471 lines
16 KiB
C
471 lines
16 KiB
C
/*
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** © 2009-2015 by Kornel Lesiński.
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**
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** This file is part of libimagequant.
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**
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** libimagequant is free software: you can redistribute it and/or modify
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** it under the terms of the GNU General Public License as published by
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** the Free Software Foundation, either version 3 of the License, or
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** (at your option) any later version.
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**
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** libimagequant is distributed in the hope that it will be useful,
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** but WITHOUT ANY WARRANTY; without even the implied warranty of
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** MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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** GNU General Public License for more details.
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**
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** You should have received a copy of the GNU General Public License
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** along with libimagequant. If not, see <http://www.gnu.org/licenses/>.
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*/
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/*
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** Copyright (C) 1989, 1991 by Jef Poskanzer.
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** Copyright (C) 1997, 2000, 2002 by Greg Roelofs; based on an idea by
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** Stefan Schneider.
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**
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** Permission to use, copy, modify, and distribute this software and its
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** documentation for any purpose and without fee is hereby granted, provided
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** that the above copyright notice appear in all copies and that both that
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** copyright notice and this permission notice appear in supporting
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** documentation. This software is provided "as is" without express or
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** implied warranty.
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*/
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#include <stdlib.h>
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#include <stddef.h>
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#include "libimagequant.h"
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#include "pam.h"
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#include "mediancut.h"
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#define index_of_channel(ch) (offsetof(f_pixel,ch)/sizeof(float))
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static f_pixel averagepixels(unsigned int clrs, const hist_item achv[]);
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struct box {
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f_pixel color;
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f_pixel variance;
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double sum, total_error, max_error;
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unsigned int ind;
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unsigned int colors;
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};
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ALWAYS_INLINE static double variance_diff(double val, const double good_enough);
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inline static double variance_diff(double val, const double good_enough)
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{
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val *= val;
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if (val < good_enough*good_enough) return val*0.25;
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return val;
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}
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/** Weighted per-channel variance of the box. It's used to decide which channel to split by */
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static f_pixel box_variance(const hist_item achv[], const struct box *box)
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{
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f_pixel mean = box->color;
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double variancea=0, variancer=0, varianceg=0, varianceb=0;
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for(unsigned int i = 0; i < box->colors; ++i) {
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const f_pixel px = achv[box->ind + i].acolor;
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double weight = achv[box->ind + i].adjusted_weight;
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variancea += variance_diff(mean.a - px.a, 2.0/256.0)*weight;
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variancer += variance_diff(mean.r - px.r, 1.0/256.0)*weight;
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varianceg += variance_diff(mean.g - px.g, 1.0/256.0)*weight;
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varianceb += variance_diff(mean.b - px.b, 1.0/256.0)*weight;
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}
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return (f_pixel){
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.a = variancea*(4.0/16.0),
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.r = variancer*(7.0/16.0),
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.g = varianceg*(9.0/16.0),
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.b = varianceb*(5.0/16.0),
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};
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}
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static double box_max_error(const hist_item achv[], const struct box *box)
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{
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f_pixel mean = box->color;
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double max_error = 0;
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for(unsigned int i = 0; i < box->colors; ++i) {
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const double diff = colordifference(mean, achv[box->ind + i].acolor);
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if (diff > max_error) {
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max_error = diff;
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}
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}
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return max_error;
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}
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ALWAYS_INLINE static double color_weight(f_pixel median, hist_item h);
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static inline void hist_item_swap(hist_item *l, hist_item *r)
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{
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if (l != r) {
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hist_item t = *l;
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*l = *r;
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*r = t;
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}
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}
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ALWAYS_INLINE static unsigned int qsort_pivot(const hist_item *const base, const unsigned int len);
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inline static unsigned int qsort_pivot(const hist_item *const base, const unsigned int len)
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{
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if (len < 32) {
