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elbg.c
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1 /*
2  * Copyright (C) 2007 Vitor Sessak <vitor1001@gmail.com>
3  *
4  * This file is part of FFmpeg.
5  *
6  * FFmpeg is free software; you can redistribute it and/or
7  * modify it under the terms of the GNU Lesser General Public
8  * License as published by the Free Software Foundation; either
9  * version 2.1 of the License, or (at your option) any later version.
10  *
11  * FFmpeg is distributed in the hope that it will be useful,
12  * but WITHOUT ANY WARRANTY; without even the implied warranty of
13  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14  * Lesser General Public License for more details.
15  *
16  * You should have received a copy of the GNU Lesser General Public
17  * License along with FFmpeg; if not, write to the Free Software
18  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
19  */
20 
21 /**
22  * @file
23  * Codebook Generator using the ELBG algorithm
24  */
25 
26 #include <string.h>
27 
28 #include "libavutil/avassert.h"
29 #include "libavutil/common.h"
30 #include "libavutil/lfg.h"
31 #include "elbg.h"
32 #include "avcodec.h"
33 
34 #define DELTA_ERR_MAX 0.1 ///< Precision of the ELBG algorithm (as percentual error)
35 
36 /**
37  * In the ELBG jargon, a cell is the set of points that are closest to a
38  * codebook entry. Not to be confused with a RoQ Video cell. */
39 typedef struct cell_s {
40  int index;
41  struct cell_s *next;
42 } cell;
43 
44 /**
45  * ELBG internal data
46  */
47 typedef struct{
48  int error;
49  int dim;
50  int numCB;
51  int *codebook;
53  int *utility;
54  int64_t *utility_inc;
55  int *nearest_cb;
56  int *points;
58  int *scratchbuf;
59 } elbg_data;
60 
61 static inline int distance_limited(int *a, int *b, int dim, int limit)
62 {
63  int i, dist=0;
64  for (i=0; i<dim; i++) {
65  dist += (a[i] - b[i])*(a[i] - b[i]);
66  if (dist > limit)
67  return INT_MAX;
68  }
69 
70  return dist;
71 }
72 
73 static inline void vect_division(int *res, int *vect, int div, int dim)
74 {
75  int i;
76  if (div > 1)
77  for (i=0; i<dim; i++)
78  res[i] = ROUNDED_DIV(vect[i],div);
79  else if (res != vect)
80  memcpy(res, vect, dim*sizeof(int));
81 
82 }
83 
84 static int eval_error_cell(elbg_data *elbg, int *centroid, cell *cells)
85 {
86  int error=0;
87  for (; cells; cells=cells->next)
88  error += distance_limited(centroid, elbg->points + cells->index*elbg->dim, elbg->dim, INT_MAX);
89 
90  return error;
91 }
92 
93 static int get_closest_codebook(elbg_data *elbg, int index)
94 {
95  int i, pick=0, diff, diff_min = INT_MAX;
96  for (i=0; i<elbg->numCB; i++)
97  if (i != index) {
98  diff = distance_limited(elbg->codebook + i*elbg->dim, elbg->codebook + index*elbg->dim, elbg->dim, diff_min);
99  if (diff < diff_min) {
100  pick = i;
101  diff_min = diff;
102  }
103  }
104  return pick;
105 }
106 
108 {
109  int i=0;
110  /* Using linear search, do binary if it ever turns to be speed critical */
111  uint64_t r;
112 
113  if (elbg->utility_inc[elbg->numCB-1] < INT_MAX) {
114  r = av_lfg_get(elbg->rand_state) % (unsigned int)elbg->utility_inc[elbg->numCB-1] + 1;
115  } else {
116  r = av_lfg_get(elbg->rand_state);
117  r = (av_lfg_get(elbg->rand_state) + (r<<32)) % elbg->utility_inc[elbg->numCB-1] + 1;
118  }
119 
120  while (elbg->utility_inc[i] < r) {
121  i++;
122  }
123 
124  av_assert2(elbg->cells[i]);
125 
126  return i;
127 }
128 
129 /**
130  * Implementation of the simple LBG algorithm for just two codebooks
131  */
132 static int simple_lbg(elbg_data *elbg,
133  int dim,
134  int *centroid[3],
135  int newutility[3],
136  int *points,
137  cell *cells)
138 {
139  int i, idx;
140  int numpoints[2] = {0,0};
