1// Copyright 2011 Google Inc. All Rights Reserved.
2//
3// Use of this source code is governed by a BSD-style license
4// that can be found in the COPYING file in the root of the source
5// tree. An additional intellectual property rights grant can be found
6// in the file PATENTS. All contributing project authors may
7// be found in the AUTHORS file in the root of the source tree.
8// -----------------------------------------------------------------------------
9//
10// Quantize levels for specified number of quantization-levels ([2, 256]).
11// Min and max values are preserved (usual 0 and 255 for alpha plane).
12//
13// Author: Skal (pascal.massimino@gmail.com)
14
15#include <assert.h>
16
17#include "./quant_levels.h"
18
19#define NUM_SYMBOLS     256
20
21#define MAX_ITER  6             // Maximum number of convergence steps.
22#define ERROR_THRESHOLD 1e-4    // MSE stopping criterion.
23
24// -----------------------------------------------------------------------------
25// Quantize levels.
26
27int QuantizeLevels(uint8_t* const data, int width, int height,
28                   int num_levels, uint64_t* const sse) {
29  int freq[NUM_SYMBOLS] = { 0 };
30  int q_level[NUM_SYMBOLS] = { 0 };
31  double inv_q_level[NUM_SYMBOLS] = { 0 };
32  int min_s = 255, max_s = 0;
33  const size_t data_size = height * width;
34  int i, num_levels_in, iter;
35  double last_err = 1.e38, err = 0.;
36  const double err_threshold = ERROR_THRESHOLD * data_size;
37
38  if (data == NULL) {
39    return 0;
40  }
41
42  if (width <= 0 || height <= 0) {
43    return 0;
44  }
45
46  if (num_levels < 2 || num_levels > 256) {
47    return 0;
48  }
49
50  {
51    size_t n;
52    num_levels_in = 0;
53    for (n = 0; n < data_size; ++n) {
54      num_levels_in += (freq[data[n]] == 0);
55      if (min_s > data[n]) min_s = data[n];
56      if (max_s < data[n]) max_s = data[n];
57      ++freq[data[n]];
58    }
59  }
60
61  if (num_levels_in <= num_levels) goto End;  // nothing to do!
62
63  // Start with uniformly spread centroids.
64  for (i = 0; i < num_levels; ++i) {
65    inv_q_level[i] = min_s + (double)(max_s - min_s) * i / (num_levels - 1);
66  }
67
68  // Fixed values. Won't be changed.
69  q_level[min_s] = 0;
70  q_level[max_s] = num_levels - 1;
71  assert(inv_q_level[0] == min_s);
72  assert(inv_q_level[num_levels - 1] == max_s);
73
74  // k-Means iterations.
75  for (iter = 0; iter < MAX_ITER; ++iter) {
76    double q_sum[NUM_SYMBOLS] = { 0 };
77    double q_count[NUM_SYMBOLS] = { 0 };
78    int s, slot = 0;
79
80    // Assign classes to representatives.
81    for (s = min_s; s <= max_s; ++s) {
82      // Keep track of the nearest neighbour 'slot'
83      while (slot < num_levels - 1 &&
84             2 * s > inv_q_level[slot] + inv_q_level[slot + 1]) {
85        ++slot;
86      }
87      if (freq[s] > 0) {
88        q_sum[slot] += s * freq[s];
89        q_count[slot] += freq[s];
90      }
91      q_level[s] = slot;
92    }
93
94    // Assign new representatives to classes.
95    if (num_levels > 2) {
96      for (slot = 1; slot < num_levels - 1; ++slot) {
97        const double count = q_count[slot];
98        if (count > 0.) {
99          inv_q_level[slot] = q_sum[slot] / count;
100        }
101      }
102    }
103
104    // Compute convergence error.
105    err = 0.;
106    for (s = min_s; s <= max_s; ++s) {
107      const double error = s - inv_q_level[q_level[s]];
108      err += freq[s] * error * error;
109    }
110
111    // Check for convergence: we stop as soon as the error is no
112    // longer improving.
113    if (last_err - err < err_threshold) break;
114    last_err = err;
115  }
116
117  // Remap the alpha plane to quantized values.
118  {
119    // double->int rounding operation can be costly, so we do it
120    // once for all before remapping. We also perform the data[] -> slot
121    // mapping, while at it (avoid one indirection in the final loop).
122    uint8_t map[NUM_SYMBOLS];
123    int s;
124    size_t n;
125    for (s = min_s; s <= max_s; ++s) {
126      const int slot = q_level[s];
127      map[s] = (uint8_t)(inv_q_level[slot] + .5);
128    }
129    // Final pass.
130    for (n = 0; n < data_size; ++n) {
131      data[n] = map[data[n]];
132    }
133  }
134 End:
135  // Store sum of squared error if needed.
136  if (sse != NULL) *sse = (uint64_t)err;
137
138  return 1;
139}
140
141