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return len/2;
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}
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const unsigned int aidx=8, bidx=len/2, cidx=len-1;
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const unsigned int a=base[aidx].tmp.sort_value, b=base[bidx].tmp.sort_value, c=base[cidx].tmp.sort_value;
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return (a < b) ? ((b < c) ? bidx : ((a < c) ? cidx : aidx ))
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: ((b > c) ? bidx : ((a < c) ? aidx : cidx ));
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}
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ALWAYS_INLINE static unsigned int qsort_partition(hist_item *const base, const unsigned int len);
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inline static unsigned int qsort_partition(hist_item *const base, const unsigned int len)
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{
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unsigned int l = 1, r = len;
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if (len >= 8) {
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hist_item_swap(&base[0], &base[qsort_pivot(base,len)]);
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}
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const unsigned int pivot_value = base[0].tmp.sort_value;
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while (l < r) {
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if (base[l].tmp.sort_value >= pivot_value) {
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l++;
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} else {
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while(l < --r && base[r].tmp.sort_value <= pivot_value) {}
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hist_item_swap(&base[l], &base[r]);
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}
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}
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l--;
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hist_item_swap(&base[0], &base[l]);
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return l;
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}
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/** quick select algorithm */
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static void hist_item_sort_range(hist_item *base, unsigned int len, unsigned int sort_start)
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{
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for(;;) {
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const unsigned int l = qsort_partition(base, len), r = l+1;
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if (l > 0 && sort_start < l) {
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len = l;
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}
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else if (r < len && sort_start > r) {
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base += r; len -= r; sort_start -= r;
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}
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else break;
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}
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}
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/** sorts array to make sum of weights lower than halfvar one side, returns edge between <halfvar and >halfvar parts of the set */
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static hist_item *hist_item_sort_halfvar(hist_item *base, unsigned int len, double *const lowervar, const double halfvar)
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{
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do {
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const unsigned int l = qsort_partition(base, len), r = l+1;
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// check if sum of left side is smaller than half,
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// if it is, then it doesn't need to be sorted
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unsigned int t = 0; double tmpsum = *lowervar;
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while (t <= l && tmpsum < halfvar) tmpsum += base[t++].color_weight;
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if (tmpsum < halfvar) {
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*lowervar = tmpsum;
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} else {
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if (l > 0) {
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hist_item *res = hist_item_sort_halfvar(base, l, lowervar, halfvar);
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if (res) return res;
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} else {
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// End of left recursion. This will be executed in order from the first element.
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*lowervar += base[0].color_weight;
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if (*lowervar > halfvar) return &base[0];
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}
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}
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if (len > r) {
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base += r; len -= r; // tail-recursive "call"
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} else {
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*lowervar += base[r].color_weight;
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return (*lowervar > halfvar) ? &base[r] : NULL;
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}
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} while(1);
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}
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static f_pixel get_median(const struct box *b, hist_item achv[]);
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typedef struct {
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unsigned int chan; float variance;
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} channelvariance;
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static int comparevariance(const void *ch1, const void *ch2)
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{
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return ((const channelvariance*)ch1)->variance > ((const channelvariance*)ch2)->variance ? -1 :
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(((const channelvariance*)ch1)->variance < ((const channelvariance*)ch2)->variance ? 1 : 0);
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}
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/** Finds which channels need to be sorted first and preproceses achv for fast sort */
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static double prepare_sort(struct box *b, hist_item achv[])
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{
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/*
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** Sort dimensions by their variance, and then sort colors first by dimension with highest variance
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*/
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channelvariance channels[4] = {
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{index_of_channel(a), b->variance.a},
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{index_of_channel(r), b->variance.r},
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{index_of_channel(g), b->variance.g},
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{index_of_channel(b), b->variance.b},
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};
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qsort(channels, 4, sizeof(channels[0]), comparevariance);
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for(unsigned int i=0; i < b->colors; i++) {
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const float *chans = (const float *)&achv[b->ind + i].acolor;
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// Only the first channel really matters. When trying median cut many times
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// with different histogram weights, I don't want sort randomness to influence outcome.