141  int *newcentroid[2] = {
142  elbg->scratchbuf + 3*dim,
143  elbg->scratchbuf + 4*dim
144  };
145  cell *tempcell;
146 
147  memset(newcentroid[0], 0, 2 * dim * sizeof(*newcentroid[0]));
148 
149  newutility[0] =
150  newutility[1] = 0;
151 
152  for (tempcell = cells; tempcell; tempcell=tempcell->next) {
153  idx = distance_limited(centroid[0], points + tempcell->index*dim, dim, INT_MAX)>=
154  distance_limited(centroid[1], points + tempcell->index*dim, dim, INT_MAX);
155  numpoints[idx]++;
156  for (i=0; i<dim; i++)
157  newcentroid[idx][i] += points[tempcell->index*dim + i];
158  }
159 
160  vect_division(centroid[0], newcentroid[0], numpoints[0], dim);
161  vect_division(centroid[1], newcentroid[1], numpoints[1], dim);
162 
163  for (tempcell = cells; tempcell; tempcell=tempcell->next) {
164  int dist[2] = {distance_limited(centroid[0], points + tempcell->index*dim, dim, INT_MAX),
165  distance_limited(centroid[1], points + tempcell->index*dim, dim, INT_MAX)};
166  int idx = dist[0] > dist[1];
167  newutility[idx] += dist[idx];
168  }
169 
170  return newutility[0] + newutility[1];
171 }
172 
173 static void get_new_centroids(elbg_data *elbg, int huc, int *newcentroid_i,
174  int *newcentroid_p)
175 {
176  cell *tempcell;
177  int *min = newcentroid_i;
178  int *max = newcentroid_p;
179  int i;
180 
181  for (i=0; i< elbg->dim; i++) {
182  min[i]=INT_MAX;
183  max[i]=0;
184  }
185 
186  for (tempcell = elbg->cells[huc]; tempcell; tempcell = tempcell->next)
187  for(i=0; i<elbg->dim; i++) {
188  min[i]=FFMIN(min[i], elbg->points[tempcell->index*elbg->dim + i]);
189  max[i]=FFMAX(max[i], elbg->points[tempcell->index*elbg->dim + i]);
190  }
191 
192  for (i=0; i<elbg->dim; i++) {
193  int ni = min[i] + (max[i] - min[i])/3;
194  int np = min[i] + (2*(max[i] - min[i]))/3;
195  newcentroid_i[i] = ni;
196  newcentroid_p[i] = np;
197  }
198 }
199 
200 /**
201  * Add the points in the low utility cell to its closest cell. Split the high
202  * utility cell, putting the separate points in the (now empty) low utility
203  * cell.
204  *
205  * @param elbg Internal elbg data
206  * @param indexes {luc, huc, cluc}
207  * @param newcentroid A vector with the position of the new centroids
208  */
209 static void shift_codebook(elbg_data *elbg, int *indexes,
210  int *newcentroid[3])
211 {
212  cell *tempdata;
213  cell **pp = &elbg->cells[indexes[2]];
214 
215  while(*pp)
216  pp= &(*pp)->next;
217 
218  *pp = elbg->cells[indexes[0]];
219 
220  elbg->cells[indexes[0]] = NULL;
221  tempdata = elbg->cells[indexes[1]];
222  elbg->cells[indexes[1]] = NULL;
223 
224  while(tempdata) {
225  cell *tempcell2 = tempdata->next;
226  int idx = distance_limited(elbg->points + tempdata->index*elbg->dim,
227  newcentroid[0], elbg->dim, INT_MAX) >
228  distance_limited(elbg->points + tempdata->index*elbg->dim,
229  newcentroid[1], elbg->dim, INT_MAX);
230 
231  tempdata->next = elbg->cells[indexes[idx]];
232  elbg->cells[indexes[idx]] = tempdata;
233  tempdata = tempcell2;
234  }
235 }
236 
237 static void evaluate_utility_inc(elbg_data *elbg)
238 {
239  int i;
240  int64_t inc=0;
241 
242  for (i=0; i < elbg->numCB; i++) {
243  if (elbg->numCB*elbg->utility[i] > elbg->error)
244  inc += elbg->utility[i];
245  elbg->utility_inc[i] = inc;
246  }
247 }
248 
249 
250 static void update_utility_and_n_cb(elbg_data *elbg, int idx, int newutility)
251 {
252  cell *tempcell;
253 
254  elbg->utility[idx] = newutility;
255  for (tempcell=elbg->cells[idx]; tempcell; tempcell=tempcell->next)
256  elbg->nearest_cb[tempcell->index] = idx;
257 }
258 
259 /**
260  * Evaluate if a shift lower the error. If it does, call shift_codebooks
261  * and update elbg->error, elbg->utility and elbg->nearest_cb.
