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// Copyright 2011 Google Inc. All Rights Reserved.
//
// This code is licensed under the same terms as WebM:
// Software License Agreement: http://www.webmproject.org/license/software/
// Additional IP Rights Grant: http://www.webmproject.org/license/additional/
// -----------------------------------------------------------------------------
//
// Quantize levels for specified number of quantization-levels ([2, 256]).
// Min and max values are preserved (usual 0 and 255 for alpha plane).
//
// Author: Skal (pascal.massimino@gmail.com)
#include <assert.h>
#include "./quant_levels.h"
#if defined(__cplusplus) || defined(c_plusplus)
extern "C" {
#endif
#define NUM_SYMBOLS 256
#define MAX_ITER 6 // Maximum number of convergence steps.
#define ERROR_THRESHOLD 1e-4 // MSE stopping criterion.
// -----------------------------------------------------------------------------
// Quantize levels.
int QuantizeLevels(uint8_t* const data, int width, int height,
int num_levels, uint64_t* const sse) {
int freq[NUM_SYMBOLS] = { 0 };
int q_level[NUM_SYMBOLS] = { 0 };
double inv_q_level[NUM_SYMBOLS] = { 0 };
int min_s = 255, max_s = 0;
const size_t data_size = height * width;
int i, num_levels_in, iter;
double last_err = 1.e38, err = 0.;
const double err_threshold = ERROR_THRESHOLD * data_size;
if (data == NULL) {
return 0;
}
if (width <= 0 || height <= 0) {
return 0;
}
if (num_levels < 2 || num_levels > 256) {
return 0;
}
{
size_t n;
num_levels_in = 0;
for (n = 0; n < data_size; ++n) {
num_levels_in += (freq[data[n]] == 0);
if (min_s > data[n]) min_s = data[n];
if (max_s < data[n]) max_s = data[n];
++freq[data[n]];
}
}
if (num_levels_in <= num_levels) goto End; // nothing to do!
// Start with uniformly spread centroids.
for (i = 0; i < num_levels; ++i) {
inv_q_level[i] = min_s + (double)(max_s - min_s) * i / (num_levels - 1);
}
// Fixed values. Won't be changed.
q_level[min_s] = 0;
q_level[max_s] = num_levels - 1;
assert(inv_q_level[0] == min_s);
assert(inv_q_level[num_levels - 1] == max_s);
// k-Means iterations.
for (iter = 0; iter < MAX_ITER; ++iter) {
double q_sum[NUM_SYMBOLS] = { 0 };
double q_count[NUM_SYMBOLS] = { 0 };
int s, slot = 0;
// Assign classes to representatives.
for (s = min_s; s <= max_s; ++s) {
// Keep track of the nearest neighbour 'slot'
while (slot < num_levels - 1 &&
2 * s > inv_q_level[slot] + inv_q_level[slot + 1]) {
++slot;
}
if (freq[s] > 0) {
q_sum[slot] += s * freq[s];
q_count[slot] += freq[s];
}
q_level[s] = slot;
}
// Assign new representatives to classes.
if (num_levels > 2) {
for (slot = 1; slot < num_levels - 1; ++slot) {
const double count = q_count[slot];
if (count > 0.) {
inv_q_level[slot] = q_sum[slot] / count;
}
}
}
// Compute convergence error.
err = 0.;
for (s = min_s; s <= max_s; ++s) {
const double error = s - inv_q_level[q_level[s]];
err += freq[s] * error * error;
}
// Check for convergence: we stop as soon as the error is no
// longer improving.
if (last_err - err < err_threshold) break;
last_err = err;
}
// Remap the alpha plane to quantized values.
{
// double->int rounding operation can be costly, so we do it
// once for all before remapping. We also perform the data[] -> slot
// mapping, while at it (avoid one indirection in the final loop).
uint8_t map[NUM_SYMBOLS];
int s;
size_t n;
for (s = min_s; s <= max_s; ++s) {
const int slot = q_level[s];
map[s] = (uint8_t)(inv_q_level[slot] + .5);
}
// Final pass.
for (n = 0; n < data_size; ++n) {
data[n] = map[data[n]];
}
}
End:
// Store sum of squared error if needed.
if (sse != NULL) *sse = (uint64_t)err;
return 1;
}
int DequantizeLevels(uint8_t* const data, int width, int height) {
if (data == NULL || width <= 0 || height <= 0) return 0;
// TODO(skal): implement gradient smoothing.
(void)data;
(void)width;
(void)height;
return 1;
}
#if defined(__cplusplus) || defined(c_plusplus)
} // extern "C"
#endif
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