXCOLOR], temp;
ClearTables();
/* input R,G,B components into Ir, Ig, Ib;
set size to width*height */
// screen_debug_msg("Reducing to %d cols",K);
Ir=(BYTE*)malloc(size);
Ig=(BYTE*)malloc(size);
Ib=(BYTE*)malloc(size);
/* Split in data into RGB buffers */
for(i=0;i<size;i++)
{
Ir[i]=*Src++;
Ig[i]=*Src++;
Ib[i]=*Src++;
}
Hist3d(&wt[0][0][0], &mr[0][0][0], &mg[0][0][0], &mb[0][0][0], &gm2[0][0][0], size);
free(Ig); free(Ib); free(Ir);
M3d(&wt[0][0][0], &mr[0][0][0], &mg[0][0][0], &mb[0][0][0], &gm2[0][0][0]);
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<K; ++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.f;
vv[i] = (cube[i].vol>1) ? Var(&cube[i]) : 0.f;
} 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) {
K = i+1;
break;
}
}
/* the space for array gm2 can be freed now */
tag = (unsigned char *)malloc(33*33*33);
if (tag==NULL)
GObject::Error(ERM_OUTOFMEM);
for(k=0; k<K; ++k){
Mark(&cube[k], k, tag);
weight = Vol(&cube[k], &wt[0][0][0]);
if (weight) {
lut_r[k] = (unsigned char)(Vol(&cube[k], &mr[0][0][0]) / weight);
lut_g[k] = (unsigned char)(Vol(&cube[k], &mg[0][0][0]) / weight);
lut_b[k] = (unsigned char)(Vol(&cube[k], &mb[0][0][0]) / weight);
}
else{
lut_r[k] = lut_g[k] = lut_b[k] = 0;
}
}
for(i=0; i<size; ++i) Qadd[i] = tag[Qadd[i]];
/* output lut_r, lut_g, lut_b as color look-up table contents,
Qadd as the quantized image (array of table addresses). */
for(i=0; i<size; ++i) *Dst++ = (unsigned char)Qadd[i];
free(Qadd);
for(i=0;i<K;i++)
{
*Pal++=lut_r[i];
*Pal++=lut_g[i];
*Pal++=lut_b[i];
}
free(tag);
}