262  *
263  * @param elbg Internal elbg data
264  * @param idx {luc (low utility cell, huc (high utility cell), cluc (closest cell to low utility cell)}
265  */
266 static void try_shift_candidate(elbg_data *elbg, int idx[3])
267 {
268  int j, k, olderror=0, newerror, cont=0;
269  int newutility[3];
270  int *newcentroid[3] = {
271  elbg->scratchbuf,
272  elbg->scratchbuf + elbg->dim,
273  elbg->scratchbuf + 2*elbg->dim
274  };
275  cell *tempcell;
276 
277  for (j=0; j<3; j++)
278  olderror += elbg->utility[idx[j]];
279 
280  memset(newcentroid[2], 0, elbg->dim*sizeof(int));
281 
282  for (k=0; k<2; k++)
283  for (tempcell=elbg->cells[idx[2*k]]; tempcell; tempcell=tempcell->next) {
284  cont++;
285  for (j=0; j<elbg->dim; j++)
286  newcentroid[2][j] += elbg->points[tempcell->index*elbg->dim + j];
287  }
288 
289  vect_division(newcentroid[2], newcentroid[2], cont, elbg->dim);
290 
291  get_new_centroids(elbg, idx[1], newcentroid[0], newcentroid[1]);
292 
293  newutility[2] = eval_error_cell(elbg, newcentroid[2], elbg->cells[idx[0]]);
294  newutility[2] += eval_error_cell(elbg, newcentroid[2], elbg->cells[idx[2]]);
295 
296  newerror = newutility[2];
297 
298  newerror += simple_lbg(elbg, elbg->dim, newcentroid, newutility, elbg->points,
299  elbg->cells[idx[1]]);
300 
301  if (olderror > newerror) {
302  shift_codebook(elbg, idx, newcentroid);
303 
304  elbg->error += newerror - olderror;
305 
306  for (j=0; j<3; j++)
307  update_utility_and_n_cb(elbg, idx[j], newutility[j]);
308 
309  evaluate_utility_inc(elbg);
310  }
311  }
312 
313 /**
314  * Implementation of the ELBG block
315  */
316 static void do_shiftings(elbg_data *elbg)
317 {
318  int idx[3];
319 
320  evaluate_utility_inc(elbg);
321 
322  for (idx[0]=0; idx[0] < elbg->numCB; idx[0]++)
323  if (elbg->numCB*elbg->utility[idx[0]] < elbg->error) {
324  if (elbg->utility_inc[elbg->numCB-1] == 0)
325  return;
326 
327  idx[1] = get_high_utility_cell(elbg);
328  idx[2] = get_closest_codebook(elbg, idx[0]);
329 
330  if (idx[1] != idx[0] && idx[1] != idx[2])
331  try_shift_candidate(elbg, idx);
332  }
333 }
334 
335 #define BIG_PRIME 433494437LL
336 
337 int avpriv_init_elbg(int *points, int dim, int numpoints, int *codebook,
338  int numCB, int max_steps, int *closest_cb,
339  AVLFG *rand_state)
340 {
341  int i, k, ret = 0;
342 
343  if (numpoints > 24*numCB) {
344  /* ELBG is very costly for a big number of points. So if we have a lot
345  of them, get a good initial codebook to save on iterations */
346  int *temp_points = av_malloc_array(dim, (numpoints/8)*sizeof(int));
347  if (!temp_points)
348  return AVERROR(ENOMEM);
349  for (i=0; i<numpoints/8; i++) {
350  k = (i*BIG_PRIME) % numpoints;
351  memcpy(temp_points + i*dim, points + k*dim, dim*sizeof(int));
352  }
353 
354  ret = avpriv_init_elbg(temp_points, dim, numpoints / 8, codebook,
355  numCB, 2 * max_steps, closest_cb, rand_state);
356  if (ret < 0) {
357  av_freep(&temp_points);
358  return ret;
359  }
360  ret = avpriv_do_elbg(temp_points, dim, numpoints / 8, codebook,
361  numCB, 2 * max_steps, closest_cb, rand_state);
362  av_free(temp_points);
363 
364  } else // If not, initialize the codebook with random positions