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achv[b->ind + i].tmp.sort_value = ((unsigned int)(chans[channels[0].chan]*65535.0)<<16) |
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(unsigned int)((chans[channels[2].chan] + chans[channels[1].chan]/2.0 + chans[channels[3].chan]/4.0)*65535.0);
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}
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const f_pixel median = get_median(b, achv);
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// box will be split to make color_weight of each side even
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const unsigned int ind = b->ind, end = ind+b->colors;
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double totalvar = 0;
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for(unsigned int j=ind; j < end; j++) totalvar += (achv[j].color_weight = color_weight(median, achv[j]));
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return totalvar / 2.0;
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}
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/** finds median in unsorted set by sorting only minimum required */
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static f_pixel get_median(const struct box *b, hist_item achv[])
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{
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const unsigned int median_start = (b->colors-1)/2;
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hist_item_sort_range(&(achv[b->ind]), b->colors,
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median_start);
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if (b->colors&1) return achv[b->ind + median_start].acolor;
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// technically the second color is not guaranteed to be sorted correctly
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// but most of the time it is good enough to be useful
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return averagepixels(2, &achv[b->ind + median_start]);
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}
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/*
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** Find the best splittable box. -1 if no boxes are splittable.
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*/
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static int best_splittable_box(struct box* bv, unsigned int boxes, const double max_mse)
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{
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int bi=-1; double maxsum=0;
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for(unsigned int i=0; i < boxes; i++) {
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if (bv[i].colors < 2) {
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continue;
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}
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// looks only at max variance, because it's only going to split by it
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const double cv = MAX(bv[i].variance.r, MAX(bv[i].variance.g,bv[i].variance.b));
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double thissum = bv[i].sum * MAX(bv[i].variance.a, cv);
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if (bv[i].max_error > max_mse) {
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thissum = thissum* bv[i].max_error/max_mse;
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}
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if (thissum > maxsum) {
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maxsum = thissum;
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bi = i;
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}
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}
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return bi;
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}
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inline static double color_weight(f_pixel median, hist_item h)
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{
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float diff = colordifference(median, h.acolor);
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return sqrt(diff) * (sqrt(1.0+h.adjusted_weight)-1.0);
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}
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static void set_colormap_from_boxes(colormap *map, struct box* bv, unsigned int boxes, hist_item *achv);
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static void adjust_histogram(hist_item *achv, const struct box* bv, unsigned int boxes);
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static double box_error(const struct box *box, const hist_item achv[])
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{
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f_pixel avg = box->color;
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double total_error=0;
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for (unsigned int i = 0; i < box->colors; ++i) {
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total_error += colordifference(avg, achv[box->ind + i].acolor) * achv[box->ind + i].perceptual_weight;
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}
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return total_error;
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}
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static bool total_box_error_below_target(double target_mse, struct box bv[], unsigned int boxes, const histogram *hist)
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{
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target_mse *= hist->total_perceptual_weight;
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double total_error=0;
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for(unsigned int i=0; i < boxes; i++) {
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// error is (re)calculated lazily
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if (bv[i].total_error >= 0) {
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total_error += bv[i].total_error;
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}
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if (total_error > target_mse) return false;
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}
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for(unsigned int i=0; i < boxes; i++) {
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if (bv[i].total_error < 0) {
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bv[i].total_error = box_error(&bv[i], hist->achv);
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total_error += bv[i].total_error;
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}
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if (total_error > target_mse) return false;
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}
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return true;
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}
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static void box_init(struct box *box, const hist_item *achv, const unsigned int ind, const unsigned int colors, const double sum) {
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box->ind = ind;
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box->colors = colors;
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box->sum = sum;
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box->total_error = -1;
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box->color = averagepixels(colors, &achv[ind]);
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box->variance = box_variance(achv, box);
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box->max_error = box_max_error(achv, box);
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}
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/*
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** Here is the fun part, the median-cut colormap generator. This is based
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** on Paul Heckbert's paper, "Color Image Quantization for Frame Buffer
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** Display," SIGGRAPH 1982 Proceedings, page 297.
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*/
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LIQ_PRIVATE colormap *mediancut(histogram *hist, unsigned int newcolors, const double target_mse, const double max_mse, void* (*malloc)(size_t), void (*free)(void*))
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{
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hist_item *achv = hist->achv;
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struct box bv[newcolors];
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/*
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** Set up the initial box.
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*/
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double sum = 0;
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for(unsigned int i=0; i < hist->size; i++) {
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sum += achv[i].adjusted_weight;
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}
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box_init(&bv[0], achv, 0, hist->size, sum);
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unsigned int boxes = 1;
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/*
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** Main loop: split boxes until we have enough.
