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+///////////////////////////////////////////////////////////////////////
+// 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 "Quantizers.h"
+#include "FreeImage.h"
+#include "Utilities.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;
+
+ 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;
+ }
+ }
+
+ 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;
+}
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