365  for (i=0; i < numCB; i++)
366  memcpy(codebook + i*dim, points + ((i*BIG_PRIME)%numpoints)*dim,
367  dim*sizeof(int));
368  return ret;
369 }
370 
371 int avpriv_do_elbg(int *points, int dim, int numpoints, int *codebook,
372  int numCB, int max_steps, int *closest_cb,
373  AVLFG *rand_state)
374 {
375  int dist;
376  elbg_data elbg_d;
377  elbg_data *elbg = &elbg_d;
378  int i, j, k, last_error, steps = 0, ret = 0;
379  int *dist_cb = av_malloc_array(numpoints, sizeof(int));
380  int *size_part = av_malloc_array(numCB, sizeof(int));
381  cell *list_buffer = av_malloc_array(numpoints, sizeof(cell));
382  cell *free_cells;
383  int best_dist, best_idx = 0;
384 
385  elbg->error = INT_MAX;
386  elbg->dim = dim;
387  elbg->numCB = numCB;
388  elbg->codebook = codebook;
389  elbg->cells = av_malloc_array(numCB, sizeof(cell *));
390  elbg->utility = av_malloc_array(numCB, sizeof(int));
391  elbg->nearest_cb = closest_cb;
392  elbg->points = points;
393  elbg->utility_inc = av_malloc_array(numCB, sizeof(*elbg->utility_inc));
394  elbg->scratchbuf = av_malloc_array(5*dim, sizeof(int));
395 
396  if (!dist_cb || !size_part || !list_buffer || !elbg->cells ||
397  !elbg->utility || !elbg->utility_inc || !elbg->scratchbuf) {
398  ret = AVERROR(ENOMEM);
399  goto out;
400  }
401 
402  elbg->rand_state = rand_state;
403 
404  do {
405  free_cells = list_buffer;
406  last_error = elbg->error;
407  steps++;
408  memset(elbg->utility, 0, numCB*sizeof(int));
409  memset(elbg->cells, 0, numCB*sizeof(cell *));
410 
411  elbg->error = 0;
412 
413  /* This loop evaluate the actual Voronoi partition. It is the most
414  costly part of the algorithm. */
415  for (i=0; i < numpoints; i++) {
416  best_dist = distance_limited(elbg->points + i*elbg->dim, elbg->codebook + best_idx*elbg->dim, dim, INT_MAX);
417  for (k=0; k < elbg->numCB; k++) {
418  dist = distance_limited(elbg->points + i*elbg->dim, elbg->codebook + k*elbg->dim, dim, best_dist);
419  if (dist < best_dist) {
420  best_dist = dist;
421  best_idx = k;
422  }
423  }
424  elbg->nearest_cb[i] = best_idx;
425  dist_cb[i] = best_dist;
426  elbg->error += dist_cb[i];
427  elbg->utility[elbg->nearest_cb[i]] += dist_cb[i];
428  free_cells->index = i;
429  free_cells->next = elbg->cells[elbg->nearest_cb[i]];
430  elbg->cells[elbg->nearest_cb[i]] = free_cells;
431  free_cells++;
432  }
433 
434  do_shiftings(elbg);
435 
436  memset(size_part, 0, numCB*sizeof(int));
437 
438  memset(elbg->codebook, 0, elbg->numCB*dim*sizeof(int));
439 
440  for (i=0; i < numpoints; i++) {
441  size_part[elbg->nearest_cb[i]]++;
442  for (j=0; j < elbg->dim; j++)
443  elbg->codebook[elbg->nearest_cb[i]*elbg->dim + j] +=
444  elbg->points[i*elbg->dim + j];
445  }
446 
447  for (i=0; i < elbg->numCB; i++)
448  vect_division(elbg->codebook + i*elbg->dim,
449  elbg->codebook + i*elbg->dim, size_part[i], elbg->dim);
450 
451  } while(((last_error - elbg->error) > DELTA_ERR_MAX*elbg->error) &&
452  (steps < max_steps));
453 
454 out:
455  av_free(dist_cb);
456  av_free(size_part);
457  av_free(elbg->utility);
458  av_free(list_buffer);
459  av_free(elbg->cells);
460  av_free(elbg->utility_inc);
461  av_free(elbg->scratchbuf);
462  return ret;
463 }