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*/
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while (boxes < newcolors) {
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// first splits boxes that exceed quality limit (to have colors for things like odd green pixel),
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// later raises the limit to allow large smooth areas/gradients get colors.
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const double current_max_mse = max_mse + (boxes/(double)newcolors)*16.0*max_mse;
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const int bi = best_splittable_box(bv, boxes, current_max_mse);
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if (bi < 0)
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break; /* ran out of colors! */
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unsigned int indx = bv[bi].ind;
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unsigned int clrs = bv[bi].colors;
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/*
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Classic implementation tries to get even number of colors or pixels in each subdivision.
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Here, instead of popularity I use (sqrt(popularity)*variance) metric.
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Each subdivision balances number of pixels (popular colors) and low variance -
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boxes can be large if they have similar colors. Later boxes with high variance
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will be more likely to be split.
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Median used as expected value gives much better results than mean.
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*/
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const double halfvar = prepare_sort(&bv[bi], achv);
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double lowervar=0;
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// hist_item_sort_halfvar sorts and sums lowervar at the same time
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// returns item to break at …minus one, which does smell like an off-by-one error.
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hist_item *break_p = hist_item_sort_halfvar(&achv[indx], clrs, &lowervar, halfvar);
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unsigned int break_at = MIN(clrs-1, break_p - &achv[indx] + 1);
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/*
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** Split the box.
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*/
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double sm = bv[bi].sum;
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double lowersum = 0;
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for(unsigned int i=0; i < break_at; i++) lowersum += achv[indx + i].adjusted_weight;
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box_init(&bv[bi], achv, bv[bi].ind, break_at, lowersum);
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box_init(&bv[boxes], achv, indx + break_at, clrs - break_at, sm - lowersum);
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++boxes;
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if (total_box_error_below_target(target_mse, bv, boxes, hist)) {
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break;
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}
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}
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colormap *map = pam_colormap(boxes, malloc, free);
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set_colormap_from_boxes(map, bv, boxes, achv);
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adjust_histogram(achv, bv, boxes);
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return map;
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}
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static void set_colormap_from_boxes(colormap *map, struct box* bv, unsigned int boxes, hist_item *achv)
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{
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/*
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** Ok, we've got enough boxes. Now choose a representative color for
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** each box. There are a number of possible ways to make this choice.
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** One would be to choose the center of the box; this ignores any structure
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** within the boxes. Another method would be to average all the colors in
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** the box - this is the method specified in Heckbert's paper.
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*/
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for(unsigned int bi = 0; bi < boxes; ++bi) {
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map->palette[bi].acolor = bv[bi].color;
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/* store total color popularity (perceptual_weight is approximation of it) */
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map->palette[bi].popularity = 0;
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for(unsigned int i=bv[bi].ind; i < bv[bi].ind+bv[bi].colors; i++) {
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map->palette[bi].popularity += achv[i].perceptual_weight;
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}
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}
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}
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/* increase histogram popularity by difference from the final color (this is used as part of feedback loop) */
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static void adjust_histogram(hist_item *achv, const struct box* bv, unsigned int boxes)
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{
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for(unsigned int bi = 0; bi < boxes; ++bi) {
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for(unsigned int i=bv[bi].ind; i < bv[bi].ind+bv[bi].colors; i++) {
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achv[i].tmp.likely_colormap_index = bi;
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}
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}
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}
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static f_pixel averagepixels(unsigned int clrs, const hist_item achv[])
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{
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double r = 0, g = 0, b = 0, a = 0, sum = 0;
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for(unsigned int i = 0; i < clrs; i++) {
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const f_pixel px = achv[i].acolor;
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const double weight = achv[i].adjusted_weight;
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sum += weight;
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a += px.a * weight;
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r += px.r * weight;
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g += px.g * weight;
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b += px.b * weight;
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}
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if (sum) {
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a /= sum;
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r /= sum;
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g /= sum;
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b /= sum;
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}
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assert(!isnan(r) && !isnan(g) && !isnan(b) && !isnan(a));
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return (f_pixel){.r=r, .g=g, .b=b, .a=a};
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}
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